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</div> <nav class="vector-user-links vector-user-links-wide" aria-label="Eines personals"> <div class="vector-user-links-main"> <div id="p-vector-user-menu-preferences" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-userpage" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <nav class="vector-appearance-landmark" aria-label="Aparença"> <div id="vector-appearance-dropdown" class="vector-dropdown " title="Change the appearance of the page's font size, width, and color" > <input type="checkbox" id="vector-appearance-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-appearance-dropdown" class="vector-dropdown-checkbox " aria-label="Aparença" > <label id="vector-appearance-dropdown-label" for="vector-appearance-dropdown-checkbox" 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href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_ca.wikipedia.org&uselang=ca" class=""><span>Donatius</span></a> </li> <li id="pt-createaccount-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Especial:Crea_compte&returnto=Nucli+at%C3%B2mic" title="Us animem a crear un compte i iniciar una sessió, encara que no és obligatori" class=""><span>Crea un compte</span></a> </li> <li id="pt-login-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Especial:Registre_i_entrada&returnto=Nucli+at%C3%B2mic" title="Us animem a registrar-vos, però no és obligatori [o]" accesskey="o" class=""><span>Inicia la sessió</span></a> </li> </ul> </div> </div> </div> <div id="vector-user-links-dropdown" class="vector-dropdown vector-user-menu vector-button-flush-right 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class="vector-menu-heading"> Pàgines per a editors no registrats <a href="/wiki/Ajuda:Introducci%C3%B3" aria-label="Vegeu més informació sobre l'edició"><span>més informació</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/Especial:Contribucions_pr%C3%B2pies" title="Una llista de les modificacions fetes des d'aquesta adreça IP [y]" accesskey="y"><span>Contribucions</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Especial:Discussi%C3%B3_personal" title="Discussió sobre les edicions per aquesta adreça ip. [n]" accesskey="n"><span>Discussió per aquest IP</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="Lloc"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="Contingut" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Contingut</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">mou a la barra lateral</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">amaga</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">Inici</div> </a> </li> <li id="toc-Història" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Història"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Història</span> </div> </a> <ul id="toc-Història-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Propietats" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Propietats"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Propietats</span> </div> </a> <button aria-controls="toc-Propietats-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Commuta la subsecció Propietats</span> </button> <ul id="toc-Propietats-sublist" class="vector-toc-list"> <li id="toc-Nucleons" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Nucleons"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Nucleons</span> </div> </a> <ul id="toc-Nucleons-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Càrrega_i_massa" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Càrrega_i_massa"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Càrrega i massa</span> </div> </a> <ul id="toc-Càrrega_i_massa-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Dimensions_i_forma" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Dimensions_i_forma"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3</span> <span>Dimensions i forma</span> </div> </a> <ul id="toc-Dimensions_i_forma-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Moment_angular" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Moment_angular"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.4</span> <span>Moment angular</span> </div> </a> <ul id="toc-Moment_angular-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Moment_magnètic_nuclear" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Moment_magnètic_nuclear"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.5</span> <span>Moment magnètic nuclear</span> </div> </a> <ul id="toc-Moment_magnètic_nuclear-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Energia_de_lligadura" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Energia_de_lligadura"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Energia de lligadura</span> </div> </a> <button aria-controls="toc-Energia_de_lligadura-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Commuta la subsecció Energia de lligadura</span> </button> <ul id="toc-Energia_de_lligadura-sublist" class="vector-toc-list"> <li id="toc-Estabilitat_nuclear" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Estabilitat_nuclear"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Estabilitat nuclear</span> </div> </a> <ul id="toc-Estabilitat_nuclear-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Models_nuclears" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Models_nuclears"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Models nuclears</span> </div> </a> <button aria-controls="toc-Models_nuclears-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Commuta la subsecció Models nuclears</span> </button> <ul id="toc-Models_nuclears-sublist" class="vector-toc-list"> <li id="toc-Model_de_gota_de_líquid" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Model_de_gota_de_líquid"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Model de gota de líquid</span> </div> </a> <ul id="toc-Model_de_gota_de_líquid-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Model_de_capes" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Model_de_capes"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>Model de capes</span> </div> </a> <ul id="toc-Model_de_capes-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Referències" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Referències"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Referències</span> </div> </a> <ul id="toc-Referències-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Vegeu_també" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Vegeu_també"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Vegeu també</span> </div> </a> <ul id="toc-Vegeu_també-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contingut" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Commuta la taula de continguts." > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Commuta la taula de continguts.</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Nucli atòmic</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Vés a un article en una altra llengua. Disponible en 120 llengües" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-120" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">120 llengües</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Atoomkern" title="Atoomkern - afrikaans" lang="af" hreflang="af" data-title="Atoomkern" data-language-autonym="Afrikaans" data-language-local-name="afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-anp mw-list-item"><a href="https://anp.wikipedia.org/wiki/%E0%A4%AA%E0%A4%B0%E0%A4%AE%E0%A4%BE%E0%A4%A3%E0%A5%81_%E0%A4%A8%E0%A4%BE%E0%A4%AD%E0%A4%BF%E0%A4%95" title="परमाणु नाभिक - angika" lang="anp" hreflang="anp" data-title="परमाणु नाभिक" data-language-autonym="अंगिका" data-language-local-name="angika" class="interlanguage-link-target"><span>अंगिका</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%86%D9%88%D8%A7%D8%A9_%D8%A7%D9%84%D8%B0%D8%B1%D8%A9" title="نواة الذرة - àrab" lang="ar" hreflang="ar" data-title="نواة الذرة" data-language-autonym="العربية" data-language-local-name="àrab" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ary mw-list-item"><a href="https://ary.wikipedia.org/wiki/%D9%86%D9%88%D9%8A%D8%A9_%D8%AF_%D8%AF%D8%B1%D8%A9" title="نوية د درة - Moroccan Arabic" lang="ary" hreflang="ary" data-title="نوية د درة" data-language-autonym="الدارجة" data-language-local-name="Moroccan Arabic" class="interlanguage-link-target"><span>الدارجة</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Nucleu_at%C3%B3micu" title="Nucleu atómicu - asturià" lang="ast" hreflang="ast" data-title="Nucleu atómicu" data-language-autonym="Asturianu" data-language-local-name="asturià" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Atomun_n%C3%BCv%C9%99si" title="Atomun nüvəsi - azerbaidjanès" lang="az" hreflang="az" data-title="Atomun nüvəsi" data-language-autonym="Azərbaycanca" data-language-local-name="azerbaidjanès" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-azb mw-list-item"><a href="https://azb.wikipedia.org/wiki/%D8%A2%D8%AA%D9%88%D9%85_%DA%86%DA%A9%DB%8C%D8%B1%D8%AF%DA%AF%DB%8C" title="آتوم چکیردگی - South Azerbaijani" lang="azb" hreflang="azb" data-title="آتوم چکیردگی" data-language-autonym="تۆرکجه" data-language-local-name="South Azerbaijani" class="interlanguage-link-target"><span>تۆرکجه</span></a></li><li class="interlanguage-link interwiki-bat-smg mw-list-item"><a href="https://bat-smg.wikipedia.org/wiki/Atuoma_kondouls" title="Atuoma kondouls - Samogitian" lang="sgs" hreflang="sgs" data-title="Atuoma kondouls" data-language-autonym="Žemaitėška" data-language-local-name="Samogitian" class="interlanguage-link-target"><span>Žemaitėška</span></a></li><li class="interlanguage-link interwiki-bcl mw-list-item"><a href="https://bcl.wikipedia.org/wiki/Atomikong_nukleyus" title="Atomikong nukleyus - Central Bikol" lang="bcl" hreflang="bcl" data-title="Atomikong nukleyus" data-language-autonym="Bikol Central" data-language-local-name="Central Bikol" class="interlanguage-link-target"><span>Bikol Central</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%90%D1%82%D0%B0%D0%BC%D0%BD%D0%B0%D0%B5_%D1%8F%D0%B4%D1%80%D0%BE" title="Атамнае ядро - belarús" lang="be" hreflang="be" data-title="Атамнае ядро" data-language-autonym="Беларуская" data-language-local-name="belarús" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%90%D1%82%D0%B0%D0%BC%D0%BD%D0%B0%D0%B5_%D1%8F%D0%B4%D1%80%D0%BE" title="Атамнае ядро - Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Атамнае ядро" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%90%D1%82%D0%BE%D0%BC%D0%BD%D0%BE_%D1%8F%D0%B4%D1%80%D0%BE" title="Атомно ядро - búlgar" lang="bg" hreflang="bg" data-title="Атомно ядро" data-language-autonym="Български" data-language-local-name="búlgar" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bh mw-list-item"><a href="https://bh.wikipedia.org/wiki/%E0%A4%AA%E0%A4%B0%E0%A4%AE%E0%A4%BE%E0%A4%A3%E0%A4%B5%E0%A4%BF%E0%A4%95_%E0%A4%AA%E0%A4%A6%E0%A4%B0%E0%A5%8D%E0%A4%A5%E0%A4%AC%E0%A4%BF%E0%A4%A6%E0%A5%8D%E0%A4%AF%E0%A4%BE" title="परमाणविक पदर्थबिद्या - Bhojpuri" lang="bh" hreflang="bh" data-title="परमाणविक पदर्थबिद्या" data-language-autonym="भोजपुरी" data-language-local-name="Bhojpuri" class="interlanguage-link-target"><span>भोजपुरी</span></a></li><li class="interlanguage-link interwiki-blk mw-list-item"><a href="https://blk.wikipedia.org/wiki/%E1%80%94%E1%80%BB%E1%80%B0%E1%80%B8%E1%80%80%E1%80%9C%E1%80%AE%E1%80%B8%E1%80%9A%E1%80%95%E1%80%BA" title="နျူးကလီးယပ် - Pa'O" lang="blk" hreflang="blk" data-title="နျူးကလီးယပ်" data-language-autonym="ပအိုဝ်ႏဘာႏသာႏ" data-language-local-name="Pa'O" class="interlanguage-link-target"><span>ပအိုဝ်ႏဘာႏသာႏ</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%AA%E0%A6%BE%E0%A6%B0%E0%A6%AE%E0%A6%BE%E0%A6%A3%E0%A6%AC%E0%A6%BF%E0%A6%95_%E0%A6%A8%E0%A6%BF%E0%A6%89%E0%A6%95%E0%A7%8D%E0%A6%B2%E0%A6%BF%E0%A6%AF%E0%A6%BC%E0%A6%BE%E0%A6%B8" title="পারমাণবিক নিউক্লিয়াস - bengalí" lang="bn" hreflang="bn" data-title="পারমাণবিক নিউক্লিয়াস" data-language-autonym="বাংলা" data-language-local-name="bengalí" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-br mw-list-item"><a href="https://br.wikipedia.org/wiki/Nukle%C3%BCs_(an_atomo%C3%B9)" title="Nukleüs (an atomoù) - bretó" lang="br" hreflang="br" data-title="Nukleüs (an atomoù)" data-language-autonym="Brezhoneg" data-language-local-name="bretó" class="interlanguage-link-target"><span>Brezhoneg</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Atomsko_jezgro" title="Atomsko jezgro - bosnià" lang="bs" hreflang="bs" data-title="Atomsko jezgro" data-language-autonym="Bosanski" data-language-local-name="bosnià" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-cdo mw-list-item"><a href="https://cdo.wikipedia.org/wiki/Ngu%C3%B2ng-c%E1%B9%B3%CC%84_h%C5%8Fk" title="Nguòng-cṳ̄ hŏk - Mindong" lang="cdo" hreflang="cdo" data-title="Nguòng-cṳ̄ hŏk" data-language-autonym="閩東語 / Mìng-dĕ̤ng-ngṳ̄" data-language-local-name="Mindong" class="interlanguage-link-target"><span>閩東語 / Mìng-dĕ̤ng-ngṳ̄</span></a></li><li class="interlanguage-link interwiki-co mw-list-item"><a href="https://co.wikipedia.org/wiki/Nucleu_Atomicu" title="Nucleu Atomicu - cors" lang="co" hreflang="co" data-title="Nucleu Atomicu" data-language-autonym="Corsu" data-language-local-name="cors" class="interlanguage-link-target"><span>Corsu</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Atomov%C3%A9_j%C3%A1dro" title="Atomové jádro - txec" lang="cs" hreflang="cs" data-title="Atomové jádro" data-language-autonym="Čeština" data-language-local-name="txec" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%9D%D1%83%D0%BA%D0%BB%D0%BE%D0%BD%D1%81%D0%B0%D1%80" title="Нуклонсар - txuvaix" lang="cv" hreflang="cv" data-title="Нуклонсар" data-language-autonym="Чӑвашла" data-language-local-name="txuvaix" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Niwclews_atomig" title="Niwclews atomig - gal·lès" lang="cy" hreflang="cy" data-title="Niwclews atomig" data-language-autonym="Cymraeg" data-language-local-name="gal·lès" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Atomkerne" title="Atomkerne - danès" lang="da" hreflang="da" data-title="Atomkerne" data-language-autonym="Dansk" data-language-local-name="danès" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Atomkern" title="Atomkern - alemany" lang="de" hreflang="de" data-title="Atomkern" data-language-autonym="Deutsch" data-language-local-name="alemany" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-diq mw-list-item"><a href="https://diq.wikipedia.org/wiki/Dend%C4%B1k%C3%AA_atomi" title="Dendıkê atomi - Zazaki" lang="diq" hreflang="diq" data-title="Dendıkê atomi" data-language-autonym="Zazaki" data-language-local-name="Zazaki" class="interlanguage-link-target"><span>Zazaki</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%91%CF%84%CE%BF%CE%BC%CE%B9%CE%BA%CF%8C%CF%82_%CF%80%CF%85%CF%81%CE%AE%CE%BD%CE%B1%CF%82" title="Ατομικός πυρήνας - grec" lang="el" hreflang="el" data-title="Ατομικός πυρήνας" data-language-autonym="Ελληνικά" data-language-local-name="grec" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Atomic_nucleus" title="Atomic nucleus - anglès" lang="en" hreflang="en" data-title="Atomic nucleus" data-language-autonym="English" data-language-local-name="anglès" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Atomkerno" title="Atomkerno - esperanto" lang="eo" hreflang="eo" data-title="Atomkerno" data-language-autonym="Esperanto" data-language-local-name="esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/N%C3%BAcleo_at%C3%B3mico" title="Núcleo atómico - espanyol" lang="es" hreflang="es" data-title="Núcleo atómico" data-language-autonym="Español" data-language-local-name="espanyol" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Aatomituum" title="Aatomituum - estonià" lang="et" hreflang="et" data-title="Aatomituum" data-language-autonym="Eesti" data-language-local-name="estonià" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Atomo_nukleo" title="Atomo nukleo - basc" lang="eu" hreflang="eu" data-title="Atomo nukleo" data-language-autonym="Euskara" data-language-local-name="basc" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%87%D8%B3%D8%AA%D9%87_%D8%A7%D8%AA%D9%85" title="هسته اتم - persa" lang="fa" hreflang="fa" data-title="هسته اتم" data-language-autonym="فارسی" data-language-local-name="persa" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Atomiydin" title="Atomiydin - finès" lang="fi" hreflang="fi" data-title="Atomiydin" data-language-autonym="Suomi" data-language-local-name="finès" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fiu-vro mw-list-item"><a href="https://fiu-vro.wikipedia.org/wiki/Aadomis%C3%A4s%C3%BC" title="Aadomisäsü - Võro" lang="vro" hreflang="vro" data-title="Aadomisäsü" data-language-autonym="Võro" data-language-local-name="Võro" class="interlanguage-link-target"><span>Võro</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Noyau_atomique" title="Noyau atomique - francès" lang="fr" hreflang="fr" data-title="Noyau atomique" data-language-autonym="Français" data-language-local-name="francès" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-fy mw-list-item"><a href="https://fy.wikipedia.org/wiki/Atoomkearn" title="Atoomkearn - frisó occidental" lang="fy" hreflang="fy" data-title="Atoomkearn" data-language-autonym="Frysk" data-language-local-name="frisó occidental" class="interlanguage-link-target"><span>Frysk</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/N%C3%BAicl%C3%A9as_adamhach" title="Núicléas adamhach - irlandès" lang="ga" hreflang="ga" data-title="Núicléas adamhach" data-language-autonym="Gaeilge" data-language-local-name="irlandès" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gd mw-list-item"><a href="https://gd.wikipedia.org/wiki/Ni%C3%B9clas" title="Niùclas - gaèlic escocès" lang="gd" hreflang="gd" data-title="Niùclas" data-language-autonym="Gàidhlig" data-language-local-name="gaèlic escocès" class="interlanguage-link-target"><span>Gàidhlig</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/N%C3%BAcleo_at%C3%B3mico" title="Núcleo atómico - gallec" lang="gl" hreflang="gl" data-title="Núcleo atómico" data-language-autonym="Galego" data-language-local-name="gallec" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%92%D7%A8%D7%A2%D7%99%D7%9F_%D7%94%D7%90%D7%98%D7%95%D7%9D" title="גרעין האטום - hebreu" lang="he" hreflang="he" data-title="גרעין האטום" data-language-autonym="עברית" data-language-local-name="hebreu" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%AA%E0%A4%B0%E0%A4%AE%E0%A4%BE%E0%A4%A3%E0%A5%81_%E0%A4%A8%E0%A4%BE%E0%A4%AD%E0%A4%BF%E0%A4%95" title="परमाणु नाभिक - hindi" lang="hi" hreflang="hi" data-title="परमाणु नाभिक" data-language-autonym="हिन्दी" data-language-local-name="hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Atomska_jezgra" title="Atomska jezgra - croat" lang="hr" hreflang="hr" data-title="Atomska jezgra" data-language-autonym="Hrvatski" data-language-local-name="croat" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Nwayo_atomik" title="Nwayo atomik - crioll d’Haití" lang="ht" hreflang="ht" data-title="Nwayo atomik" data-language-autonym="Kreyòl ayisyen" data-language-local-name="crioll d’Haití" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Atommag" title="Atommag - hongarès" lang="hu" hreflang="hu" data-title="Atommag" data-language-autonym="Magyar" data-language-local-name="hongarès" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%84%D5%AB%D5%BB%D5%B8%D6%82%D5%AF_(%D5%A1%D5%BF%D5%B8%D5%B4)" title="Միջուկ (ատոմ) - armeni" lang="hy" hreflang="hy" data-title="Միջուկ (ատոմ)" data-language-autonym="Հայերեն" data-language-local-name="armeni" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Nucleo_atomic" title="Nucleo atomic - interlingua" lang="ia" hreflang="ia" data-title="Nucleo atomic" data-language-autonym="Interlingua" data-language-local-name="interlingua" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Inti_atom" title="Inti atom - indonesi" lang="id" hreflang="id" data-title="Inti atom" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonesi" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Nukleo_atomala" title="Nukleo atomala - ido" lang="io" hreflang="io" data-title="Nukleo atomala" data-language-autonym="Ido" data-language-local-name="ido" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Frumeindakjarni" title="Frumeindakjarni - islandès" lang="is" hreflang="is" data-title="Frumeindakjarni" data-language-autonym="Íslenska" data-language-local-name="islandès" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Nucleo_atomico" title="Nucleo atomico - italià" lang="it" hreflang="it" data-title="Nucleo atomico" data-language-autonym="Italiano" data-language-local-name="italià" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E5%8E%9F%E5%AD%90%E6%A0%B8" title="原子核 - japonès" lang="ja" hreflang="ja" data-title="原子核" data-language-autonym="日本語" data-language-local-name="japonès" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-jv mw-list-item"><a href="https://jv.wikipedia.org/wiki/Inti_Atom" title="Inti Atom - javanès" lang="jv" hreflang="jv" data-title="Inti Atom" data-language-autonym="Jawa" data-language-local-name="javanès" class="interlanguage-link-target"><span>Jawa</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%90%E1%83%A2%E1%83%9D%E1%83%9B%E1%83%98%E1%83%A1_%E1%83%91%E1%83%98%E1%83%A0%E1%83%97%E1%83%95%E1%83%98" title="ატომის ბირთვი - georgià" lang="ka" hreflang="ka" data-title="ატომის ბირთვი" data-language-autonym="ქართული" data-language-local-name="georgià" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kab mw-list-item"><a href="https://kab.wikipedia.org/wiki/A%C9%A3yay_abelkam" title="Aɣyay abelkam - cabilenc" lang="kab" hreflang="kab" data-title="Aɣyay abelkam" data-language-autonym="Taqbaylit" data-language-local-name="cabilenc" class="interlanguage-link-target"><span>Taqbaylit</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%90%D1%82%D0%BE%D0%BC_%D1%8F%D0%B4%D1%80%D0%BE%D1%81%D1%8B" title="Атом ядросы - kazakh" lang="kk" hreflang="kk" data-title="Атом ядросы" data-language-autonym="Қазақша" data-language-local-name="kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%AC%E0%B3%88%E0%B2%9C%E0%B2%BF%E0%B2%95_%E0%B2%95%E0%B3%87%E0%B2%82%E0%B2%A6%E0%B3%8D%E0%B2%B0" title="ಬೈಜಿಕ ಕೇಂದ್ರ - kannada" lang="kn" hreflang="kn" data-title="ಬೈಜಿಕ ಕೇಂದ್ರ" data-language-autonym="ಕನ್ನಡ" data-language-local-name="kannada" class="interlanguage-link-target"><span>ಕನ್ನಡ</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%9B%90%EC%9E%90%ED%95%B5" title="원자핵 - coreà" lang="ko" hreflang="ko" data-title="원자핵" data-language-autonym="한국어" data-language-local-name="coreà" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-ks mw-list-item"><a href="https://ks.wikipedia.org/wiki/%DA%A9%D9%86%DB%81%D9%95_%D9%85%D9%95%D8%B1" title="کنہٕ مٕر - caixmiri" lang="ks" hreflang="ks" data-title="کنہٕ مٕر" data-language-autonym="कॉशुर / کٲشُر" data-language-local-name="caixmiri" class="interlanguage-link-target"><span>कॉशुर / کٲشُر</span></a></li><li class="interlanguage-link interwiki-ku mw-list-item"><a href="https://ku.wikipedia.org/wiki/Navok" title="Navok - kurd" lang="ku" hreflang="ku" data-title="Navok" data-language-autonym="Kurdî" data-language-local-name="kurd" class="interlanguage-link-target"><span>Kurdî</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Nucleus_atomi" title="Nucleus atomi - llatí" lang="la" hreflang="la" data-title="Nucleus atomi" data-language-autonym="Latina" data-language-local-name="llatí" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-li mw-list-item"><a href="https://li.wikipedia.org/wiki/Atoamkaen" title="Atoamkaen - limburguès" lang="li" hreflang="li" data-title="Atoamkaen" data-language-autonym="Limburgs" data-language-local-name="limburguès" class="interlanguage-link-target"><span>Limburgs</span></a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/Nucli_(fisega)" title="Nucli (fisega) - llombard" lang="lmo" hreflang="lmo" data-title="Nucli (fisega)" data-language-autonym="Lombard" data-language-local-name="llombard" class="interlanguage-link-target"><span>Lombard</span></a></li><li class="interlanguage-link interwiki-ln mw-list-item"><a href="https://ln.wikipedia.org/wiki/Mok%C3%B3k%C3%B3l%C3%B3_mwa_atome" title="Mokókóló mwa atome - lingala" lang="ln" hreflang="ln" data-title="Mokókóló mwa atome" data-language-autonym="Lingála" data-language-local-name="lingala" class="interlanguage-link-target"><span>Lingála</span></a></li><li class="interlanguage-link interwiki-lo mw-list-item"><a href="https://lo.wikipedia.org/wiki/%E0%BB%81%E0%BA%81%E0%BA%99%E0%BA%9B%E0%BA%B0%E0%BA%A5%E0%BB%8D%E0%BA%B2%E0%BA%A1%E0%BA%B0%E0%BA%99%E0%BA%B9" title="ແກນປະລໍາມະນູ - laosià" lang="lo" hreflang="lo" data-title="ແກນປະລໍາມະນູ" data-language-autonym="ລາວ" data-language-local-name="laosià" class="interlanguage-link-target"><span>ລາວ</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Atomo_branduolys" title="Atomo branduolys - lituà" lang="lt" hreflang="lt" data-title="Atomo branduolys" data-language-autonym="Lietuvių" data-language-local-name="lituà" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Atoma_kodols" title="Atoma kodols - letó" lang="lv" hreflang="lv" data-title="Atoma kodols" data-language-autonym="Latviešu" data-language-local-name="letó" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-map-bms mw-list-item"><a href="https://map-bms.wikipedia.org/wiki/Nukleus" title="Nukleus - Banyumasan" lang="jv-x-bms" hreflang="jv-x-bms" data-title="Nukleus" data-language-autonym="Basa Banyumasan" data-language-local-name="Banyumasan" class="interlanguage-link-target"><span>Basa Banyumasan</span></a></li><li class="interlanguage-link interwiki-mhr mw-list-item"><a href="https://mhr.wikipedia.org/wiki/%D0%90%D1%82%D0%BE%D0%BC_%D1%82%D0%BE%D0%BC" title="Атом том - Eastern Mari" lang="mhr" hreflang="mhr" data-title="Атом том" data-language-autonym="Олык марий" data-language-local-name="Eastern Mari" class="interlanguage-link-target"><span>Олык марий</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%90%D1%82%D0%BE%D0%BC%D1%81%D0%BA%D0%BE_%D1%98%D0%B0%D0%B4%D1%80%D0%BE" title="Атомско јадро - macedoni" lang="mk" hreflang="mk" data-title="Атомско јадро" data-language-autonym="Македонски" data-language-local-name="macedoni" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%85%E0%B4%A3%E0%B5%81%E0%B4%95%E0%B5%87%E0%B4%A8%E0%B5%8D%E0%B4%A6%E0%B5%8D%E0%B4%B0%E0%B4%82" title="അണുകേന്ദ്രം - malaiàlam" lang="ml" hreflang="ml" data-title="അണുകേന്ദ്രം" data-language-autonym="മലയാളം" data-language-local-name="malaiàlam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%90%D1%82%D0%BE%D0%BC%D1%8B%D0%BD_%D1%86%D3%A9%D0%BC" title="Атомын цөм - mongol" lang="mn" hreflang="mn" data-title="Атомын цөм" data-language-autonym="Монгол" data-language-local-name="mongol" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%85%E0%A4%A3%E0%A5%81%E0%A4%95%E0%A5%87%E0%A4%82%E0%A4%A6%E0%A5%8D%E0%A4%B0" title="अणुकेंद्र - marathi" lang="mr" hreflang="mr" data-title="अणुकेंद्र" data-language-autonym="मराठी" data-language-local-name="marathi" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Nukleus_atom" title="Nukleus atom - malai" lang="ms" hreflang="ms" data-title="Nukleus atom" data-language-autonym="Bahasa Melayu" data-language-local-name="malai" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%A1%E1%80%80%E1%80%BA%E1%80%BA%E1%80%90%E1%80%99%E1%80%BA%E1%81%8F_%E1%80%94%E1%80%BB%E1%80%B0%E1%80%80%E1%80%9C%E1%80%AD%E1%80%9A" title="အက််တမ်၏ နျူကလိယ - birmà" lang="my" hreflang="my" data-title="အက််တမ်၏ နျူကလိယ" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="birmà" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Atoomkern" title="Atoomkern - neerlandès" lang="nl" hreflang="nl" data-title="Atoomkern" data-language-autonym="Nederlands" data-language-local-name="neerlandès" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Atomkjerne" title="Atomkjerne - noruec nynorsk" lang="nn" hreflang="nn" data-title="Atomkjerne" data-language-autonym="Norsk nynorsk" data-language-local-name="noruec nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Atomkjerne" title="Atomkjerne - noruec bokmål" lang="nb" hreflang="nb" data-title="Atomkjerne" data-language-autonym="Norsk bokmål" data-language-local-name="noruec bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-nov mw-list-item"><a href="https://nov.wikipedia.org/wiki/Nukleus" title="Nukleus - novial" lang="nov" hreflang="nov" data-title="Nukleus" data-language-autonym="Novial" data-language-local-name="novial" class="interlanguage-link-target"><span>Novial</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Nucl%C3%A8u_atomic" title="Nuclèu atomic - occità" lang="oc" hreflang="oc" data-title="Nuclèu atomic" data-language-autonym="Occitan" data-language-local-name="occità" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-om mw-list-item"><a href="https://om.wikipedia.org/wiki/Niwukilasii_atoomii" title="Niwukilasii atoomii - oromo" lang="om" hreflang="om" data-title="Niwukilasii atoomii" data-language-autonym="Oromoo" data-language-local-name="oromo" class="interlanguage-link-target"><span>Oromoo</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%AA%E0%A8%B0%E0%A8%AE%E0%A8%BE%E0%A8%A3%E0%A9%82_%E0%A8%A8%E0%A8%BE%E0%A8%AD" title="ਪਰਮਾਣੂ ਨਾਭ - panjabi" lang="pa" hreflang="pa" data-title="ਪਰਮਾਣੂ ਨਾਭ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="panjabi" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/J%C4%85dro_atomowe" title="Jądro atomowe - polonès" lang="pl" hreflang="pl" data-title="Jądro atomowe" data-language-autonym="Polski" data-language-local-name="polonès" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%D8%A7%DB%8C%D9%B9%D9%85%DB%8C_%D9%86%DB%8C%D9%88%DA%A9%D9%84%DB%8C%D8%B3" title="ایٹمی نیوکلیس - Western Punjabi" lang="pnb" hreflang="pnb" data-title="ایٹمی نیوکلیس" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/N%C3%BAcleo_at%C3%B3mico" title="Núcleo atómico - portuguès" lang="pt" hreflang="pt" data-title="Núcleo atómico" data-language-autonym="Português" data-language-local-name="portuguès" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-qu mw-list-item"><a href="https://qu.wikipedia.org/wiki/I%C3%B1uku_huk%27i" title="Iñuku huk'i - quítxua" lang="qu" hreflang="qu" data-title="Iñuku huk'i" data-language-autonym="Runa Simi" data-language-local-name="quítxua" class="interlanguage-link-target"><span>Runa Simi</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Nucleu_atomic" title="Nucleu atomic - romanès" lang="ro" hreflang="ro" data-title="Nucleu atomic" data-language-autonym="Română" data-language-local-name="romanès" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%90%D1%82%D0%BE%D0%BC%D0%BD%D0%BE%D0%B5_%D1%8F%D0%B4%D1%80%D0%BE" title="Атомное ядро - rus" lang="ru" hreflang="ru" data-title="Атомное ядро" data-language-autonym="Русский" data-language-local-name="rus" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-rue mw-list-item"><a href="https://rue.wikipedia.org/wiki/%D0%90%D1%82%D0%BE%D0%BC%D0%BE%D0%B2%D0%B5_%D1%8F%D0%B4%D1%80%D0%BE" title="Атомове ядро - Rusyn" lang="rue" hreflang="rue" data-title="Атомове ядро" data-language-autonym="Русиньскый" data-language-local-name="Rusyn" class="interlanguage-link-target"><span>Русиньскый</span></a></li><li class="interlanguage-link interwiki-sco mw-list-item"><a href="https://sco.wikipedia.org/wiki/Atomic_nucleus" title="Atomic nucleus - escocès" lang="sco" hreflang="sco" data-title="Atomic nucleus" data-language-autonym="Scots" data-language-local-name="escocès" class="interlanguage-link-target"><span>Scots</span></a></li><li class="interlanguage-link interwiki-sd mw-list-item"><a href="https://sd.wikipedia.org/wiki/%D8%A7%D9%8A%D9%BD%D9%85%D9%8A_%D9%86%D9%8A%D9%88%DA%AA%D9%84%D9%8A%D8%B3" title="ايٽمي نيوڪليس - sindi" lang="sd" hreflang="sd" data-title="ايٽمي نيوڪليس" data-language-autonym="سنڌي" data-language-local-name="sindi" class="interlanguage-link-target"><span>سنڌي</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Atomsko_jezgro" title="Atomsko jezgro - serbocroat" lang="sh" hreflang="sh" data-title="Atomsko jezgro" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="serbocroat" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Atomic_nucleus" title="Atomic nucleus - Simple English" lang="en-simple" hreflang="en-simple" data-title="Atomic nucleus" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/At%C3%B3mov%C3%A9_jadro" title="Atómové jadro - eslovac" lang="sk" hreflang="sk" data-title="Atómové jadro" data-language-autonym="Slovenčina" data-language-local-name="eslovac" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Atomsko_jedro" title="Atomsko jedro - eslovè" lang="sl" hreflang="sl" data-title="Atomsko jedro" data-language-autonym="Slovenščina" data-language-local-name="eslovè" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/B%C3%ABrthama_e_atomit" title="Bërthama e atomit - albanès" lang="sq" hreflang="sq" data-title="Bërthama e atomit" data-language-autonym="Shqip" data-language-local-name="albanès" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%90%D1%82%D0%BE%D0%BC%D1%81%D0%BA%D0%BE_%D1%98%D0%B5%D0%B7%D0%B3%D1%80%D0%BE" title="Атомско језгро - serbi" lang="sr" hreflang="sr" data-title="Атомско језгро" data-language-autonym="Српски / srpski" data-language-local-name="serbi" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-stq mw-list-item"><a href="https://stq.wikipedia.org/wiki/Atomk%C3%A4%C3%A4den" title="Atomkääden - Saterland Frisian" lang="stq" hreflang="stq" data-title="Atomkääden" data-language-autonym="Seeltersk" data-language-local-name="Saterland Frisian" class="interlanguage-link-target"><span>Seeltersk</span></a></li><li class="interlanguage-link interwiki-su mw-list-item"><a href="https://su.wikipedia.org/wiki/Inti_atom" title="Inti atom - sondanès" lang="su" hreflang="su" data-title="Inti atom" data-language-autonym="Sunda" data-language-local-name="sondanès" class="interlanguage-link-target"><span>Sunda</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Atomk%C3%A4rna" title="Atomkärna - suec" lang="sv" hreflang="sv" data-title="Atomkärna" data-language-autonym="Svenska" data-language-local-name="suec" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://sw.wikipedia.org/wiki/Kiini_cha_atomu" title="Kiini cha atomu - suahili" lang="sw" hreflang="sw" data-title="Kiini cha atomu" data-language-autonym="Kiswahili" data-language-local-name="suahili" class="interlanguage-link-target"><span>Kiswahili</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%85%E0%AE%A3%E0%AF%81%E0%AE%95%E0%AF%8D%E0%AE%95%E0%AE%B0%E0%AF%81" title="அணுக்கரு - tàmil" lang="ta" hreflang="ta" data-title="அணுக்கரு" data-language-autonym="தமிழ்" data-language-local-name="tàmil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-te mw-list-item"><a href="https://te.wikipedia.org/wiki/%E0%B0%AA%E0%B0%B0%E0%B0%AE%E0%B0%BE%E0%B0%A3%E0%B1%81_%E0%B0%95%E0%B1%87%E0%B0%82%E0%B0%A6%E0%B1%8D%E0%B0%B0%E0%B0%95%E0%B0%82" title="పరమాణు కేంద్రకం - telugu" lang="te" hreflang="te" data-title="పరమాణు కేంద్రకం" data-language-autonym="తెలుగు" data-language-local-name="telugu" class="interlanguage-link-target"><span>తెలుగు</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%99%E0%B8%B4%E0%B8%A7%E0%B9%80%E0%B8%84%E0%B8%A5%E0%B8%B5%E0%B8%A2%E0%B8%AA%E0%B8%82%E0%B8%AD%E0%B8%87%E0%B8%AD%E0%B8%B0%E0%B8%95%E0%B8%AD%E0%B8%A1" title="นิวเคลียสของอะตอม - tai" lang="th" hreflang="th" data-title="นิวเคลียสของอะตอม" data-language-autonym="ไทย" data-language-local-name="tai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Atomikong_nukleyus" title="Atomikong nukleyus - tagal" lang="tl" hreflang="tl" data-title="Atomikong nukleyus" data-language-autonym="Tagalog" data-language-local-name="tagal" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Atom_%C3%A7ekirde%C4%9Fi" title="Atom çekirdeği - turc" lang="tr" hreflang="tr" data-title="Atom çekirdeği" data-language-autonym="Türkçe" data-language-local-name="turc" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk badge-Q17437798 badge-goodarticle mw-list-item" title="article bo"><a href="https://uk.wikipedia.org/wiki/%D0%AF%D0%B4%D1%80%D0%BE_%D0%B0%D1%82%D0%BE%D0%BC%D0%B0" title="Ядро атома - ucraïnès" lang="uk" hreflang="uk" data-title="Ядро атома" data-language-autonym="Українська" data-language-local-name="ucraïnès" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D8%AC%D9%88%DB%81%D8%B1%DB%8C_%D9%86%D9%88%DB%8C%DB%81" title="جوہری نویہ - urdú" lang="ur" hreflang="ur" data-title="جوہری نویہ" data-language-autonym="اردو" data-language-local-name="urdú" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Atom_yadrosi" title="Atom yadrosi - uzbek" lang="uz" hreflang="uz" data-title="Atom yadrosi" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="uzbek" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/H%E1%BA%A1t_nh%C3%A2n_nguy%C3%AAn_t%E1%BB%AD" title="Hạt nhân nguyên tử - vietnamita" lang="vi" hreflang="vi" data-title="Hạt nhân nguyên tử" data-language-autonym="Tiếng Việt" data-language-local-name="vietnamita" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-war badge-Q70893996 mw-list-item" title=""><a href="https://war.wikipedia.org/wiki/Nukleyus_hin_atomo" title="Nukleyus hin atomo - waray" lang="war" hreflang="war" data-title="Nukleyus hin atomo" data-language-autonym="Winaray" data-language-local-name="waray" class="interlanguage-link-target"><span>Winaray</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E5%8E%9F%E5%AD%90%E6%A0%B8" title="原子核 - xinès wu" lang="wuu" hreflang="wuu" data-title="原子核" data-language-autonym="吴语" data-language-local-name="xinès wu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-yi mw-list-item"><a href="https://yi.wikipedia.org/wiki/%D7%90%D7%98%D7%90%D7%9E%D7%A7%D7%A2%D7%A8%D7%9F" title="אטאמקערן - ídix" lang="yi" hreflang="yi" data-title="אטאמקערן" data-language-autonym="ייִדיש" data-language-local-name="ídix" class="interlanguage-link-target"><span>ייִדיש</span></a></li><li class="interlanguage-link interwiki-yo mw-list-item"><a href="https://yo.wikipedia.org/wiki/N%C3%BAkl%C3%A9%C3%B9_%C3%A1t%E1%BB%8D%CC%80m%C3%B9" title="Núkléù átọ̀mù - ioruba" lang="yo" hreflang="yo" data-title="Núkléù átọ̀mù" data-language-autonym="Yorùbá" data-language-local-name="ioruba" class="interlanguage-link-target"><span>Yorùbá</span></a></li><li class="interlanguage-link interwiki-za mw-list-item"><a href="https://za.wikipedia.org/wiki/Yenzswjhaed" title="Yenzswjhaed - zhuang" lang="za" hreflang="za" data-title="Yenzswjhaed" data-language-autonym="Vahcuengh" data-language-local-name="zhuang" class="interlanguage-link-target"><span>Vahcuengh</span></a></li><li class="interlanguage-link interwiki-zgh mw-list-item"><a href="https://zgh.wikipedia.org/wiki/%E2%B5%93%E2%B5%A5%E2%B5%8E_%E2%B4%B0%E2%B5%A1%E2%B4%B1%E2%B5%8D%E2%B4%BD%E2%B5%89%E2%B5%8E" title="ⵓⵥⵎ ⴰⵡⴱⵍⴽⵉⵎ - amazic estàndard marroquí" lang="zgh" hreflang="zgh" data-title="ⵓⵥⵎ ⴰⵡⴱⵍⴽⵉⵎ" data-language-autonym="ⵜⴰⵎⴰⵣⵉⵖⵜ ⵜⴰⵏⴰⵡⴰⵢⵜ" data-language-local-name="amazic estàndard marroquí" class="interlanguage-link-target"><span>ⵜⴰⵎⴰⵣⵉⵖⵜ ⵜⴰⵏⴰⵡⴰⵢⵜ</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E5%8E%9F%E5%AD%90%E6%A0%B8" title="原子核 - xinès" lang="zh" hreflang="zh" data-title="原子核" data-language-autonym="中文" data-language-local-name="xinès" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-classical mw-list-item"><a href="https://zh-classical.wikipedia.org/wiki/%E5%8E%9F%E5%AD%90%E6%A0%B8" title="原子核 - xinès clàssic" lang="lzh" hreflang="lzh" data-title="原子核" data-language-autonym="文言" data-language-local-name="xinès clàssic" class="interlanguage-link-target"><span>文言</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/Go%C3%A2n-ch%C3%BA-hu%CC%8Dt" title="Goân-chú-hu̍t - xinès min del sud" lang="nan" hreflang="nan" data-title="Goân-chú-hu̍t" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="xinès min del sud" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E5%8E%9F%E5%AD%90%E6%A0%B8" title="原子核 - cantonès" lang="yue" hreflang="yue" data-title="原子核" data-language-autonym="粵語" data-language-local-name="cantonès" class="interlanguage-link-target"><span>粵語</span></a></li><li class="interlanguage-link interwiki-zu mw-list-item"><a href="https://zu.wikipedia.org/wiki/INuzi_lechwe" title="INuzi lechwe - zulu" lang="zu" hreflang="zu" data-title="INuzi lechwe" data-language-autonym="IsiZulu" 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srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f0/Nucleus_drawing.svg/330px-Nucleus_drawing.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f0/Nucleus_drawing.svg/440px-Nucleus_drawing.svg.png 2x" data-file-width="400" data-file-height="400" /></a><figcaption>Model d'un nucli atòmic amb els protons en vermell i els neutrons en blau</figcaption></figure> <p>El <b>nucli atòmic</b> és la part central de l'<a href="/wiki/%C3%80tom" title="Àtom">àtom</a> que conté la major part de la <a href="/wiki/Mat%C3%A8ria" title="Matèria">matèria</a> que el forma però que, tanmateix, n'ocupa un volum relativament molt petit. Està format per <a href="/wiki/Bari%C3%B3" title="Barió">barions</a>, concretament per <a href="/wiki/Prot%C3%B3" title="Protó">protons</a> i <a href="/wiki/Neutrons" class="mw-redirect" title="Neutrons">neutrons</a>, en nombre variable,<sup id="cite_ref-gec_1-0" class="reference"><a href="#cite_note-gec-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> però sempre més neutrons que protons. En són una excepció el nucli de l'<a href="/wiki/Hidrogen" title="Hidrogen">hidrogen</a> ordinari (format per un únic protó) i els dels àtoms més lleugers, en què el nombre de protons i el de neutrons sol ser igual. El nombre de protons s'anomena <a href="/wiki/Nombre_at%C3%B2mic" title="Nombre atòmic">nombre atòmic</a> i és el paràmetre que determina a quin <a href="/wiki/Element_qu%C3%ADmic" title="Element químic">element químic</a> correspon l'àtom. El nombre de neutrons d'àtoms del mateix <a href="/wiki/Element_qu%C3%ADmic" title="Element químic">element</a> pot ser variable: els nuclis amb el mateix nombre atòmic, però diferent nombre de neutrons, s'anomenen <a href="/wiki/Is%C3%B2tops" class="mw-redirect" title="Isòtops">isòtops</a>. </p><p>La força que manté units els <a href="/wiki/Bari%C3%B3" title="Barió">barions</a> que formen el nucli atòmic, els quals s'anomenen <a href="/wiki/Nucleons" class="mw-redirect" title="Nucleons">nucleons</a>, és la <a href="/wiki/For%C3%A7a_nuclear_forta" title="Força nuclear forta">força nuclear forta</a>.<sup id="cite_ref-gec_1-1" class="reference"><a href="#cite_note-gec-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p><p>Alguns <a href="/wiki/%C3%80toms" class="mw-redirect" title="Àtoms">àtoms</a> es descomponen espontàniament mitjançant processos <a href="/wiki/Radioactivitat" title="Radioactivitat">radioactius</a> que consisteixen en l'emissió d'<a href="/wiki/Electrons" class="mw-redirect" title="Electrons">electrons</a> (<a href="/wiki/Emissi%C3%B3_beta" class="mw-redirect" title="Emissió beta">rajos beta</a>) o nuclis d'<a href="/wiki/Heli" title="Heli">heli</a> (<a href="/wiki/Part%C3%ADcula_alfa" class="mw-redirect" title="Partícula alfa">rajos alfa</a>) altament energètics. Alguns nuclis són extremadament estables, en canvi d'altres es descomponen molt ràpidament. L'estabilitat d'un nucli atòmic depèn del nombre total de nucleons (els elements de nombre atòmic superior al del <a href="/wiki/Plom" title="Plom">plom</a> són tots <a href="/wiki/Radioactivitat" title="Radioactivitat">radioactius</a> i el plom i els que tenen un nombre atòmic inferior no ho solen ser) i també de la proporció entre el nombre de protons i neutrons: per això en un mateix element, diferents isòtops poden tenir una <a href="/wiki/Vida_mitjana" title="Vida mitjana">vida mitjana</a> diferent. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Història"><span id="Hist.C3.B2ria"></span>Història</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Nucli_at%C3%B2mic&action=edit&section=1" title="Modifica la secció: Història"><span>modifica</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Fitxer:Ernest_Rutherford_1908.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/de/Ernest_Rutherford_1908.jpg/220px-Ernest_Rutherford_1908.jpg" decoding="async" width="220" height="292" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/de/Ernest_Rutherford_1908.jpg/330px-Ernest_Rutherford_1908.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/de/Ernest_Rutherford_1908.jpg/440px-Ernest_Rutherford_1908.jpg 2x" data-file-width="3227" data-file-height="4288" /></a><figcaption>Ernest Rutherford el 1908</figcaption></figure> <p>A principis del 1896, el físic francès <a href="/wiki/Antoine_Henri_Becquerel" title="Antoine Henri Becquerel">Henry Becquerel</a> (1852–1908) descobrí casualment la <a href="/wiki/Radioactivitat" title="Radioactivitat">radioactivitat</a> quan realitzava estudis de <a href="/wiki/Fosforesc%C3%A8ncia" title="Fosforescència">fosforescència</a> amb mostres de minerals d'<a href="/wiki/Urani" title="Urani">urani</a>,<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> data que se considera la del naixement de la <a href="/wiki/F%C3%ADsica_nuclear" title="Física nuclear">Física Nuclear</a>. Tot seguit altres científics, entre els quals destaquen la física polonesa <a href="/wiki/Marie_Curie" title="Marie Curie">Marie Curie</a> (1867–1934) i el seu marit, el físic francès <a href="/wiki/Pierre_Curie" title="Pierre Curie">Pierre Curie</a> (1859–1906), iniciaren la investigació de la naturalesa de la radioactivitat la qual cosa conduí a l'estudi de l'estructura del nucli atòmic, encara no descobert en aquells anys. El neozelandès <a href="/wiki/Ernest_Rutherford" title="Ernest Rutherford">Ernest Rutherford</a> (1871-1937) demostrà que la radiació emesa per les substàncies radioactives correspon a tres tipus diferents, <a href="/wiki/Radioactivitat_alfa" class="mw-redirect" title="Radioactivitat alfa">raigs alfa</a>, <a href="/wiki/Radioactivitat_beta" class="mw-redirect" title="Radioactivitat beta">beta</a> i <a href="/wiki/Radiaci%C3%B3_gamma" title="Radiació gamma">gamma</a>, que després s'identificaren com a nuclis d'<a href="/wiki/Heli" title="Heli">heli</a> els raigs alfa, <a href="/wiki/Electr%C3%B3" title="Electró">electrons</a> els beta i <a href="/wiki/Fot%C3%B3" title="Fotó">fotons</a> d'alta energia els gamma. </p><p>El 1911 Rutherford, el físic alemany <a href="/wiki/Hans_Geiger" title="Hans Geiger">Hans Geiger</a> (1882–1945) i el físic britànic <a href="/wiki/Ernest_Marsden" title="Ernest Marsden">Ernest Marsden</a> (1889–1979) realitzaren l'<a href="/wiki/Experiment_de_Rutherford" title="Experiment de Rutherford">experiment de la làmina d'or</a>, en el qual dispersaven partícules alfa contra nuclis d'<a href="/wiki/Or" title="Or">or</a> i altres metalls pesants. Aquests experiments posaren de manifest existeix una zona central de l'àtom, que Rutherford anomenà nucli, que conté tota la càrrega positiva, quasi tota la massa i que té un volum extremadament petit al comparar-lo amb el volum de l'àtom.<sup id="cite_ref-:0_3-0" class="reference"><a href="#cite_note-:0-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> El 1929 el físic rus <a href="/wiki/George_Gamow" title="George Gamow">George Gamow</a> (1904–1968) proposà tractar el nucli com una gota de <a href="/wiki/L%C3%ADquid" title="Líquid">líquid</a>.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p><p>El 1930 els físics britànics <a href="/wiki/John_Douglas_Cockcroft" title="John Douglas Cockcroft">John Cockroft</a> (1897–1967) i <a href="/wiki/Ernest_Walton" title="Ernest Walton">Ernest Walton</a> (1903–1995), sota la direcció de Rutherford, realitzaren les primeres reaccions nuclears emprant nuclis accelerats mitjançant un <a href="/wiki/Camp_el%C3%A8ctric" title="Camp elèctric">camp elèctric</a>. El 1932 el físic britànic <a href="/wiki/James_Chadwick" title="James Chadwick">James Chadwick</a> (1891–1974) descobrí el neutró.<sup id="cite_ref-Chad19322_6-0" class="reference"><a href="#cite_note-Chad19322-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Carl_Friedrich_von_Weizs%C3%A4cker" title="Carl Friedrich von Weizsäcker">Carl Friedrich von Weizsäcker</a> (1912–2007) el 1935, seguint la proposta de Gamow d'interpretar el nucli com una gota de líquid, i incorporant la hipòtesi protó–neutró del nucli del físic alemany <a href="/wiki/Werner_Heisenberg" title="Werner Heisenberg">Werner Heisenberg</a> (1901–1976)<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> i del físic rus <a href="/wiki/Dmitri_Ivanenko" title="Dmitri Ivanenko">Dmitri Ivanenko</a><sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> i el treball del físic italià <a href="/wiki/Ettore_Majorana" title="Ettore Majorana">Ettore Majorana</a> (1906–1938) sobre les forces nuclears, elaborà un model complet de nucli.<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Fitxer:Maria_Goeppert-Mayer_portrait.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7b/Maria_Goeppert-Mayer_portrait.jpg/220px-Maria_Goeppert-Mayer_portrait.jpg" decoding="async" width="220" height="279" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7b/Maria_Goeppert-Mayer_portrait.jpg/330px-Maria_Goeppert-Mayer_portrait.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/7b/Maria_Goeppert-Mayer_portrait.jpg/440px-Maria_Goeppert-Mayer_portrait.jpg 2x" data-file-width="2227" data-file-height="2823" /></a><figcaption>Maria Göppert-Mayer</figcaption></figure> <p>El 1934 es descobrí la radioactivitat artificial per part dels físics francesos <a href="/wiki/Ir%C3%A8ne_Joliot-Curie" title="Irène Joliot-Curie">Irène</a> (1897–1956) i <a href="/wiki/Fr%C3%A9d%C3%A9ric_Joliot-Curie" title="Frédéric Joliot-Curie">Frédéric Joliot-Curie</a> (1900–1958). El 1938 es realitzà el descobriment de la fissió nuclear per la física <a href="/wiki/Imperi_Austrohongar%C3%A8s" title="Imperi Austrohongarès">austrohongaresa</a> <a href="/wiki/Lise_Meitner" title="Lise Meitner">Leise Meitner</a> (1878–1968) i els químics alemanys <a href="/wiki/Otto_Hahn" title="Otto Hahn">Otto Hahn</a> (1879–1968) i <a href="/wiki/Friedrich_Wilhelm_Strassmann" title="Friedrich Wilhelm Strassmann">Fritz Strassmann</a> (1902–1980). El 1939 <a href="/wiki/Niels_Bohr" title="Niels Bohr">Niels Bohr</a> (1885–1962) i <a href="/wiki/John_Archibald_Wheeler" title="John Archibald Wheeler">John Archibald Wheeler</a> (1911–2008) desenvoluparen el model de la gota de líquid per explicar la <a href="/wiki/Fissi%C3%B3_nuclear" title="Fissió nuclear">fissió nuclear</a> descoberta només sis mesos abans.<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> </p><p>El 1942 es desenvolupà el primer reactor de fissió controlat pel físic italià <a href="/wiki/Enrico_Fermi" title="Enrico Fermi">Enrico Fermi</a> (1901–1954) i col·laboradors. El 1949 es desenvolupà el model de capes del nucli de forma independent per diferents científics, destacant <a href="/wiki/Eugene_Paul_Wigner" title="Eugene Paul Wigner">Eugene Paul Wigner</a>, <a href="/wiki/Maria_G%C3%B6ppert-Mayer" title="Maria Göppert-Mayer">Maria Göppert-Mayer</a><sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> i <a href="/wiki/Johannes_Hans_Jensen" title="Johannes Hans Jensen">J. Hans D. Jensen</a>.<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> </p><p>En descobrir-se que els nuclis estaven formats per protons sorgí el problema de la seva estabilitat, ja que no era possible que els protons es mantenguessin units degut a l'acció de repulsió de la <a href="/wiki/Llei_de_Coulomb" title="Llei de Coulomb">força de Coulomb</a> entre càrregues del mateix signe. La solució es trobà en identificar una nova força fonamental, la <a href="/wiki/For%C3%A7a_nuclear_forta" title="Força nuclear forta">força forta</a>, que només actua a curtes distàncies, inferiors a 10<sup>–14</sup> m, i que atreu els protons entre ells. Actualment s'explica amb la teoria anomenada <a href="/wiki/Cromodin%C3%A0mica_qu%C3%A0ntica" title="Cromodinàmica quàntica">cromodinàmica quàntica</a>, proposada al començament dels anys <a href="/wiki/1970" title="1970">1970</a> pels físics estatunidencs <a href="/wiki/David_Politzer" title="David Politzer">David Politzer</a> (1949), <a href="/wiki/Frank_Wilczek" title="Frank Wilczek">Frank Wilczek</a> (1951) i <a href="/wiki/David_Gross" title="David Gross">David Gross</a> (1941). </p> <div class="mw-heading mw-heading2"><h2 id="Propietats">Propietats</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Nucli_at%C3%B2mic&action=edit&section=2" title="Modifica la secció: Propietats"><span>modifica</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Fitxer:Proton_and_neutron.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7b/Proton_and_neutron.jpg/220px-Proton_and_neutron.jpg" decoding="async" width="220" height="118" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7b/Proton_and_neutron.jpg/330px-Proton_and_neutron.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/7b/Proton_and_neutron.jpg/440px-Proton_and_neutron.jpg 2x" data-file-width="1412" data-file-height="760" /></a><figcaption>Els protons estan constituïts per tres quarks (uud) i el neutró també per tres quarks, però diferents (udd)</figcaption></figure> <div class="mw-heading mw-heading3"><h3 id="Nucleons">Nucleons</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Nucli_at%C3%B2mic&action=edit&section=3" title="Modifica la secció: Nucleons"><span>modifica</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Tots els nuclis dels àtoms estan constituïts per dos tipus de partícules: <a href="/wiki/Protons" class="mw-redirect" title="Protons">protons</a> i <a href="/wiki/Neutrons" class="mw-redirect" title="Neutrons">neutrons</a>, anomenats genèricament <a href="/wiki/Nucle%C3%B3" title="Nucleó">nucleons</a>. Només l'<a href="/wiki/Hidrogen" title="Hidrogen">hidrogen</a> està constituït per un únic protó. Així el nucli atòmic es descriu amb els nombres: </p> <ul><li><a href="/wiki/Nombre_at%C3%B2mic" title="Nombre atòmic">Nombre atòmic</a>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Z}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Z</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Z}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1cc6b75e09a8aa3f04d8584b11db534f88fb56bd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.68ex; height:2.176ex;" alt="{\displaystyle Z}"></span>, que és igual al nombre de protons.</li> <li>Nombre de neutrons, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle N}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>N</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f5e3890c981ae85503089652feb48b191b57aae3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.064ex; height:2.176ex;" alt="{\displaystyle N}"></span>.</li> <li><a href="/wiki/Nombre_m%C3%A0ssic" title="Nombre màssic">Nombre màssic</a>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A=Z+N}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>=</mo> <mi>Z</mi> <mo>+</mo> <mi>N</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A=Z+N}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e8129ddaf56e93bf84a31a705dd866daed150682" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:11.426ex; height:2.343ex;" alt="{\displaystyle A=Z+N}"></span>, que és igual al nombre total de nucleons, protons més neutrons.<sup id="cite_ref-:5_18-0" class="reference"><a href="#cite_note-:5-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup></li></ul> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Fitxer:Isotopes_and_half-life.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/80/Isotopes_and_half-life.svg/langca-220px-Isotopes_and_half-life.svg.png" decoding="async" width="220" height="264" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/80/Isotopes_and_half-life.svg/langca-330px-Isotopes_and_half-life.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/80/Isotopes_and_half-life.svg/langca-440px-Isotopes_and_half-life.svg.png 2x" data-file-width="640" data-file-height="768" /></a><figcaption>Isòtops amb la seva vida mitjana</figcaption></figure> <p>Els nuclis se simbolitzen mitjançant el símbol <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle _{Z}^{A}X}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <msubsup> <mi></mi> <mrow class="MJX-TeXAtom-ORD"> <mi>Z</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msubsup> <mi>X</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle _{Z}^{A}X}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f9b865f6daeab3a5a2802a01fa5565e9fe0d9791" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.445ex; height:3.176ex;" alt="{\textstyle _{Z}^{A}X}"></span>, on <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>X</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/68baa052181f707c662844a465bfeeb135e82bab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.98ex; height:2.176ex;" alt="{\displaystyle X}"></span> representa el símbol de l'<a href="/wiki/Element_qu%C3%ADmic" title="Element químic">element químic</a>, i <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}"></span> i <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Z}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Z</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Z}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1cc6b75e09a8aa3f04d8584b11db534f88fb56bd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.68ex; height:2.176ex;" alt="{\displaystyle Z}"></span> els nombres màssic i atòmic, respectivament. Així un nucli que se simbolitzi com <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\ce {_{26}^{56}Fe}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mmultiscripts> <mtext>Fe</mtext> <none /> <none /> <mprescripts /> <mn>26</mn> <mn>56</mn> </mmultiscripts> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\ce {_{26}^{56}Fe}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/916e7fbaae20e61cff146a4d8773a9b8380ccdc8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.368ex; height:3.176ex;" alt="{\displaystyle {\ce {_{26}^{56}Fe}}}"></span> indica que l'element és el <a href="/wiki/Ferro" title="Ferro">ferro</a> i que al nucli hi ha 26 protons i 56 nucleons, d'on es pot deduir el nombre de neutrons: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle N=A-Z=56-26=30\;{\text{neutrons}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>N</mi> <mo>=</mo> <mi>A</mi> <mo>−</mo> <mi>Z</mi> <mo>=</mo> <mn>56</mn> <mo>−</mo> <mn>26</mn> <mo>=</mo> <mn>30</mn> <mspace width="thickmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mtext>neutrons</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N=A-Z=56-26=30\;{\text{neutrons}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/415762c469463677c63291fd9e6abe8e970b4e69" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:36.888ex; height:2.343ex;" alt="{\displaystyle N=A-Z=56-26=30\;{\text{neutrons}}}"></span><sup id="cite_ref-:2_19-0" class="reference"><a href="#cite_note-:2-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> </p><p>Els nuclis de tots els àtoms d'un mateix element químic tenen el mateix nombre de protons o, el que és equivalent, el mateix nombre atòmic <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Z}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Z</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Z}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1cc6b75e09a8aa3f04d8584b11db534f88fb56bd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.68ex; height:2.176ex;" alt="{\displaystyle Z}"></span>, però freqüentment contenen quantitats diferents de neutrons. Aquests tipus de nuclis s'anomenen <a href="/wiki/Is%C3%B2top" title="Isòtop">isòtops</a>. Els isòtops tenen el mateix nombre atòmic <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Z}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Z</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Z}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1cc6b75e09a8aa3f04d8584b11db534f88fb56bd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.68ex; height:2.176ex;" alt="{\displaystyle Z}"></span>, però diferent nombre màssic <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}"></span> perquè tenen diferent nombre de neutrons. Per exemple el <a href="/wiki/Carboni" title="Carboni">carboni</a> té quatre isòtops naturals: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\ce {_6^{11}C, \, _6^{12}C, \, _6^{13}C, \, _6^{14}C}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mmultiscripts> <mtext>C</mtext> <none /> <none /> <mprescripts /> <mn>6</mn> <mn>11</mn> </mmultiscripts> <mo>,</mo> <mspace width="thinmathspace" /> <mmultiscripts> <mtext>C</mtext> <none /> <none /> <mprescripts /> <mn>6</mn> <mn>12</mn> </mmultiscripts> <mo>,</mo> <mspace width="thinmathspace" /> <mmultiscripts> <mtext>C</mtext> <none /> <none /> <mprescripts /> <mn>6</mn> <mn>13</mn> </mmultiscripts> <mo>,</mo> <mspace width="thinmathspace" /> <mmultiscripts> <mtext>C</mtext> <none /> <none /> <mprescripts /> <mn>6</mn> <mn>14</mn> </mmultiscripts> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\ce {_6^{11}C, \, _6^{12}C, \, _6^{13}C, \, _6^{14}C}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/82d11dbb0dc6e89f3a05a62e01ae4e7b5d8e52ce" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:18.248ex; height:3.176ex;" alt="{\displaystyle {\ce {_6^{11}C, \, _6^{12}C, \, _6^{13}C, \, _6^{14}C}}}"></span>, que es presenten en diferents proporcions, essent majoritari el carboni-12 (98,9 %).<sup id="cite_ref-:2_19-1" class="reference"><a href="#cite_note-:2-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> Tots aquests isòtops tenen el mateix nombre atòmic, 6, però nombres màssics diferents: 11, 12, 13 i 14, perquè tenen diferent nombre de neutrons: 5, 6, 7 i 8, respectivament. </p><p>Els nuclis atòmics que tenen el mateix nombre màssic, però amb diferents proporcions de protons i neutrons, s'anomenen isòbars,<sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> com ara <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\ce {_6^{14}C}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mmultiscripts> <mtext>C</mtext> <none /> <none /> <mprescripts /> <mn>6</mn> <mn>14</mn> </mmultiscripts> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\ce {_6^{14}C}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/11994041c28f892be189a9967ee4621f3e206899" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.496ex; height:3.176ex;" alt="{\displaystyle {\ce {_6^{14}C}}}"></span> i <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\ce {_7^{14}N}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mmultiscripts> <mtext>N</mtext> <none /> <none /> <mprescripts /> <mn>7</mn> <mn>14</mn> </mmultiscripts> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\ce {_7^{14}N}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/361e28dc833d84193df8a1e1435ea7c24c7b3101" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.561ex; height:3.176ex;" alt="{\displaystyle {\ce {_7^{14}N}}}"></span>, ambdós amb <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A=14}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>=</mo> <mn>14</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A=14}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/73c39485aa20d67a8ecc62f449091cac76b435bb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.166ex; height:2.176ex;" alt="{\displaystyle A=14}"></span>. Els que tenen el mateix nombre de neutrons són dits isòtons.<sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> És el cas de <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\ce {_6^{13}C}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mmultiscripts> <mtext>C</mtext> <none /> <none /> <mprescripts /> <mn>6</mn> <mn>13</mn> </mmultiscripts> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\ce {_6^{13}C}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f6e2169a5bfa8a6a8cbf1f73e57fa907c18a92a2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.496ex; height:3.176ex;" alt="{\displaystyle {\ce {_6^{13}C}}}"></span> i <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\ce {_7^{14}N}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mmultiscripts> <mtext>N</mtext> <none /> <none /> <mprescripts /> <mn>7</mn> <mn>14</mn> </mmultiscripts> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\ce {_7^{14}N}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/361e28dc833d84193df8a1e1435ea7c24c7b3101" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.561ex; height:3.176ex;" alt="{\displaystyle {\ce {_7^{14}N}}}"></span>, on ambdós tenen 7 neutrons, que s'obtenen restant <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle A-Z}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mi>A</mi> <mo>−</mo> <mi>Z</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle A-Z}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0a7d1a35ca2f674e4a3fa9db3c4c8742c6f319ea" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:6.264ex; height:2.343ex;" alt="{\textstyle A-Z}"></span>. S'anomenen nuclis mirall els nuclis en els quals el nombre de neutrons de l'un és igual al de protons de l'altre, com en el cas de <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\ce {_6^{13}C}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mmultiscripts> <mtext>C</mtext> <none /> <none /> <mprescripts /> <mn>6</mn> <mn>13</mn> </mmultiscripts> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\ce {_6^{13}C}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f6e2169a5bfa8a6a8cbf1f73e57fa907c18a92a2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.496ex; height:3.176ex;" alt="{\displaystyle {\ce {_6^{13}C}}}"></span> que té 6 protons i 7 neutrons i el <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\ce {_7^{13}N}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mmultiscripts> <mtext>N</mtext> <none /> <none /> <mprescripts /> <mn>7</mn> <mn>13</mn> </mmultiscripts> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\ce {_7^{13}N}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bedb21bf323eddbbf1aa34e5320d33384364f31d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.561ex; height:3.176ex;" alt="{\displaystyle {\ce {_7^{13}N}}}"></span> que té 7 protons i 6 neutrons. El seu estudi ha permès l'obtenció de dades sobre la magnitud de les forces nuclears i de repulsió electroestàtica que tenen lloc a escala nuclear.<sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Càrrega_i_massa"><span id="C.C3.A0rrega_i_massa"></span>Càrrega i massa</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Nucli_at%C3%B2mic&action=edit&section=4" title="Modifica la secció: Càrrega i massa"><span>modifica</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>El protó té una <a href="/wiki/C%C3%A0rrega_el%C3%A8ctrica" title="Càrrega elèctrica">càrrega elèctrica</a> positiva, igual a la <a href="/wiki/C%C3%A0rrega_el%C3%A8ctrica_elemental" title="Càrrega elèctrica elemental">càrrega elemental</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle e=+1,602\cdot 10^{-19}\;\mathrm {C} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>e</mi> <mo>=</mo> <mo>+</mo> <mn>1</mn> <mo>,</mo> <mn>602</mn> <mo>⋅</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>19</mn> </mrow> </msup> <mspace width="thickmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">C</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle e=+1,602\cdot 10^{-19}\;\mathrm {C} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0bd026af8794ba5010be2a932371e36068b650bc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:21.156ex; height:3.009ex;" alt="{\displaystyle e=+1,602\cdot 10^{-19}\;\mathrm {C} }"></span>, mentre que el neutró és elèctricament neutre, per la qual cosa la càrrega nuclear es correspon a la suma de les càrregues de tots els protons, o bé al producte del nombre atòmic <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Z}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Z</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Z}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1cc6b75e09a8aa3f04d8584b11db534f88fb56bd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.68ex; height:2.176ex;" alt="{\displaystyle Z}"></span> per la càrrega elemental <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle e}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mi>e</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle e}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ddd2bd906fc55b6e7cef6d70b52a9fbd1df8f8b2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.083ex; height:1.676ex;" alt="{\textstyle e}"></span>: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle Q=Z\cdot e}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mi>Q</mi> <mo>=</mo> <mi>Z</mi> <mo>⋅</mo> <mi>e</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle Q=Z\cdot e}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a2b89e066a8cadf19428e9a22807e7528909f72a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:9.38ex; height:2.509ex;" alt="{\textstyle Q=Z\cdot e}"></span>.<sup id="cite_ref-:3_23-0" class="reference"><a href="#cite_note-:3-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup> Els nuclis naturals tenen valors des de <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Q=1,602\cdot 10^{-19}\;C}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Q</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>602</mn> <mo>⋅</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>19</mn> </mrow> </msup> <mspace width="thickmathspace" /> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Q=1,602\cdot 10^{-19}\;C}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/24b723b90751a599c55a5e5162f862c1c6b28df3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:20.191ex; height:3.009ex;" alt="{\displaystyle Q=1,602\cdot 10^{-19}\;C}"></span> de l'hidrogen <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\ce {_1^{1}H}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mmultiscripts> <mtext>H</mtext> <none /> <none /> <mprescripts /> <mn>1</mn> <mn>1</mn> </mmultiscripts> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\ce {_1^{1}H}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fd3231f020e15ae88903b9410752cc70c58960a0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:2.739ex; height:3.176ex;" alt="{\displaystyle {\ce {_1^{1}H}}}"></span> fins a <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle Q=147,4\cdot 10^{-19}\;\mathrm {C} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mi>Q</mi> <mo>=</mo> <mn>147</mn> <mo>,</mo> <mn>4</mn> <mo>⋅</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>19</mn> </mrow> </msup> <mspace width="thickmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">C</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle Q=147,4\cdot 10^{-19}\;\mathrm {C} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5292de08424c8fed9dbe136f49eabc035644c15d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:20.103ex; height:3.009ex;" alt="{\textstyle Q=147,4\cdot 10^{-19}\;\mathrm {C} }"></span> de l'<a href="/wiki/Urani" title="Urani">urani</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\ce {_{92}^{238}U}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mmultiscripts> <mtext>U</mtext> <none /> <none /> <mprescripts /> <mn>92</mn> <mn>238</mn> </mmultiscripts> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\ce {_{92}^{238}U}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5981ecdaadc1105b9812c7cc627e26a00c769255" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.383ex; height:3.176ex;" alt="{\displaystyle {\ce {_{92}^{238}U}}}"></span>. </p><p>Les masses del protó i del neutró són, respectivament, 1,672 62·10<sup>–27</sup> kg i 1,674 93·10<sup>–27</sup> kg. Sembla que la massa del nucli hauria de ser la suma de les masses dels protons i dels neutrons, però pels nuclis estables sempre és inferior. Aquesta diferència, anomenada <a href="/wiki/Defecte_m%C3%A0ssic" title="Defecte màssic">defecte de massa</a>, és una quantitat que s'ha perdut en formar-se el nucli i que es correspon a l'<a href="/wiki/Energia_de_lligadura" title="Energia de lligadura">energia de lligadura</a> dels nucleons. Es pot calcular aquesta energia a partir de l'equació d'Einstein que relaciona la massa amb l'energia: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle E=m\cdot c^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mi>E</mi> <mo>=</mo> <mi>m</mi> <mo>⋅</mo> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle E=m\cdot c^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/433bb44ddfee385eb550712c7ecb5fae86015327" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:10.655ex; height:2.509ex;" alt="{\textstyle E=m\cdot c^{2}}"></span>.<sup id="cite_ref-:3_23-1" class="reference"><a href="#cite_note-:3-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup> La massa d'un nucli, en unitats relatives de massa atòmica, sempre és propera al valor del nombre màssic, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a118c6ad00742b3f5dccd2f0e74b5e369df6fd31" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\textstyle A}"></span>, i van de 1,0078 per a l'hidrogen <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\ce {_1^{1}H}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mmultiscripts> <mtext>H</mtext> <none /> <none /> <mprescripts /> <mn>1</mn> <mn>1</mn> </mmultiscripts> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\ce {_1^{1}H}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fd3231f020e15ae88903b9410752cc70c58960a0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:2.739ex; height:3.176ex;" alt="{\displaystyle {\ce {_1^{1}H}}}"></span> a 238,05 de l'urani <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle _{92}^{238}U}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <msubsup> <mi></mi> <mrow class="MJX-TeXAtom-ORD"> <mn>92</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>238</mn> </mrow> </msubsup> <mi>U</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle _{92}^{238}U}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/816d7db80f3ab3cb47e01272ae7f16572c3db48e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.481ex; height:3.176ex;" alt="{\textstyle _{92}^{238}U}"></span>. </p> <div class="mw-heading mw-heading3"><h3 id="Dimensions_i_forma">Dimensions i forma</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Nucli_at%C3%B2mic&action=edit&section=5" title="Modifica la secció: Dimensions i forma"><span>modifica</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Fitxer:Helium_atom_QMuniv.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/20/Helium_atom_QMuniv.svg/220px-Helium_atom_QMuniv.svg.png" decoding="async" width="220" height="191" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/20/Helium_atom_QMuniv.svg/330px-Helium_atom_QMuniv.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/20/Helium_atom_QMuniv.svg/440px-Helium_atom_QMuniv.svg.png 2x" data-file-width="570" data-file-height="495" /></a><figcaption>Comparació de les dimensions del nucli i l'àtom d'heli</figcaption></figure> <p>Ernest Rutherford arribà a la conclusió de que la càrrega positiva d'un àtom està concentrada en una petita esfera, que anomenà nucli, i el qual radi no és superior a aproximadament 10<sup>–14</sup> m, o 10 <a href="/wiki/Femt%C3%B2metre" class="mw-redirect" title="Femtòmetre">fm</a>.<sup id="cite_ref-:0_3-1" class="reference"><a href="#cite_note-:0-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> Per una altra banda, a principis dels anys 1920 se sabia que el nucli d'un àtom contenia <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Z}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Z</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Z}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1cc6b75e09a8aa3f04d8584b11db534f88fb56bd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.68ex; height:2.176ex;" alt="{\displaystyle Z}"></span> protons i tenia una massa equivalent a la d'<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a118c6ad00742b3f5dccd2f0e74b5e369df6fd31" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\textstyle A}"></span> protons, complint-se que per a àtoms lleugers (amb <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Z\leq 20}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Z</mi> <mo>≤</mo> <mn>20</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Z\leq 20}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9c0530fad5c12d8805df6fa93f82f83930a6cf31" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:7.104ex; height:2.343ex;" alt="{\displaystyle Z\leq 20}"></span>) és <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A\approx 2Z}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>≈</mo> <mn>2</mn> <mi>Z</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A\approx 2Z}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fcf162b9fe6e10815336610c6caceca927dbc20d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.684ex; height:2.176ex;" alt="{\displaystyle A\approx 2Z}"></span> i per a àtoms més pesants <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A>2Z}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>></mo> <mn>2</mn> <mi>Z</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A>2Z}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a9e67d4a80042048463cc5e99b7d1cdf55c3818f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.684ex; height:2.176ex;" alt="{\displaystyle A>2Z}"></span>. Per això, el 1920, Rutherford proposà l'existència dels neutrons,<sup id="cite_ref-BakLec_24-0" class="reference"><a href="#cite_note-BakLec-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> els quals foren descoberts el 1932 per Chadwick.<sup id="cite_ref-Chad1932_25-0" class="reference"><a href="#cite_note-Chad1932-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-26" class="reference"><a href="#cite_note-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup> </p><p>Els experiments realitzats demostren que el nucli és aproximadament esfèric amb un radi mitjà <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle r}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mi>r</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle r}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f2dfb06630b52c9e18fcc0a4688da10774206729" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.049ex; height:1.676ex;" alt="{\textstyle r}"></span> que ve donat per la fórmula: </p><p> <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r=r_{0}\cdot A^{1/3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> <mo>=</mo> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>⋅</mo> <msup> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>3</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r=r_{0}\cdot A^{1/3}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ccfcadd48f72dbd5cd2e5e3efcae5432e71b64c7" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:12.37ex; height:3.176ex;" alt="{\displaystyle r=r_{0}\cdot A^{1/3}}"></span></p><figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Fitxer:Ellipsoid_3d.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/95/Ellipsoid_3d.jpg/220px-Ellipsoid_3d.jpg" decoding="async" width="220" height="176" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/9/95/Ellipsoid_3d.jpg 1.5x" data-file-width="300" data-file-height="240" /></a><figcaption>El·lipsoide</figcaption></figure><p>on <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a118c6ad00742b3f5dccd2f0e74b5e369df6fd31" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\textstyle A}"></span> és el <a href="/wiki/Nombre_m%C3%A0ssic" title="Nombre màssic">nombre màssic</a> i <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle r_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle r_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8cb8596b2e48f44abb1799c0b14e65289005923e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.103ex; height:2.009ex;" alt="{\textstyle r_{0}}"></span> és un valor que decreix de <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle r_{0}=1,3\cdot 10^{-15}\,\mathrm {m} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>3</mn> <mo>⋅</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>15</mn> </mrow> </msup> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle r_{0}=1,3\cdot 10^{-15}\,\mathrm {m} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/52190966579afff6800b0ca49a2a445e1cf36c75" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:18.042ex; height:3.009ex;" alt="{\textstyle r_{0}=1,3\cdot 10^{-15}\,\mathrm {m} }"></span> pels nuclis més lleugers, fins a <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle r_{0}=1,2\cdot 10^{-15}\,\mathrm {m} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>⋅</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>15</mn> </mrow> </msup> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle r_{0}=1,2\cdot 10^{-15}\,\mathrm {m} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fa1be4241357d681e0f967faf954c3db1df2d23c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:18.042ex; height:3.009ex;" alt="{\textstyle r_{0}=1,2\cdot 10^{-15}\,\mathrm {m} }"></span> per a la resta de nuclis.<sup id="cite_ref-:3_23-2" class="reference"><a href="#cite_note-:3-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup> Com que el volum d'una esfera és proporcional al cub del seu radi, resulta d'aquesta equació anterior que el volum d'un nucli atòmic és proporcional al nombre màssic <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a118c6ad00742b3f5dccd2f0e74b5e369df6fd31" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\textstyle A}"></span>, i val: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V_{nucli}={\tfrac {4}{3}}\cdot \pi \cdot r_{0}^{3}\cdot A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mi>u</mi> <mi>c</mi> <mi>l</mi> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn>4</mn> <mn>3</mn> </mfrac> </mstyle> </mrow> <mo>⋅</mo> <mi>π</mi> <mo>⋅</mo> <msubsup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msubsup> <mo>⋅</mo> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V_{nucli}={\tfrac {4}{3}}\cdot \pi \cdot r_{0}^{3}\cdot A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/09223fbeecfdfdb1af53e6a903d264fd110158c6" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:20.255ex; height:3.676ex;" alt="{\displaystyle V_{nucli}={\tfrac {4}{3}}\cdot \pi \cdot r_{0}^{3}\cdot A}"></span> </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Fitxer:Angular_momentum_circle.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e4/Angular_momentum_circle.svg/220px-Angular_momentum_circle.svg.png" decoding="async" width="220" height="186" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e4/Angular_momentum_circle.svg/330px-Angular_momentum_circle.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e4/Angular_momentum_circle.svg/440px-Angular_momentum_circle.svg.png 2x" data-file-width="512" data-file-height="433" /></a><figcaption>Moment angular <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\vec {L}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>L</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {L}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a0c139fc28d6ca3873993892f44e7331e5ff18fd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.583ex; height:2.843ex;" alt="{\displaystyle {\vec {L}}}"></span> d'una partícula de massa <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0a07d98bb302f3856cbabc47b2b9016692e3f7bc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.04ex; height:1.676ex;" alt="{\displaystyle m}"></span> que descriu una trajectòria circular de radi <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\vec {r}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>r</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {r}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6aec3c9ce13b53e9e24c98e7cce4212627884c91" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.223ex; height:2.343ex;" alt="{\displaystyle {\vec {r}}}"></span> amb velocitat <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\vec {v}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>v</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {v}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/85820588abd7333ef4d0c56539cb31c20e730753" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.175ex; height:2.343ex;" alt="{\displaystyle {\vec {v}}}"></span></figcaption></figure> <p>La <a href="/wiki/Densitat" title="Densitat">densitat</a> es pot deduir de forma aproximada suposant que protons i neutrons tenen la mateixa massa i negligint el petit defecte de massa, donant 2,3·10<sup>17</sup> kg/m³, una densitat molt elevada, unes 2,3·10¹⁴ vegades superior a la de l'aigua líquida.<sup id="cite_ref-:2_19-2" class="reference"><a href="#cite_note-:2-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> </p><p>El <a href="/w/index.php?title=Moment_quadrupolar_el%C3%A8ctric&action=edit&redlink=1" class="new" title="Moment quadrupolar elèctric (encara no existeix)">moment quadrupolar elèctric</a>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle Q}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mi>Q</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle Q}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/131bb2da649dd6c113517c5ae8c26370654ee8fa" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.838ex; height:2.509ex;" alt="{\textstyle Q}"></span>, d'una distribució de càrrega elèctrica respecte d'una direcció donada indica la deformació respecte d'una esfera perfecta d'un nucli. Els nuclis que tenen <a href="/wiki/Moment_angular" title="Moment angular">moment angular</a> 0 o 1/2 tenen <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle Q=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mi>Q</mi> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle Q=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/54266c8291b52684bb40157d1ea9b4d20ae70a76" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.099ex; height:2.509ex;" alt="{\textstyle Q=0}"></span>, la qual cosa significa que són esfèrics. Tanmateix hi ha nuclis que tenen moments quadrupolars elèctrics molt diferents de zero, com són <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle Q(_{71}^{176}\mathrm {Lu} )=8\cdot 10^{-28}\;\mathrm {m} ^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mi>Q</mi> <msubsup> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>71</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>176</mn> </mrow> </msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">L</mi> <mi mathvariant="normal">u</mi> </mrow> <mo stretchy="false">)</mo> <mo>=</mo> <mn>8</mn> <mo>⋅</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>28</mn> </mrow> </msup> <mspace width="thickmathspace" /> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle Q(_{71}^{176}\mathrm {Lu} )=8\cdot 10^{-28}\;\mathrm {m} ^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2611b0dff3f60ec67ff39622fafdabcedc349cd5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:24.146ex; height:3.343ex;" alt="{\textstyle Q(_{71}^{176}\mathrm {Lu} )=8\cdot 10^{-28}\;\mathrm {m} ^{2}}"></span> o <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle Q(_{94}^{241}\mathrm {Pu} )=5,6\cdot 10^{-28}\;\mathrm {m} ^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mi>Q</mi> <msubsup> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>94</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>241</mn> </mrow> </msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">P</mi> <mi mathvariant="normal">u</mi> </mrow> <mo stretchy="false">)</mo> <mo>=</mo> <mn>5</mn> <mo>,</mo> <mn>6</mn> <mo>⋅</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>28</mn> </mrow> </msup> <mspace width="thickmathspace" /> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle Q(_{94}^{241}\mathrm {Pu} )=5,6\cdot 10^{-28}\;\mathrm {m} ^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9ecc8fb66c6be0f1036bdea7f83325047c96d2e9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:26.473ex; height:3.343ex;" alt="{\textstyle Q(_{94}^{241}\mathrm {Pu} )=5,6\cdot 10^{-28}\;\mathrm {m} ^{2}}"></span>. Aquests valors indiquen que presenten importants deformacions i tenen forma d'<a href="/wiki/El%C2%B7lipsoide" title="El·lipsoide">el·lipsoides</a> més que d'esferes.<sup id="cite_ref-:5_18-1" class="reference"><a href="#cite_note-:5-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Moment_angular">Moment angular</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Nucli_at%C3%B2mic&action=edit&section=6" title="Modifica la secció: Moment angular"><span>modifica</span></a><span class="mw-editsection-bracket">]</span></span></div><p> El <a href="/wiki/Moment_angular" title="Moment angular">moment angular</a>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\vec {L}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>L</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {L}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a0c139fc28d6ca3873993892f44e7331e5ff18fd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.583ex; height:2.843ex;" alt="{\displaystyle {\vec {L}}}"></span>, és una <a href="/wiki/Vector_(f%C3%ADsica)" title="Vector (física)">magnitud vectorial</a> pròpia dels cossos en moviment curvilini que s'obté com a <a href="/wiki/Producte_vectorial" title="Producte vectorial">producte vectorial</a> del <a href="/wiki/Radi_(geometria)" title="Radi (geometria)">radi</a> de la trajectòria, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\vec {r}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>r</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {r}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6aec3c9ce13b53e9e24c98e7cce4212627884c91" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.223ex; height:2.343ex;" alt="{\displaystyle {\vec {r}}}"></span>, pel <a href="/wiki/Quantitat_de_moviment" title="Quantitat de moviment">moment lineal</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle {\vec {p}}=m{\vec {v}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>p</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>=</mo> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>v</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle {\vec {p}}=m{\vec {v}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/57a4751f1169a793bc004c9e9c5402d1e8b614da" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:7.729ex; height:2.676ex;" alt="{\textstyle {\vec {p}}=m{\vec {v}}}"></span>. En els nuclis atòmics hi ha nucleons que giren sobre ells mateixos i es mouen dintre del nucli, per la qual cosa també el nucli té un moment angular, anomenat <a href="/wiki/Esp%C3%ADn" title="Espín">espín</a> nuclear. L'espín nuclear se simbolitza per <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle {\vec {J}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>J</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle {\vec {J}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87ed15912a79f75ab0845add3f1664f6ef999ded" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.788ex; height:2.843ex;" alt="{\textstyle {\vec {J}}}"></span>, i s'obté combinant de forma apropiada els moments angulars orbitals (rotació dels nucleons al voltant del centre del nucli) i els espins dels nucleons (rotació sobre ells mateixos).<sup id="cite_ref-:5_18-2" class="reference"><a href="#cite_note-:5-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> </p><figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Fitxer:LoopCurrentMagneticMoment.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/84/LoopCurrentMagneticMoment.png/220px-LoopCurrentMagneticMoment.png" decoding="async" width="220" height="165" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/84/LoopCurrentMagneticMoment.png/330px-LoopCurrentMagneticMoment.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/84/LoopCurrentMagneticMoment.png/440px-LoopCurrentMagneticMoment.png 2x" data-file-width="1200" data-file-height="900" /></a><figcaption>Moment magnètic</figcaption></figure><p>L'espín nuclear s'identifica amb un número quàntic <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle J}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mi>J</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle J}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e61cd093040143a8df673790bc7295dea6c191b7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.471ex; height:2.176ex;" alt="{\textstyle J}"></span>, de manera que el mòdul de dit espín val <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle |{\vec {J}}|=\hbar {\sqrt {J(J+1)}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>J</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mo>=</mo> <mi class="MJX-variant">ℏ</mi> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mi>J</mi> <mo stretchy="false">(</mo> <mi>J</mi> <mo>+</mo> <mn>1</mn> <mo stretchy="false">)</mo> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle |{\vec {J}}|=\hbar {\sqrt {J(J+1)}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/584f4f94537a222d1aca8697d328748bcacd4a44" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:18.566ex; height:3.509ex;" alt="{\textstyle |{\vec {J}}|=\hbar {\sqrt {J(J+1)}}}"></span>. Segons el <a href="/wiki/Principi_d%27incertesa_de_Heisenberg" title="Principi d'incertesa de Heisenberg">principi d'incertesa de Heisenberg</a> l'espín nuclear és inobservable, però sí ho és la seva component segons una direcció determinada, que ve donada per <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle m_{J}\hbar }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>J</mi> </mrow> </msub> <mi class="MJX-variant">ℏ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle m_{J}\hbar }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/52ea62eafa244f335222536dcb5bbecc5833ebf0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.62ex; height:2.509ex;" alt="{\textstyle m_{J}\hbar }"></span>, on <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle m_{J}=\pm J,\pm (J-1),...,\pm {\tfrac {1}{2}}\;\mathrm {o} \;0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>J</mi> </mrow> </msub> <mo>=</mo> <mo>±</mo> <mi>J</mi> <mo>,</mo> <mo>±</mo> <mo stretchy="false">(</mo> <mi>J</mi> <mo>−</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <mo>±</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mstyle> </mrow> <mspace width="thickmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">o</mi> </mrow> <mspace width="thickmathspace" /> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle m_{J}=\pm J,\pm (J-1),...,\pm {\tfrac {1}{2}}\;\mathrm {o} \;0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5e3724897ff1edbd788ceb8bce41947ccbeeb6e7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:32.068ex; height:3.509ex;" alt="{\textstyle m_{J}=\pm J,\pm (J-1),...,\pm {\tfrac {1}{2}}\;\mathrm {o} \;0}"></span>, segons sigui <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle J}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mi>J</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle J}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e61cd093040143a8df673790bc7295dea6c191b7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.471ex; height:2.176ex;" alt="{\textstyle J}"></span> semienter o enter. D'aquí es pot deduir que hi ha <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle 2J+1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mn>2</mn> <mi>J</mi> <mo>+</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle 2J+1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c74584003187adfc68eef6cb16ddf7cf595947b8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:6.637ex; height:2.343ex;" alt="{\textstyle 2J+1}"></span> orientacions possibles de l'espín nuclear. Els espins dels nucleons, com el de l'electró estan quantitzats i valen 1/2. Per aquest fet els nuclis amb nombre màssic imparell tenen espins nuclears fraccionaris. Per exemple: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle J(_{26}^{57}\mathrm {Fe} )={\frac {1}{2}},\;J(_{27}^{57}\mathrm {Co} )={\frac {7}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mi>J</mi> <msubsup> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>26</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>57</mn> </mrow> </msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">F</mi> <mi mathvariant="normal">e</mi> </mrow> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mo>,</mo> <mspace width="thickmathspace" /> <mi>J</mi> <msubsup> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>27</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>57</mn> </mrow> </msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">C</mi> <mi mathvariant="normal">o</mi> </mrow> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>7</mn> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle J(_{26}^{57}\mathrm {Fe} )={\frac {1}{2}},\;J(_{27}^{57}\mathrm {Co} )={\frac {7}{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f4698e9cf9ecd12da85afda4c2f1e1469023a6af" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:26.897ex; height:3.676ex;" alt="{\textstyle J(_{26}^{57}\mathrm {Fe} )={\frac {1}{2}},\;J(_{27}^{57}\mathrm {Co} )={\frac {7}{2}}}"></span>. Per contra els nuclis amb nombre màssic parell el tenen zero o un nombre sencer fins a 7. Exemples: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle J(_{26}^{56}\mathrm {Fe} )=0,\;J(_{27}^{56}\mathrm {Co} )=4}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mi>J</mi> <msubsup> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>26</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>56</mn> </mrow> </msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">F</mi> <mi mathvariant="normal">e</mi> </mrow> <mo stretchy="false">)</mo> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mspace width="thickmathspace" /> <mi>J</mi> <msubsup> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>27</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>56</mn> </mrow> </msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">C</mi> <mi mathvariant="normal">o</mi> </mrow> <mo stretchy="false">)</mo> <mo>=</mo> <mn>4</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle J(_{26}^{56}\mathrm {Fe} )=0,\;J(_{27}^{56}\mathrm {Co} )=4}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d444e59b7a1d82d08363a8a3739fba9bd3501d81" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:25.905ex; height:3.176ex;" alt="{\textstyle J(_{26}^{56}\mathrm {Fe} )=0,\;J(_{27}^{56}\mathrm {Co} )=4}"></span>.<sup id="cite_ref-:5_18-3" class="reference"><a href="#cite_note-:5-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> </p><div class="mw-heading mw-heading3"><h3 id="Moment_magnètic_nuclear"><span id="Moment_magn.C3.A8tic_nuclear"></span>Moment magnètic nuclear</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Nucli_at%C3%B2mic&action=edit&section=7" title="Modifica la secció: Moment magnètic nuclear"><span>modifica</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Fitxer:Pr%C3%A4zession2.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/93/Pr%C3%A4zession2.png/220px-Pr%C3%A4zession2.png" decoding="async" width="220" height="369" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/93/Pr%C3%A4zession2.png/330px-Pr%C3%A4zession2.png 1.5x, //upload.wikimedia.org/wikipedia/commons/9/93/Pr%C3%A4zession2.png 2x" data-file-width="392" data-file-height="658" /></a><figcaption>Precessió de Larmor</figcaption></figure> <p>Associat amb l'espín nuclear hi ha el <a href="/wiki/Moment_magn%C3%A8tic_nuclear" title="Moment magnètic nuclear">moment magnètic nuclear</a>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle {\vec {\mu }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>μ</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle {\vec {\mu }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/44bc91b14acb5f613bd31d2880ee2c771716dab9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.402ex; height:2.843ex;" alt="{\textstyle {\vec {\mu }}}"></span>, que produeix <a href="/wiki/Camp_magn%C3%A8tic" title="Camp magnètic">interaccions magnètiques</a> amb el medi que envolta el nucli. El <a href="/wiki/Moment_magn%C3%A8tic" title="Moment magnètic">moment magnètic</a> és una <a href="/wiki/Vector_(f%C3%ADsica)" title="Vector (física)">magnitud vectorial</a> que resulta del producte de la <a href="/wiki/Corrent_el%C3%A8ctric" title="Corrent elèctric">intensitat de corrent elèctric</a>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle I}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mi>I</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle I}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/abfab7b61b17518d4537eba5d4491e0ecec5773c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.172ex; height:2.176ex;" alt="{\textstyle I}"></span>, que recorre una corba tancada per la superfície d'aquesta, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\vec {\mu }}=I{\vec {S}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>μ</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>=</mo> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>S</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {\mu }}=I{\vec {S}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/18f83ad33ce4c8c70b7fd594d5970df0c8f4963f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.21ex; height:3.509ex;" alt="{\displaystyle {\vec {\mu }}=I{\vec {S}}}"></span>. Equival a un petit <a href="/wiki/Imant" title="Imant">imant</a> on el sentit de <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle {\vec {\mu }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>μ</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle {\vec {\mu }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/44bc91b14acb5f613bd31d2880ee2c771716dab9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.402ex; height:2.843ex;" alt="{\textstyle {\vec {\mu }}}"></span> va del sud al nord magnètic. Els nuclis atòmics contenen protons carregats positivament, els quals es mouen i originen petits moments magnètics. Els moments magnètics als nuclis estan quantitzats i s'expressen en termes de l'espín nuclear, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle {\vec {J}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>J</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle {\vec {J}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87ed15912a79f75ab0845add3f1664f6ef999ded" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.788ex; height:2.843ex;" alt="{\textstyle {\vec {J}}}"></span>, amb l'expressió: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\vec {\mu }}=g{\frac {e}{2m_{p}}}{\vec {J}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>μ</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>=</mo> <mi>g</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>e</mi> <mrow> <mn>2</mn> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>J</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {\mu }}=g{\frac {e}{2m_{p}}}{\vec {J}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e6b78e0b7e8604853bba3bb1071dde9185533966" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:12.503ex; height:5.343ex;" alt="{\displaystyle {\vec {\mu }}=g{\frac {e}{2m_{p}}}{\vec {J}}}"></span> </p><p>on: </p> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle g}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mi>g</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle g}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/38dc9ad184fe5486391b456b9e68767ff77f3719" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.116ex; height:2.009ex;" alt="{\textstyle g}"></span> s'anomena factor giromagnètic i presenta valors diferents pel protó i el neutró</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle e}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mi>e</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle e}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ddd2bd906fc55b6e7cef6d70b52a9fbd1df8f8b2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.083ex; height:1.676ex;" alt="{\textstyle e}"></span> és la càrrega elemental</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle m_{p}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle m_{p}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/86e1191c0dbde0cbad323b59baeadc7dcbf97aee" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.1ex; height:2.343ex;" alt="{\textstyle m_{p}}"></span>és la massa del protó</li></ul> <p>Si se situa un moment magnètic dintre d'un <a href="/wiki/Camp_magn%C3%A8tic" title="Camp magnètic">camp magnètic</a>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\vec {B}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>B</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {B}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/83ae7d80cab55b606de217162280b2279142bbb4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.843ex;" alt="{\displaystyle {\vec {B}}}"></span> es produeix un <a href="/wiki/Moment_de_for%C3%A7a" class="mw-redirect" title="Moment de força">moment de força</a>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\vec {\Gamma }}={\vec {\mu }}\times {\vec {B}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="normal">Γ</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>μ</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>×</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>B</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {\Gamma }}={\vec {\mu }}\times {\vec {B}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/17e56585f3a0d42ba549dfa85b3a8f70b8871f7a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.557ex; height:3.343ex;" alt="{\displaystyle {\vec {\Gamma }}={\vec {\mu }}\times {\vec {B}}}"></span>, que tendeix a alinear el moment magnètic amb la direcció i sentit del camp magnètic. Tanmateix no es produeix el mateix efecte a nivell atòmic. Els nuclis, que tenen un moment magnètic, no canvien d'orientació, però inicien un moviment de precessió al voltant de la direcció del camp magnètic, anomenada <a href="/wiki/Precessi%C3%B3_de_Larmor" title="Precessió de Larmor">precessió de Larmor</a>. La freqüència de gir s'anomena freqüència de Larmor. La component del moment magnètic sobre la direcció del camp magnètic pot estar orientada en el mateix sentit del camp o en sentit contrari, la qual cosa representa dos estats de diferent energia. Es pot passar del d'energia més baixa, el primer, al d'energia més alta, el segon, mitjançant absorció de <a href="/wiki/Radiaci%C3%B3_electromagn%C3%A8tica" title="Radiació electromagnètica">radiació electromagnètica</a>, en concret <a href="/wiki/Ones_de_r%C3%A0dio" class="mw-redirect" title="Ones de ràdio">ones de radio</a>. Si el nucli passa a l'estat més energètic a continuació es relaxa i torna al menys energètic emeten radiació electromagnètica. Aquest és el principi de la <a href="/wiki/Resson%C3%A0ncia_magn%C3%A8tica_nuclear" title="Ressonància magnètica nuclear">ressonància magnètica nuclear</a> o RMN, emprada com a tècnica d'anàlisi estructural de substàncies i en l'estudi dels teixits blans de l'organisme. </p> <div class="mw-heading mw-heading2"><h2 id="Energia_de_lligadura">Energia de lligadura</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Nucli_at%C3%B2mic&action=edit&section=8" title="Modifica la secció: Energia de lligadura"><span>modifica</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>La formació d'un nucli atòmic és un procés exoenergètic, es desprèn energia, la qual cosa significa que el nucli té menys energia que els nucleons aïllats, per tant més estable. L'energia que es desprèn en formar-se un nucli atòmic a partir dels nucleons lliures, <a href="/wiki/Fusi%C3%B3_nuclear" title="Fusió nuclear">fusió nuclear</a>, s'anomena energia de lligadura. Si es volen separar els nucleons d'un nucli caldrà aportar aquesta quantitat d'energia. Aquesta energia prové de la massa que es perd en el procés de formació del nucli, ja que la massa dels nuclis estables és lleugerament inferior a la suma de les masses del nucleons. L'equivalència entre massa i energia ve donada per l'equació d'Einstein: </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/w/index.php?title=Fitxer:Energie_de_liaison_par_nucl%C3%A9on.svg&lang=ca" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a8/Energie_de_liaison_par_nucl%C3%A9on.svg/langca-220px-Energie_de_liaison_par_nucl%C3%A9on.svg.png" decoding="async" width="220" height="166" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a8/Energie_de_liaison_par_nucl%C3%A9on.svg/langca-330px-Energie_de_liaison_par_nucl%C3%A9on.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a8/Energie_de_liaison_par_nucl%C3%A9on.svg/langca-440px-Energie_de_liaison_par_nucl%C3%A9on.svg.png 2x" data-file-width="957" data-file-height="720" /></a><figcaption>Corba d'energia per nucleó en funció del número màssic A</figcaption></figure> <p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{b}=\delta m\cdot c^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> <mo>=</mo> <mi>δ</mi> <mi>m</mi> <mo>⋅</mo> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{b}=\delta m\cdot c^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/396e5d284c3a5570f6fa07a27a871d180354e56d" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:12.581ex; height:3.009ex;" alt="{\displaystyle E_{b}=\delta m\cdot c^{2}}"></span>on: </p> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{b}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{b}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/69d2e3ccd9bce33b1ae1562c2e7e831eb8f55bf3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.653ex; height:2.509ex;" alt="{\displaystyle E_{b}}"></span> és l'energia de lligadura, en joules.</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \delta m}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>δ</mi> <mi>m</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \delta m}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1c693010617212364f6f6e632d8ccf8fda5d7567" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.089ex; height:2.343ex;" alt="{\displaystyle \delta m}"></span> és el defecte de massa, la massa que s'ha perdut en kilograms.</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle c}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>c</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/86a67b81c2de995bd608d5b2df50cd8cd7d92455" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.007ex; height:1.676ex;" alt="{\displaystyle c}"></span> és la velocitat de la llum en el buit, en m/s.</li></ul> <p>Per poder comparar les energies de lligadura de diferents nuclis és convenient emprar l'energia de lligadura per nucleó, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{b}/A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{b}/A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2aee5dc9eea6ec0d1ad10e7aa8bea8627ec387ad" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.558ex; height:2.843ex;" alt="{\displaystyle E_{b}/A}"></span>, (energia de lligadura dividida pel <a href="/wiki/Nombre_m%C3%A0ssic" title="Nombre màssic">nombre màssic</a>). Aquest valor augmenta a mesura que s'augmenta el nombre de nucleons fins a un màxim que correspon al <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle _{26}^{62}Ni}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi></mi> <mrow class="MJX-TeXAtom-ORD"> <mn>26</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>62</mn> </mrow> </msubsup> <mi>N</mi> <mi>i</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle _{26}^{62}Ni}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aa5498cf27a73c164beb69cb76be779a86a18ef2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.742ex; height:3.176ex;" alt="{\displaystyle _{26}^{62}Ni}"></span>, a partir d'ell l'energia de lligadura per nucleó disminueix, és a dir, els nucleons estan cada vegada menys lligats en el nucli. Excepte pels primers elements químics, fins al <a href="/wiki/Bor" title="Bor">bor</a>, l'energia de lligadura per nucleó oscil·la al voltant dels 8 <a href="/wiki/MeV" class="mw-redirect" title="MeV">MeV</a>.<sup id="cite_ref-:2_19-3" class="reference"><a href="#cite_note-:2-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> </p><p>L'estudi detallat de les energies de lligadura del nuclis demostra que els nuclis presenten més estabilitat quan el seu nombre de protons o neutrons té un dels següents valors, anomenats <a href="/wiki/Nucleid_m%C3%A0gic" class="mw-redirect" title="Nucleid màgic">nombres màgics</a> per <a href="/wiki/Eugene_Paul_Wigner" title="Eugene Paul Wigner">Eugene P. Wigner</a>: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle 2,8,20,28,50,82,126}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mn>2</mn> <mo>,</mo> <mn>8</mn> <mo>,</mo> <mn>20</mn> <mo>,</mo> <mn>28</mn> <mo>,</mo> <mn>50</mn> <mo>,</mo> <mn>82</mn> <mo>,</mo> <mn>126</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle 2,8,20,28,50,82,126}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/77af2f52edd01b04f22a92ec159414e102856cf9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:21.316ex; height:2.509ex;" alt="{\textstyle 2,8,20,28,50,82,126}"></span>. Si tant el nombre de protons com el de neutrons coincideix amb aquests valors hom parla de nuclis "doblement màgics". És el cas dels nuclis: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\ce {_2^4He,\, _8^{16}O,\, _{20}^{40}Ca, \, _{20}^{48}Ca \; i \; _{82}^{208}Pb}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mmultiscripts> <mtext>He</mtext> <none /> <none /> <mprescripts /> <mn>2</mn> <mn>4</mn> </mmultiscripts> <mo>,</mo> <mspace width="thinmathspace" /> <mmultiscripts> <mtext>O</mtext> <none /> <none /> <mprescripts /> <mn>8</mn> <mn>16</mn> </mmultiscripts> <mo>,</mo> <mspace width="thinmathspace" /> <mmultiscripts> <mtext>Ca</mtext> <none /> <none /> <mprescripts /> <mn>20</mn> <mn>40</mn> </mmultiscripts> <mo>,</mo> <mspace width="thinmathspace" /> <mmultiscripts> <mtext>Ca</mtext> <none /> <none /> <mprescripts /> <mn>20</mn> <mn>48</mn> </mmultiscripts> <mspace width="thickmathspace" /> <mtext>i</mtext> <mspace width="thickmathspace" /> <mmultiscripts> <mtext>Pb</mtext> <none /> <none /> <mprescripts /> <mn>82</mn> <mn>208</mn> </mmultiscripts> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\ce {_2^4He,\, _8^{16}O,\, _{20}^{40}Ca, \, _{20}^{48}Ca \; i \; _{82}^{208}Pb}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/039a38d160c452305436bb496ae6c3eb41eca5d2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:28.431ex; height:3.176ex;" alt="{\displaystyle {\ce {_2^4He,\, _8^{16}O,\, _{20}^{40}Ca, \, _{20}^{48}Ca \; i \; _{82}^{208}Pb}}}"></span>. Els <a href="/wiki/Is%C3%B2top" title="Isòtop">isòtops</a> amb nombres màgics presenten major abundància a la naturalesa, els isòtops estables que finalitzen les sèries radioactives tenen nombres de protons o neutrons màgics, l'energia d'enllaç del darrer neutró és màxima quan es tracta del neutró que completa el nombre màgic i mínima pel següent, els <a href="/w/index.php?title=Moment_el%C3%A8ctric_quadrupolar&action=edit&redlink=1" class="new" title="Moment elèctric quadrupolar (encara no existeix)">moments elèctrics quadrupolars</a> són pràcticament zero per aquest nuclis amb nombres màgics.<sup id="cite_ref-:2_19-4" class="reference"><a href="#cite_note-:2-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Estabilitat_nuclear">Estabilitat nuclear</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Nucli_at%C3%B2mic&action=edit&section=9" title="Modifica la secció: Estabilitat nuclear"><span>modifica</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Fitxer:Corba_d%27estabilitat_nuclear.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8d/Corba_d%27estabilitat_nuclear.png/220px-Corba_d%27estabilitat_nuclear.png" decoding="async" width="220" height="156" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8d/Corba_d%27estabilitat_nuclear.png/330px-Corba_d%27estabilitat_nuclear.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8d/Corba_d%27estabilitat_nuclear.png/440px-Corba_d%27estabilitat_nuclear.png 2x" data-file-width="945" data-file-height="669" /></a><figcaption>Corba d'estabilitat nuclear</figcaption></figure> <p>Els neutrons lliures són inestables i es desintegren en un protó, un electró i un <a href="/wiki/Antineutr%C3%AD_electr%C3%B2nic" class="mw-redirect" title="Antineutrí electrònic">anti-neutrí electrònic</a>. La seva <a href="/wiki/Vida_mitjana" title="Vida mitjana">vida mitjana</a> lliures és d'uns 15 min. Tanmateix dins el nucli són estables.<sup id="cite_ref-:3_23-3" class="reference"><a href="#cite_note-:3-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup> </p><p>Els protons tant lliures com dins el nucli són estables. Interaccionen mitjançant forces de repulsió electroestàtiques, <a href="/wiki/Llei_de_Coulomb" title="Llei de Coulomb">força de Coulomb</a>, que tendeixen a separar-los i tots els nucleons s'atreuen per mitjà de la <a href="/wiki/For%C3%A7a_nuclear_forta" title="Força nuclear forta">força nuclear forta</a>, que té les següents característiques: </p> <ul><li>És una força d'atracció i és la més intensa de la naturalesa.</li> <li>És una força de curta distància que s'anul·la quan la separació entre nucleons és superior a varis <a href="/wiki/Femt%C3%B2metre" class="mw-redirect" title="Femtòmetre">femtòmetres</a>.</li> <li>La seva magnitud depèn de les orientacions relatives dels <a href="/wiki/Esp%C3%ADn" title="Espín">espins</a> dels nucleons.</li> <li>No depèn de la <a href="/wiki/C%C3%A0rrega_el%C3%A8ctrica" title="Càrrega elèctrica">càrrega elèctrica</a>.</li></ul> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Fitxer:Alpha_Decay.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/79/Alpha_Decay.svg/220px-Alpha_Decay.svg.png" decoding="async" width="220" height="150" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/79/Alpha_Decay.svg/330px-Alpha_Decay.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/79/Alpha_Decay.svg/440px-Alpha_Decay.svg.png 2x" data-file-width="250" data-file-height="170" /></a><figcaption>Desintegració d'un nucli per emissió d'una partícula α</figcaption></figure> <p>L'existència d'aquesta força permet que pugui haver-hi aproximadament 270 nuclis estables. Els lleugers contenen un nombre igual de protons i neutrons. A mesura que augmenta el nombre de protons també ho fa la repulsió de Coulomb i es necessiten més neutrons per compensar-la, ja que aquest només experimenten força d'atracció forta. Tanmateix a partir de Z = 83 no és possible que els neutrons compensin la repulsió electroestàtica i no existeixen nuclis estables amb més de 83 protons, que correspon a l'<a href="/wiki/Element_qu%C3%ADmic" title="Element químic">element químic</a> <a href="/wiki/Bismut" title="Bismut">bismut</a>, Bi. Els nuclis inestables presents a la naturalesa aconsegueixen estabilitat desintegrant-se mitjançant l'emissió de partícules α (<a href="/wiki/Radioactivitat_alfa" class="mw-redirect" title="Radioactivitat alfa">radiació α</a>), de partícules β<sup>–</sup> (<a href="/wiki/Radiaci%C3%B3_%CE%B2" class="mw-redirect" title="Radiació β">radiació β<sup>–</sup></a>), de raigs γ (<a href="/wiki/Radiaci%C3%B3_gamma" title="Radiació gamma">radiació γ</a>) o per mitjà de la <a href="/wiki/Fissi%C3%B3_nuclear" title="Fissió nuclear">fissió nuclear</a>. Nuclis obtinguts artificialment i inestables també poden aconseguir guanyar estabilitat seguint processos com els naturals o de tipus diferent, com la emissió de radiació β<sup>+</sup> i l'emissió de neutrons.<sup id="cite_ref-:2_19-5" class="reference"><a href="#cite_note-:2-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Models_nuclears">Models nuclears</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Nucli_at%C3%B2mic&action=edit&section=10" title="Modifica la secció: Models nuclears"><span>modifica</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Model_de_gota_de_líquid"><span id="Model_de_gota_de_l.C3.ADquid"></span>Model de gota de líquid</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Nucli_at%C3%B2mic&action=edit&section=11" title="Modifica la secció: Model de gota de líquid"><span>modifica</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Fitxer:Bundesarchiv_B_422_Bild-0174,_Carl_Friedrich_v._Weizs%C3%A4cker.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/46/Bundesarchiv_B_422_Bild-0174%2C_Carl_Friedrich_v._Weizs%C3%A4cker.jpg/220px-Bundesarchiv_B_422_Bild-0174%2C_Carl_Friedrich_v._Weizs%C3%A4cker.jpg" decoding="async" width="220" height="145" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/46/Bundesarchiv_B_422_Bild-0174%2C_Carl_Friedrich_v._Weizs%C3%A4cker.jpg/330px-Bundesarchiv_B_422_Bild-0174%2C_Carl_Friedrich_v._Weizs%C3%A4cker.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/46/Bundesarchiv_B_422_Bild-0174%2C_Carl_Friedrich_v._Weizs%C3%A4cker.jpg/440px-Bundesarchiv_B_422_Bild-0174%2C_Carl_Friedrich_v._Weizs%C3%A4cker.jpg 2x" data-file-width="800" data-file-height="529" /></a><figcaption>Carl Friedrich von Weizsäcker, 1983</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Fitxer:Thomas_Bresson_-_Stalactite-5_(by).JPG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/78/Thomas_Bresson_-_Stalactite-5_%28by%29.JPG/220px-Thomas_Bresson_-_Stalactite-5_%28by%29.JPG" decoding="async" width="220" height="331" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/78/Thomas_Bresson_-_Stalactite-5_%28by%29.JPG/330px-Thomas_Bresson_-_Stalactite-5_%28by%29.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/78/Thomas_Bresson_-_Stalactite-5_%28by%29.JPG/440px-Thomas_Bresson_-_Stalactite-5_%28by%29.JPG 2x" data-file-width="2848" data-file-height="4288" /></a><figcaption>Gotes d'aigua caient d'una estalactita. Si la gota mitjana representa un nucli de <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle _{1}^{1}H}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi></mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msubsup> <mi>H</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle _{1}^{1}H}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b4f7906ad835d2e8706a967f54b70399660d8bc3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.118ex; height:3.176ex;" alt="{\displaystyle _{1}^{1}H}"></span>, la gota major equival a un nucli de <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle _{20}^{43}Ca}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi></mi> <mrow class="MJX-TeXAtom-ORD"> <mn>20</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>43</mn> </mrow> </msubsup> <mi>C</mi> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle _{20}^{43}Ca}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e5b117bd4338c8addf6fd4a4d2d7f80fb41faa67" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.872ex; height:3.176ex;" alt="{\displaystyle _{20}^{43}Ca}"></span>.</figcaption></figure> <p>En el model de la gota de líquid se suposen les següents semblances entre una gota de líquid i un nucli: </p> <ul><li>Les forces nuclears són semblants a la <a href="/wiki/Tensi%C3%B3_superficial" title="Tensió superficial">tensió superficial</a> d'un líquid.</li> <li>Els nucleons es comporten com les <a href="/wiki/Mol%C3%A8cula" title="Molècula">molècules</a> d'un líquid.</li> <li>La densitat del nucli és independent del nombre màssic <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a118c6ad00742b3f5dccd2f0e74b5e369df6fd31" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\textstyle A}"></span>, així com la densitat d'un líquid és independent del seu volum.</li> <li>L'energia de lligadura per nucleó, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {E_{b}}{A}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> <mi>A</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {E_{b}}{A}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0b427e26d511624cc3a9e624136fafe50c053509" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:3.489ex; height:5.343ex;" alt="{\displaystyle {\frac {E_{b}}{A}}}"></span>, és semblant a l'energia de vaporització d'un líquid.</li> <li>La <a href="/wiki/Radioactivitat" title="Radioactivitat">desintegració</a> d'un nucli és un fenomen com l'<a href="/wiki/Evaporaci%C3%B3" title="Evaporació">evaporació</a> de molècules de líquid a la seva superfície.</li> <li>L'absorció de partícules en bombardejar amb elles un nucli és un procés similar a la <a href="/wiki/Condensaci%C3%B3" title="Condensació">condensació</a> sobre les gotes.</li> <li>L'energia d'un nucli es correspon amb les vibracions tèrmiques de les molècules de líquid.<sup id="cite_ref-:1_27-0" class="reference"><a href="#cite_note-:1-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup></li></ul> <p>També s'assumeix que: </p> <ul><li>El nucli és incompressible i té un radi que val <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle r=r_{0}\cdot A^{1/3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mi>r</mi> <mo>=</mo> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>⋅</mo> <msup> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>3</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle r=r_{0}\cdot A^{1/3}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a79901d66cff997660472746c0c09bf42cdea2da" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:12.37ex; height:3.009ex;" alt="{\textstyle r=r_{0}\cdot A^{1/3}}"></span>, on <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle r_{0}=1,2\;\mathrm {fm} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mspace width="thickmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">f</mi> <mi mathvariant="normal">m</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle r_{0}=1,2\;\mathrm {fm} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b29e10271b7abab385e95f5ed189a76bbbf0e9a9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:12.006ex; height:2.509ex;" alt="{\textstyle r_{0}=1,2\;\mathrm {fm} }"></span>.</li> <li>Les forces nuclears són idèntiques per a cada nucleó.</li> <li>La força nuclear per si sola manté el nucli.</li> <li>En una situació d'equilibri el nucli roman esfèric sota les forces d'atracció nuclears.<sup id="cite_ref-:1_27-1" class="reference"><a href="#cite_note-:1-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup></li></ul> <p>Cinc efectes tenen influència en l'energia de lligadura del nucli en el model proposat per <a href="/w/index.php?title=Carl_F._von_Weizs%C3%A4cker&action=edit&redlink=1" class="new" title="Carl F. von Weizsäcker (encara no existeix)">Carl F. von Weizsäcker</a>: </p> <ul><li><figure typeof="mw:File/Thumb"><a href="/wiki/Fitxer:Liquid_drop_model.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5b/Liquid_drop_model.svg/440px-Liquid_drop_model.svg.png" decoding="async" width="440" height="114" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5b/Liquid_drop_model.svg/660px-Liquid_drop_model.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5b/Liquid_drop_model.svg/880px-Liquid_drop_model.svg.png 2x" data-file-width="765" data-file-height="198" /></a><figcaption></figcaption></figure><b>Efecte del volum</b>: A partir d'<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle A>50}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mi>A</mi> <mo>></mo> <mn>50</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle A>50}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ddb1e29b43d8ba5e814879d93bdd7a6da0b18804" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.166ex; height:2.176ex;" alt="{\textstyle A>50}"></span> l'energia de lligadura per nucleó, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {E_{b}}{A}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> <mi>A</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {E_{b}}{A}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0b427e26d511624cc3a9e624136fafe50c053509" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:3.489ex; height:5.343ex;" alt="{\displaystyle {\frac {E_{b}}{A}}}"></span>, és pràcticament constant, la qual cosa indica que la força nuclear sobre un nucleó es deu exclusivament a uns pocs nucleons veïns i no pas a tots els del nucli. Així l'energia de lligadura associada amb la força nuclear per a cada nucleó és la mateixa per a tots els nuclis: la corresponent a la interacció d'uns poc nucleons veïns, per tant és proporcional a <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a118c6ad00742b3f5dccd2f0e74b5e369df6fd31" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\textstyle A}"></span> o al volum nuclear. Aquesta contribució se simbolitza per <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a_{V}A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>V</mi> </mrow> </msub> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a_{V}A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7e0c66fde8e2881cdf5051b853c749cf23b9d552" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.469ex; height:2.509ex;" alt="{\displaystyle a_{V}A}"></span>, essent <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a_{V}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>V</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a_{V}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ad98daca4fcd22c3603e5644c79848a82fdeaace" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.726ex; height:2.009ex;" alt="{\displaystyle a_{V}}"></span>una constant experimental.</li> <li><b>Efecte de superfície</b>: El nucleons de la superfície tenen menys veïns que els de l'interior, per això s'ha de reduir la seva contribució en una quantitat proporcional a l'àrea de la superfície, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 4\pi r^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>4</mn> <mi>π</mi> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 4\pi r^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b81fcce302776a01dc66fc186a1ce0a616b4d772" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.597ex; height:2.676ex;" alt="{\displaystyle 4\pi r^{2}}"></span>, i com que <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle r=r_{0}\cdot A^{1/3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mi>r</mi> <mo>=</mo> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>⋅</mo> <msup> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>3</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle r=r_{0}\cdot A^{1/3}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a79901d66cff997660472746c0c09bf42cdea2da" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:12.37ex; height:3.009ex;" alt="{\textstyle r=r_{0}\cdot A^{1/3}}"></span>, aquest terme es pot expressar com <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a_{S}A^{2/3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>S</mi> </mrow> </msub> <msup> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>3</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a_{S}A^{2/3}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d3d98742d26679af819d11598f3b2072018a1d4c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.963ex; height:3.176ex;" alt="{\displaystyle a_{S}A^{2/3}}"></span>, essent <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a_{S}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>S</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a_{S}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1533c9504259f50f11a4219785e42068ecf11610" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.522ex; height:2.009ex;" alt="{\displaystyle a_{S}}"></span>una constant experimental.</li> <li><b>Efecte de la repulsió de Coulomb</b>: Cada protó repel·leix a la resta de protons. L'energia potencial elèctrica entre dos protons val <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle K_{e}e^{2}/r}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> </mrow> </msub> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>r</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle K_{e}e^{2}/r}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8f1a1d6ce607e0f98be3265b2236f7e93dace50e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.32ex; height:3.176ex;" alt="{\displaystyle K_{e}e^{2}/r}"></span>, on <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle K_{e}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle K_{e}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/136b9bab3d46ddbd91092ecf3c171aa887e5cfd8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.971ex; height:2.509ex;" alt="{\displaystyle K_{e}}"></span> és la constant de Coulomb. L'energia potencial total serrà proporcional al nombre de parelles de protons, això és <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Z(Z-1)/2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Z</mi> <mo stretchy="false">(</mo> <mi>Z</mi> <mo>−</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Z(Z-1)/2}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6d827426bbfab33f73f587c641c2b3d79a4161d2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.498ex; height:2.843ex;" alt="{\displaystyle Z(Z-1)/2}"></span> i inversament proporcional al radi del nucli, proporcional a <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A^{1/3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>3</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A^{1/3}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/547b5cdbf33559fa4c08d2e80c681fc4eb5bcd73" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.441ex; height:2.843ex;" alt="{\displaystyle A^{1/3}}"></span>. En conjunt l'energia de Coulomb es pot expressar com <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a_{C}Z(Z-1)/A^{1/3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> <mi>Z</mi> <mo stretchy="false">(</mo> <mi>Z</mi> <mo>−</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msup> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>3</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a_{C}Z(Z-1)/A^{1/3}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c55e8c5971026d93b783e2d8278dd453109fec2e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:17.488ex; height:3.343ex;" alt="{\displaystyle a_{C}Z(Z-1)/A^{1/3}}"></span>, amb <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a_{C}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a_{C}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4e2caa2bf7f599288ca8d79628ab6fc0f265cde5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.711ex; height:2.009ex;" alt="{\displaystyle a_{C}}"></span> com a constant a determinar.</li> <li><b>Efecte de simetria</b>: Els nuclis estables tenen aproximadament el mateix nombre de protons i neutrons. Per això qualsevulla asimetria en la distribució dels nucleons reduirà l'energia de lligadura i farà que el nucli sigui menys estable. Aquest terme es pot expressar com <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a_{A}(N-Z)^{2}/A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>N</mi> <mo>−</mo> <mi>Z</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a_{A}(N-Z)^{2}/A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6b8d409311e9d772cfedc2bd30671a4be2f5edf0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:15.048ex; height:3.176ex;" alt="{\displaystyle a_{A}(N-Z)^{2}/A}"></span>, amb <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a_{A}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a_{A}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/187a574b62266ad7c236172391d575b150e69bc9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.695ex; height:2.009ex;" alt="{\displaystyle a_{A}}"></span> constant a ajustar.<sup id="cite_ref-:2_19-6" class="reference"><a href="#cite_note-:2-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup></li> <li><b>Efecte de la paritat</b>. És un terme relacionat amb el <a href="/wiki/Principi_d%27exclusi%C3%B3_de_Pauli" title="Principi d'exclusió de Pauli">principi d'exclusió de Pauli</a> i simbolitzat per <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \delta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>δ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \delta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c5321cfa797202b3e1f8620663ff43c4660ea03a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.049ex; height:2.343ex;" alt="{\displaystyle \delta }"></span>. Val 0 pels nuclis amb número màssic, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a118c6ad00742b3f5dccd2f0e74b5e369df6fd31" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\textstyle A}"></span>, imparell. Si <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a118c6ad00742b3f5dccd2f0e74b5e369df6fd31" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\textstyle A}"></span> és parell i també ho són el nombre de protons i el de neutrons, val <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle a_{P}A^{-3/4}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>P</mi> </mrow> </msub> <msup> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>3</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>4</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle a_{P}A^{-3/4}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/04c7d454dcc4d7764f09f7c9b5ab730dde709bd8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.416ex; height:3.009ex;" alt="{\textstyle a_{P}A^{-3/4}}"></span> i contribueix positivament a l'energia de lligadura. Mentre que si tant el nombre de protons com el de neutrons és imparell, essent <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a118c6ad00742b3f5dccd2f0e74b5e369df6fd31" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\textstyle A}"></span> parell, val <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle -a_{P}A^{-3/4}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mo>−</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>P</mi> </mrow> </msub> <msup> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>3</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>4</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle -a_{P}A^{-3/4}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3c850a0cfd64acaef77c7cae2361e88d67eb23ae" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.224ex; height:3.009ex;" alt="{\textstyle -a_{P}A^{-3/4}}"></span>, amb la qual cosa contribueix negativament a l'energia de lligadura.<sup id="cite_ref-:5_18-4" class="reference"><a href="#cite_note-:5-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup></li></ul> <p>L'equació final resulta l'anomenada <a href="/wiki/F%C3%B3rmula_de_Weizs%C3%A4cker" title="Fórmula de Weizsäcker">fórmula semiempírica de Weizsäcker</a>: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{b}=a_{V}A-a_{S}A^{2/3}-a_{C}{\frac {Z(Z-1)}{A^{1/3}}}-a_{A}{\frac {(N-Z)^{2}}{A}}+\delta (A,Z)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>V</mi> </mrow> </msub> <mi>A</mi> <mo>−</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>S</mi> </mrow> </msub> <msup> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>3</mn> </mrow> </msup> <mo>−</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>Z</mi> <mo stretchy="false">(</mo> <mi>Z</mi> <mo>−</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> <msup> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>3</mn> </mrow> </msup> </mfrac> </mrow> <mo>−</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo stretchy="false">(</mo> <mi>N</mi> <mo>−</mo> <mi>Z</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mi>A</mi> </mfrac> </mrow> <mo>+</mo> <mi>δ</mi> <mo stretchy="false">(</mo> <mi>A</mi> <mo>,</mo> <mi>Z</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{b}=a_{V}A-a_{S}A^{2/3}-a_{C}{\frac {Z(Z-1)}{A^{1/3}}}-a_{A}{\frac {(N-Z)^{2}}{A}}+\delta (A,Z)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bbda2d113d80d911a41904d2a29f6989e84f94cd" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:61.56ex; height:6.176ex;" alt="{\displaystyle E_{b}=a_{V}A-a_{S}A^{2/3}-a_{C}{\frac {Z(Z-1)}{A^{1/3}}}-a_{A}{\frac {(N-Z)^{2}}{A}}+\delta (A,Z)}"></span> </p> <div class="mw-heading mw-heading3"><h3 id="Model_de_capes">Model de capes</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Nucli_at%C3%B2mic&action=edit&section=12" title="Modifica la secció: Model de capes"><span>modifica</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Fitxer:Shells.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Shells.png/220px-Shells.png" decoding="async" width="220" height="346" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Shells.png/330px-Shells.png 1.5x, //upload.wikimedia.org/wikipedia/commons/e/e5/Shells.png 2x" data-file-width="429" data-file-height="675" /></a><figcaption>Nivells d'energia del nucli atòmic</figcaption></figure> <p>L'existència dels números màgics indiquen l'existència de nivells d'energia en el nucli, els quals es completen amb els números màgics. El primer model de capes del nucli fou proposat el 1932 pel físic rus <a href="/wiki/Dmitri_Ivanenko" title="Dmitri Ivanenko">Dmitri Ivanenko</a> i desenvolupat el 1949 per <a href="/wiki/Eugene_Paul_Wigner" title="Eugene Paul Wigner">Eugene Paul Wigner</a>, <a href="/wiki/Maria_G%C3%B6ppert-Mayer" title="Maria Göppert-Mayer">Maria Göppert-Mayer</a> i <a href="/wiki/Johannes_Hans_Jensen" title="Johannes Hans Jensen">J. Hans D. Jensen</a>, de forma independent. </p><p>El model de capes és en part anàleg al <a href="/wiki/Model_at%C3%B2mic_de_Bohr" title="Model atòmic de Bohr">model atòmic</a> de capes atòmiques que descriu la distribució dels electrons en un àtom, en la qual les capes plenes donen lloc a una major estabilitat. El cas del nucli és més complex per dues raons: la primera és l'existència de dos tipus de partícules, protons i neutrons, que obeeixen per separat el <a href="/wiki/Principi_d%27exclusi%C3%B3_de_Pauli" title="Principi d'exclusió de Pauli">principi d'exclusió de Pauli</a> i que donen lloc a una sèrie doble de capes; i la segona és que, contràriament als àtoms, on el nucli crea un camp central en el qual es mouen els electrons, en el nucli atòmic no existeix quelcom diferent als nucleons que crei aquest camp i són els mateixos nucleons que cooperen i produeixen un camp central mitjà en el si del qual es mouen els nucleons.<sup id="cite_ref-28" class="reference"><a href="#cite_note-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:5_18-5" class="reference"><a href="#cite_note-:5-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> Aquest camp central mitjà té la següent forma (<a href="/wiki/Potencial_de_Woods%E2%80%93Saxon" title="Potencial de Woods–Saxon">potencial de Woods-Saxon</a>): </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V={\frac {V_{0}}{1+e^{\frac {r-R}{a}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mrow> <mn>1</mn> <mo>+</mo> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>r</mi> <mo>−</mo> <mi>R</mi> </mrow> <mi>a</mi> </mfrac> </mrow> </msup> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V={\frac {V_{0}}{1+e^{\frac {r-R}{a}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/414fdd6a53eeb111c44321132c84565d63a80509" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.338ex; width:14.529ex; height:6.843ex;" alt="{\displaystyle V={\frac {V_{0}}{1+e^{\frac {r-R}{a}}}}}"></span>on: </p> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a=0,5\cdot 10^{-15}\;\mathrm {m} =0,5\;\mathrm {fm} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mn>5</mn> <mo>⋅</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>15</mn> </mrow> </msup> <mspace width="thickmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> </mrow> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mn>5</mn> <mspace width="thickmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">f</mi> <mi mathvariant="normal">m</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a=0,5\cdot 10^{-15}\;\mathrm {m} =0,5\;\mathrm {fm} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f2dacd554f3c8ae298f84a73a434b55dca7c9411" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:27.33ex; height:3.009ex;" alt="{\displaystyle a=0,5\cdot 10^{-15}\;\mathrm {m} =0,5\;\mathrm {fm} }"></span></li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R=1,33\cdot 10^{-15}\cdot A^{1/3}\;\mathrm {m} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>33</mn> <mo>⋅</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>15</mn> </mrow> </msup> <mo>⋅</mo> <msup> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>3</mn> </mrow> </msup> <mspace width="thickmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R=1,33\cdot 10^{-15}\cdot A^{1/3}\;\mathrm {m} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e8700b8a46ca5452f6431e05d1324ba9a6a4469e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:25.244ex; height:3.176ex;" alt="{\displaystyle R=1,33\cdot 10^{-15}\cdot A^{1/3}\;\mathrm {m} }"></span>, essent <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a118c6ad00742b3f5dccd2f0e74b5e369df6fd31" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\textstyle A}"></span> el nombre màssic.</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V_{0}=50-60\,MeV}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>=</mo> <mn>50</mn> <mo>−</mo> <mn>60</mn> <mspace width="thinmathspace" /> <mi>M</mi> <mi>e</mi> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V_{0}=50-60\,MeV}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7965df937b58faaadcd0156ae0c292945b407ff8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:18.698ex; height:2.509ex;" alt="{\displaystyle V_{0}=50-60\,MeV}"></span><sup id="cite_ref-29" class="reference"><a href="#cite_note-29"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup></li></ul> <p>A partir de càlculs quàntics emprant l'<a href="/wiki/Equaci%C3%B3_de_Schr%C3%B6dinger" title="Equació de Schrödinger">equació de Schrödinger</a> s'obtenen una sèrie de nivells energètics que venen caracteritzats per un nombre quàntic principal <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle N}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mi>N</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle N}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d21d55fc102ec49600d3d5522a59ae4561acc22" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.064ex; height:2.176ex;" alt="{\textstyle N}"></span>, que pot prendre els valors <i><b>0, 1, 2, 3, 4, 5,</b></i>... Cadascun d'aquest estats té una sèrie de subnivells o estats possibles caracteritzats pel número quàntic <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle l}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mi>l</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle l}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a272396a098706dc62adc4bb977a8cc79739021f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.693ex; height:2.176ex;" alt="{\textstyle l}"></span> relacionat amb el <a href="/wiki/Moment_angular" title="Moment angular">moment angular</a> orbital que, igual que a l'àtom, els seus valors se simbolitzen per <i><b>s, p, d, f, g</b></i>,... L'estat se simbolitza amb la parella <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle nl}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mi>n</mi> <mi>l</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle nl}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/474d3d29be14fcd91c885ffe4e0bb769950e4782" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.088ex; height:2.176ex;" alt="{\textstyle nl}"></span>, on <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span> fa referència al nombre de vegades que ha aparegut <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle l}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mi>l</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle l}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a272396a098706dc62adc4bb977a8cc79739021f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.693ex; height:2.176ex;" alt="{\textstyle l}"></span>. Així el primer nivell <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle N=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>N</mi> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bac661e6a8863869cdec476a5f7923be96ee0e97" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.325ex; height:2.176ex;" alt="{\displaystyle N=0}"></span> té l'estat <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 1s}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> <mi>s</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1s}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/59a6d7a59b12f82f6b269b57b2d9eca77c99d4cb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.253ex; height:2.176ex;" alt="{\displaystyle 1s}"></span> (el primer cop que apareix <i><b>s</b></i>); el segon nivell <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle N=1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>N</mi> <mo>=</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N=1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/85982022b9eb1f295b44de55023687a490db0a39" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.325ex; height:2.176ex;" alt="{\displaystyle N=1}"></span> té l'estat <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 1p}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> <mi>p</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1p}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c7edc30a0f7773171477837533638de5d9fcd810" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.332ex; height:2.509ex;" alt="{\displaystyle 1p}"></span> (el primer cop que apareix <i><b>p</b></i>); el següent nivell és el <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle N=2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>N</mi> <mo>=</mo> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N=2}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/405d64b14536deffc3465f1e81b1b7fe9358ad2a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.325ex; height:2.176ex;" alt="{\displaystyle N=2}"></span>, el qual té dos estats, els <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 1d}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> <mi>d</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1d}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5e661496b218af966df7b73f1aff5b60ce713c57" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.378ex; height:2.176ex;" alt="{\displaystyle 1d}"></span> i <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 2s}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>2</mn> <mi>s</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 2s}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bac399360184e2035dbaea694e969a385cb16a6c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.253ex; height:2.176ex;" alt="{\displaystyle 2s}"></span>; el següent nivell és el <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle N=3}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>N</mi> <mo>=</mo> <mn>3</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N=3}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b4ab951d779fcdeea3ec188bb5c73518c46b19de" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.325ex; height:2.176ex;" alt="{\displaystyle N=3}"></span>, el qual té dos estats, els <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 1f}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> <mi>f</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1f}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0fc665d92bd53990c39f71c2f039be1293a83219" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.441ex; height:2.509ex;" alt="{\displaystyle 1f}"></span> i <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 2p}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>2</mn> <mi>p</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 2p}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ff0d3e38652941fc7a2844611f6c7fa8a23104a7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.332ex; height:2.509ex;" alt="{\displaystyle 2p}"></span>; etc.<sup id="cite_ref-:4_30-0" class="reference"><a href="#cite_note-:4-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup> </p><p>A cada nivell hi ha un màxim de protons o neutrons que s'hi poden situar, que ve determinat pel <a href="/wiki/Principi_d%27exclusi%C3%B3_de_Pauli" title="Principi d'exclusió de Pauli">principi d'exclusió de Pauli</a>. A cada nivell aquest màxim ve donat per la fórmula <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Z_{N}=(N+1)(N+2)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>Z</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>N</mi> </mrow> </msub> <mo>=</mo> <mo stretchy="false">(</mo> <mi>N</mi> <mo>+</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>N</mi> <mo>+</mo> <mn>2</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Z_{N}=(N+1)(N+2)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/999943ee8022d8a794a857b3991963c3dc081a1a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:22.129ex; height:2.843ex;" alt="{\displaystyle Z_{N}=(N+1)(N+2)}"></span>. Pel nivell <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle N=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>N</mi> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bac661e6a8863869cdec476a5f7923be96ee0e97" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.325ex; height:2.176ex;" alt="{\displaystyle N=0}"></span> són <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Z_{N}=(0+1)(0+2)=2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>Z</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>N</mi> </mrow> </msub> <mo>=</mo> <mo stretchy="false">(</mo> <mn>0</mn> <mo>+</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mn>0</mn> <mo>+</mo> <mn>2</mn> <mo stretchy="false">)</mo> <mo>=</mo> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Z_{N}=(0+1)(0+2)=2}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/26fdd098cc790150b05c8241b403cb2eeb24ae57" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:24.588ex; height:2.843ex;" alt="{\displaystyle Z_{N}=(0+1)(0+2)=2}"></span>; pel nivell <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle N=1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>N</mi> <mo>=</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N=1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/85982022b9eb1f295b44de55023687a490db0a39" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.325ex; height:2.176ex;" alt="{\displaystyle N=1}"></span> són <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Z_{N}=(1+1)(1+2)=6}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>Z</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>N</mi> </mrow> </msub> <mo>=</mo> <mo stretchy="false">(</mo> <mn>1</mn> <mo>+</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mn>1</mn> <mo>+</mo> <mn>2</mn> <mo stretchy="false">)</mo> <mo>=</mo> <mn>6</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Z_{N}=(1+1)(1+2)=6}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b115d9831dcab1be943e0b49ac40f1efb4117705" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:24.588ex; height:2.843ex;" alt="{\displaystyle Z_{N}=(1+1)(1+2)=6}"></span>; pel nivell <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle N=2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>N</mi> <mo>=</mo> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N=2}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/405d64b14536deffc3465f1e81b1b7fe9358ad2a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.325ex; height:2.176ex;" alt="{\displaystyle N=2}"></span> són <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Z_{N}=(2+1)(2+2)=12}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>Z</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>N</mi> </mrow> </msub> <mo>=</mo> <mo stretchy="false">(</mo> <mn>2</mn> <mo>+</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mn>2</mn> <mo>+</mo> <mn>2</mn> <mo stretchy="false">)</mo> <mo>=</mo> <mn>12</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Z_{N}=(2+1)(2+2)=12}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/be0441d46d01a656e52a747d4d7e5a5b9c90faaa" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:25.75ex; height:2.843ex;" alt="{\displaystyle Z_{N}=(2+1)(2+2)=12}"></span>; etc. El nombre total de nucleons és la suma dels diferents valors de tots els nivells ocupats. Així si només hi ha ocupat el nivell <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle N=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>N</mi> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bac661e6a8863869cdec476a5f7923be96ee0e97" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.325ex; height:2.176ex;" alt="{\displaystyle N=0}"></span>, el nombre total és <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 2}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/901fc910c19990d0dbaaefe4726ceb1a4e217a0f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.162ex; height:2.176ex;" alt="{\displaystyle 2}"></span>; si també hi ha ocupat el nivell <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle N=1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>N</mi> <mo>=</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N=1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/85982022b9eb1f295b44de55023687a490db0a39" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.325ex; height:2.176ex;" alt="{\displaystyle N=1}"></span> s'han de sumar els seus i els del <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle N=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>N</mi> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bac661e6a8863869cdec476a5f7923be96ee0e97" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.325ex; height:2.176ex;" alt="{\displaystyle N=0}"></span>, donant <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 2+6=8}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>2</mn> <mo>+</mo> <mn>6</mn> <mo>=</mo> <mn>8</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 2+6=8}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3519017042abe19952332262c682814116c44d03" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:9.426ex; height:2.343ex;" alt="{\displaystyle 2+6=8}"></span>. D'aquesta manera s'obtenen els valors dels números màgics detectats experimentalment.<sup id="cite_ref-:4_30-1" class="reference"><a href="#cite_note-:4-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Referències"><span id="Refer.C3.A8ncies"></span>Referències</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Nucli_at%C3%B2mic&action=edit&section=13" title="Modifica la secció: Referències"><span>modifica</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="reflist {{#if: | references-column-count references-column-count-{{{col}}}" style="list-style-type: decimal;"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-gec-1"><span class="mw-cite-backlink">↑ <sup><a href="#cite_ref-gec_1-0">1,0</a></sup> <sup><a href="#cite_ref-gec_1-1">1,1</a></sup></span> <span class="reference-text"><span class="citation" style="font-style:normal">«<a rel="nofollow" class="external text" href="http://www.enciclopedia.cat/gran-enciclopedia-catalana/0235261.xml">Nucli atòmic</a>». <i><a href="/wiki/Gran_Enciclop%C3%A8dia_Catalana" title="Gran Enciclopèdia Catalana">Gran Enciclopèdia Catalana</a></i>.  Barcelona:  <a href="/wiki/Grup_Enciclop%C3%A8dia_Catalana" class="mw-redirect" title="Grup Enciclopèdia Catalana">Grup Enciclopèdia Catalana</a>.</span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><a href="#cite_ref-2">↑</a></span> <span class="reference-text"><span class="citation" style="font-style:normal" id="CITEREFBecquerel2_març1896"><span style="font-variant: small-caps;">Becquerel</span>, A.H. «<a rel="nofollow" class="external text" href="http://www.bibnum.education.fr/physique/radioactivite/sur-les-radiations-invisibles-emises-par-les-corps-phosphorescents">Sur les radiations invisibles émises par les corps phosphorescents</a>». <i>Comptes Rendus de l'Académie des Sciences</i>, 2 març1896, pàg. 501-503.</span></span> </li> <li id="cite_note-:0-3"><span class="mw-cite-backlink">↑ <sup><a href="#cite_ref-:0_3-0">3,0</a></sup> <sup><a href="#cite_ref-:0_3-1">3,1</a></sup></span> <span class="reference-text"><span class="citation" style="font-style:normal" id="CITEREFRutherford1911"><span style="font-variant: small-caps;">Rutherford</span>, E. «<a rel="nofollow" class="external text" href="http://www.lawebdefisica.com/arts/structureatom.pdf">The Scattering of α and β Particles by Matter and the Structure of the Atom</a>». <i>Philosophical Magazine</i>, Series 6, 21, 5-1911, pàg. 669-688.</span></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><a href="#cite_ref-4">↑</a></span> <span class="reference-text"><span class="citation" style="font-style:normal" id="CITEREFGamow1929"><span style="font-variant: small-caps;">Gamow</span>, G «<a rel="nofollow" class="external text" href="http://rspa.royalsocietypublishing.org/content/123/792/373">Discussion on the Structure of Atomic Nuclei</a>». <i>Proc. Roy. Soc.</i>, A123, 1929, pàg. 386. <a href="/wiki/DOI" title="DOI">DOI</a>: <a rel="nofollow" class="external text" href="https://dx.doi.org/10.1098%2Frspa.1929.0074">10.1098/rspa.1929.0074</a>.</span></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><a href="#cite_ref-5">↑</a></span> <span class="reference-text"><span class="citation" style="font-style:normal" id="CITEREFGamow1930"><span style="font-variant: small-caps;">Gamow</span>, G «<a rel="nofollow" class="external text" href="http://rspa.royalsocietypublishing.org/content/126/803/632">Mass Defect Curve and Nuclear Constitution</a>». <i>Proc. Roy. Soc.</i>, A126, 03-03-1930, pàg. 632-644. <a href="/wiki/DOI" title="DOI">DOI</a>: <a rel="nofollow" class="external text" href="https://dx.doi.org/10.1098%2Frspa.1930.0032">10.1098/rspa.1930.0032</a>.</span></span> </li> <li id="cite_note-Chad19322-6"><span class="mw-cite-backlink"><a href="#cite_ref-Chad19322_6-0">↑</a></span> <span class="reference-text"><span class="citation" style="font-style:normal" id="CITEREFChadwick1932"><span style="font-variant: small-caps;">Chadwick</span>, James «Possible Existence of a Neutron». <i><a href="/wiki/Nature" title="Nature">Nature</a></i>, 129, 3252, 1932, pàg. 312. <a href="/wiki/Bibcode" title="Bibcode">Bibcode</a>: <a rel="nofollow" class="external text" href="http://adsabs.harvard.edu/abs/1932Natur.129Q.312C">1932Natur.129Q.312C</a>. <a href="/wiki/DOI" title="DOI">DOI</a>: <a rel="nofollow" class="external text" href="https://dx.doi.org/10.1038%2F129312a0">10.1038/129312a0</a>.</span></span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><a href="#cite_ref-7">↑</a></span> <span class="reference-text"><span class="citation" style="font-style:normal" id="CITEREFHeisenberg1932"><span style="font-variant: small-caps;">Heisenberg</span>, W. «Über den Bau der Atomkerne. I». <i><a href="/w/index.php?title=Z._Phys.&action=edit&redlink=1" class="new" title="Z. Phys. (encara no existeix)">Z. Phys.</a></i>, 77, 1932, pàg. 1–11. <a href="/wiki/Bibcode" title="Bibcode">Bibcode</a>: <a rel="nofollow" class="external text" href="http://adsabs.harvard.edu/abs/1932ZPhy...77....1H">1932ZPhy...77....1H</a>. <a href="/wiki/DOI" title="DOI">DOI</a>: <a rel="nofollow" class="external text" href="https://dx.doi.org/10.1007%2FBF01342433">10.1007/BF01342433</a>.</span></span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><a href="#cite_ref-8">↑</a></span> <span class="reference-text"><span class="citation" style="font-style:normal" id="CITEREFHeisenberg1932"><span style="font-variant: small-caps;">Heisenberg</span>, W. «Über den Bau der Atomkerne. II». <i>Z. Phys.</i>, 78, 3–4, 1932, pàg. 156–164. <a href="/wiki/Bibcode" title="Bibcode">Bibcode</a>: <a rel="nofollow" class="external text" href="http://adsabs.harvard.edu/abs/1932ZPhy...78..156H">1932ZPhy...78..156H</a>. <a href="/wiki/DOI" title="DOI">DOI</a>: <a rel="nofollow" class="external text" href="https://dx.doi.org/10.1007%2FBF01337585">10.1007/BF01337585</a>.</span></span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><a href="#cite_ref-9">↑</a></span> <span class="reference-text"><span class="citation" style="font-style:normal" id="CITEREFHeisenberg1933"><span style="font-variant: small-caps;">Heisenberg</span>, W. «Über den Bau der Atomkerne. III». <i>Z. Phys.</i>, 80, 9–10, 1933, pàg. 587–596. <a href="/wiki/Bibcode" title="Bibcode">Bibcode</a>: <a rel="nofollow" class="external text" href="http://adsabs.harvard.edu/abs/1933ZPhy...80..587H">1933ZPhy...80..587H</a>. <a href="/wiki/DOI" title="DOI">DOI</a>: <a rel="nofollow" class="external text" href="https://dx.doi.org/10.1007%2FBF01335696">10.1007/BF01335696</a>.</span></span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><a href="#cite_ref-10">↑</a></span> <span class="reference-text">Iwanenko, D.D., The neutron hypothesis, Nature <b>129</b> (1932) 798.</span> </li> <li id="cite_note-11"><span class="mw-cite-backlink"><a href="#cite_ref-11">↑</a></span> <span class="reference-text"><span class="citation" style="font-style:normal" id="CITEREFvon_Weizsäcker1935"><span style="font-variant: small-caps;">von Weizsäcker</span>, C.F. «Zur Theorie der Kernmassen». <i>Z. Phys.</i>, 96, 1935, pàg. 431.</span></span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><a href="#cite_ref-12">↑</a></span> <span class="reference-text"><span class="citation book" style="font-style:normal" id="CITEREFBrownHoltKuo2010"><span style="font-variant: small-caps;">Brown</span>, G.E.; <span style="font-variant: small-caps;">Holt</span>, J.W.; <span style="font-variant: small-caps;">Kuo</span>, T.T.S.. <a rel="nofollow" class="external text" href="https://books.google.cat/books?id=ihUzFPFNfSEC&dq=Z.+Phys.+96+431+1935+Weizs%C3%A4cker&hl=ca&source=gbs_navlinks_s"><i>The Nucleon-nucleon Interaction and the Nuclear Many-body Problem: Selected Papers of Gerald E. Brown and T.T.S. Kuo</i></a> (en anglès).  World Scientific, 2010, p. 2. <span style="font-size:90%; white-space:nowrap;"><a href="/wiki/Especial:Fonts_bibliogr%C3%A0fiques/9789814289283" title="Especial:Fonts bibliogràfiques/9789814289283">ISBN 9789814289283</a></span>.</span><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Nucleon-nucleon+Interaction+and+the+Nuclear+Many-body+Problem%3A+Selected+Papers+of+Gerald+E.+Brown+and+T.T.S.+Kuo&rft.aulast=Brown&rft.aufirst=G.E.&rft.date=2010&rft.pub=World+Scientific&rft.pages=2&rft.isbn=9789814289283&rft_id=https%3A%2F%2Fbooks.google.cat%2Fbooks%3Fid%3DihUzFPFNfSEC%26dq%3DZ.%2BPhys.%2B96%2B431%2B1935%2BWeizs%25C3%25A4cker%26hl%3Dca%26source%3Dgbs_navlinks_s"><span style="display: none;"> </span></span></span> </li> <li id="cite_note-13"><span class="mw-cite-backlink"><a href="#cite_ref-13">↑</a></span> <span class="reference-text"><span class="citation" style="font-style:normal" id="CITEREFBohrWeelher1939"><span style="font-variant: small-caps;">Bohr</span>, N.; <span style="font-variant: small-caps;">Weelher</span>, J.A. «<a rel="nofollow" class="external text" href="http://journals.aps.org/pr/abstract/10.1103/PhysRev.56.426">The Mechanism of Nuclear Fission</a>». <i>Phys. Rev.</i>, 56, 01-09-1939, pàg. 426.</span></span> </li> <li id="cite_note-14"><span class="mw-cite-backlink"><a href="#cite_ref-14">↑</a></span> <span class="reference-text"><span class="citation" style="font-style:normal" id="CITEREFGoeppert-Mayer1949"><span style="font-variant: small-caps;">Goeppert-Mayer</span>, Maria «On Closed Shells in Nuclei. II». <i><a href="/wiki/Physical_Review" title="Physical Review">Physical Review</a></i>, 75, 12, 6-1949, pàg. 1969–1970. <a href="/wiki/Bibcode" title="Bibcode">Bibcode</a>: <a rel="nofollow" class="external text" href="http://adsabs.harvard.edu/abs/1949PhRv...75.1969M">1949PhRv...75.1969M</a>. <a href="/wiki/DOI" title="DOI">DOI</a>: <a rel="nofollow" class="external text" href="https://dx.doi.org/10.1103%2FPhysRev.75.1969">10.1103/PhysRev.75.1969</a>.</span></span> </li> <li id="cite_note-15"><span class="mw-cite-backlink"><a href="#cite_ref-15">↑</a></span> <span class="reference-text"><span class="citation" style="font-style:normal" id="CITEREFGoeppert-Mayer1950"><span style="font-variant: small-caps;">Goeppert-Mayer</span>, Maria «Nuclear configurations in the spin-orbit coupling model. I. Empirical Evidence». <i><a href="/wiki/Physical_Review" title="Physical Review">Physical Review</a></i>, 78, 1, 4-1950, pàg. 16–21. <a href="/wiki/Bibcode" title="Bibcode">Bibcode</a>: <a rel="nofollow" class="external text" href="http://adsabs.harvard.edu/abs/1950PhRv...78...16M">1950PhRv...78...16M</a>. <a href="/wiki/DOI" title="DOI">DOI</a>: <a rel="nofollow" class="external text" href="https://dx.doi.org/10.1103%2FPhysRev.78.16">10.1103/PhysRev.78.16</a>.</span></span> </li> <li id="cite_note-16"><span class="mw-cite-backlink"><a href="#cite_ref-16">↑</a></span> <span class="reference-text"><span class="citation" style="font-style:normal" id="CITEREFGoeppert-Mayer1950"><span style="font-variant: small-caps;">Goeppert-Mayer</span>, Maria «Nuclear Configurations in the Spin-Orbit Coupling Model. II. Theoretical Considerations». <i><a href="/wiki/Physical_Review" title="Physical Review">Physical Review</a></i>, 78, 1, 4-1950, pàg. 22–23. <a href="/wiki/Bibcode" title="Bibcode">Bibcode</a>: <a rel="nofollow" class="external text" href="http://adsabs.harvard.edu/abs/1950PhRv...78...22M">1950PhRv...78...22M</a>. <a href="/wiki/DOI" title="DOI">DOI</a>: <a rel="nofollow" class="external text" href="https://dx.doi.org/10.1103%2FPhysRev.78.22">10.1103/PhysRev.78.22</a>.</span></span> </li> <li id="cite_note-17"><span class="mw-cite-backlink"><a href="#cite_ref-17">↑</a></span> <span class="reference-text"><span class="citation" style="font-style:normal" id="CITEREFHaxelJensenSuess1949"><a href="/w/index.php?title=Otto_Haxel&action=edit&redlink=1" class="new" title="Otto Haxel (encara no existeix)"><span style="font-variant: small-caps;">Haxel</span>, Otto</a>; <a href="/wiki/J._Hans_D._Jensen" class="mw-redirect" title="J. Hans D. Jensen"><span style="font-variant: small-caps;">Jensen</span>, J. Hans D.</a>; <a href="/w/index.php?title=Hans_Suess&action=edit&redlink=1" class="new" title="Hans Suess (encara no existeix)"><span style="font-variant: small-caps;">Suess</span>, Hans</a> «On the "Magic Numbers" in Nuclear Structure». <i><a href="/wiki/Physical_Review" title="Physical Review">Physical Review</a></i>, 75, 11, 6-1949, pàg. 1766–1766. <a href="/wiki/Bibcode" title="Bibcode">Bibcode</a>: <a rel="nofollow" class="external text" href="http://adsabs.harvard.edu/abs/1949PhRv...75R1766H">1949PhRv...75R1766H</a>. <a href="/wiki/DOI" title="DOI">DOI</a>: <a rel="nofollow" class="external text" href="https://dx.doi.org/10.1103%2FPhysRev.75.1766.2">10.1103/PhysRev.75.1766.2</a>.</span></span> </li> <li id="cite_note-:5-18"><span class="mw-cite-backlink">↑ <sup><a href="#cite_ref-:5_18-0">18,0</a></sup> <sup><a href="#cite_ref-:5_18-1">18,1</a></sup> <sup><a href="#cite_ref-:5_18-2">18,2</a></sup> <sup><a href="#cite_ref-:5_18-3">18,3</a></sup> <sup><a href="#cite_ref-:5_18-4">18,4</a></sup> <sup><a href="#cite_ref-:5_18-5">18,5</a></sup></span> <span class="reference-text"><span class="citation book" style="font-style:normal" id="CITEREFAlonsoFinn1976"><span style="font-variant: small-caps;">Alonso</span>, M.; <span style="font-variant: small-caps;">Finn</span>, E.J. <i>Física</i> (en castellà). Volumen III: Fundamentos cuánticos y estadísticos.  Fondo Educativo Interamericano, 1976. <span style="font-size:90%; white-space:nowrap;"><a href="/wiki/Especial:Fonts_bibliogr%C3%A0fiques/9686630031" title="Especial:Fonts bibliogràfiques/9686630031">ISBN 9686630031</a></span>.</span><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=F%C3%ADsica&rft.aulast=Alonso&rft.aufirst=M.&rft.date=1976&rft.pub=Fondo+Educativo+Interamericano&rft.isbn=9686630031"><span style="display: none;"> </span></span></span> </li> <li id="cite_note-:2-19"><span class="mw-cite-backlink">↑ <sup><a href="#cite_ref-:2_19-0">19,0</a></sup> <sup><a href="#cite_ref-:2_19-1">19,1</a></sup> <sup><a href="#cite_ref-:2_19-2">19,2</a></sup> <sup><a href="#cite_ref-:2_19-3">19,3</a></sup> <sup><a href="#cite_ref-:2_19-4">19,4</a></sup> <sup><a href="#cite_ref-:2_19-5">19,5</a></sup> <sup><a href="#cite_ref-:2_19-6">19,6</a></sup></span> <span class="reference-text"><span class="citation book" style="font-style:normal" id="CITEREFSerwayJewett_Jr2005"><span style="font-variant: small-caps;">Serway</span>, R.A.; <span style="font-variant: small-caps;">Jewett Jr</span>, J.W.. <i>Física. Para ciencias e ingenierías</i> (en castellà). II. 6a.  Thomson, 2005. <span style="font-size:90%; white-space:nowrap;"><a href="/wiki/Especial:Fonts_bibliogr%C3%A0fiques/9706864253" title="Especial:Fonts bibliogràfiques/9706864253">ISBN 9706864253</a></span>.</span><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=F%C3%ADsica.+Para+ciencias+e+ingenier%C3%ADas&rft.aulast=Serway&rft.aufirst=R.A.&rft.date=2005&rft.edition=6a&rft.pub=Thomson&rft.isbn=9706864253"><span style="display: none;"> </span></span></span> </li> <li id="cite_note-20"><span class="mw-cite-backlink"><a href="#cite_ref-20">↑</a></span> <span class="reference-text"><span class="citation" style="font-style:normal">«<a rel="nofollow" class="external text" href="http://www.enciclopedia.cat/gran-enciclopedia-catalana/0189682.xml">Nucli atòmic</a>». <i><a href="/wiki/Gran_Enciclop%C3%A8dia_Catalana" title="Gran Enciclopèdia Catalana">Gran Enciclopèdia Catalana</a></i>.  Barcelona:  <a href="/wiki/Grup_Enciclop%C3%A8dia_Catalana" class="mw-redirect" title="Grup Enciclopèdia Catalana">Grup Enciclopèdia Catalana</a>.</span></span> </li> <li id="cite_note-21"><span class="mw-cite-backlink"><a href="#cite_ref-21">↑</a></span> <span class="reference-text"><span class="citation" style="font-style:normal">«<a rel="nofollow" class="external text" href="http://www.enciclopedia.cat/gran-enciclopedia-catalana/0118020.xml">Nucli atòmic</a>». <i><a href="/wiki/Gran_Enciclop%C3%A8dia_Catalana" title="Gran Enciclopèdia Catalana">Gran Enciclopèdia Catalana</a></i>.  Barcelona:  <a href="/wiki/Grup_Enciclop%C3%A8dia_Catalana" class="mw-redirect" title="Grup Enciclopèdia Catalana">Grup Enciclopèdia Catalana</a>.</span></span> </li> <li id="cite_note-22"><span class="mw-cite-backlink"><a href="#cite_ref-22">↑</a></span> <span class="reference-text"><span class="citation" style="font-style:normal">«<a rel="nofollow" class="external text" href="http://www.enciclopedia.cat/gran-enciclopedia-catalana/0235262.xml">Nucli atòmic</a>». <i><a href="/wiki/Gran_Enciclop%C3%A8dia_Catalana" title="Gran Enciclopèdia Catalana">Gran Enciclopèdia Catalana</a></i>.  Barcelona:  <a href="/wiki/Grup_Enciclop%C3%A8dia_Catalana" class="mw-redirect" title="Grup Enciclopèdia Catalana">Grup Enciclopèdia Catalana</a>.</span></span> </li> <li id="cite_note-:3-23"><span class="mw-cite-backlink">↑ <sup><a href="#cite_ref-:3_23-0">23,0</a></sup> <sup><a href="#cite_ref-:3_23-1">23,1</a></sup> <sup><a href="#cite_ref-:3_23-2">23,2</a></sup> <sup><a href="#cite_ref-:3_23-3">23,3</a></sup></span> <span class="reference-text"><span class="citation book" style="font-style:normal" id="CITEREFSitenkoTartakovskii2012"><span style="font-variant: small-caps;">Sitenko</span>, A.; <span style="font-variant: small-caps;">Tartakovskii</span>, V. <a rel="nofollow" class="external text" href="https://books.google.cat/books?id=e6XqCAAAQBAJ&hl=ca&source=gbs_navlinks_s"><i>Theory of Nucleus: Nuclear Structure and Nuclear Interaction</i></a> (en anglès).  Springer Science & Business Media, 2012. <span style="font-size:90%; white-space:nowrap;"><a href="/wiki/Especial:Fonts_bibliogr%C3%A0fiques/9789401157728" title="Especial:Fonts bibliogràfiques/9789401157728">ISBN 9789401157728</a></span>.</span><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Theory+of+Nucleus%3A+Nuclear+Structure+and+Nuclear+Interaction&rft.aulast=Sitenko&rft.aufirst=A.&rft.date=2012&rft.pub=Springer+Science+%26+Business+Media&rft.isbn=9789401157728&rft_id=https%3A%2F%2Fbooks.google.cat%2Fbooks%3Fid%3De6XqCAAAQBAJ%26hl%3Dca%26source%3Dgbs_navlinks_s"><span style="display: none;"> </span></span></span> </li> <li id="cite_note-BakLec-24"><span class="mw-cite-backlink"><a href="#cite_ref-BakLec_24-0">↑</a></span> <span class="reference-text"><span class="citation" style="font-style:normal">E. Rutherford «Nuclear Constitution of Atoms». <i><a href="/w/index.php?title=Proceedings_of_the_Royal_Society_A&action=edit&redlink=1" class="new" title="Proceedings of the Royal Society A (encara no existeix)">Proceedings of the Royal Society A</a></i>, 97, 686, 1920, pàg. 374. <a href="/wiki/Bibcode" title="Bibcode">Bibcode</a>: <a rel="nofollow" class="external text" href="http://adsabs.harvard.edu/abs/1920RSPSA..97..374R">1920RSPSA..97..374R</a>. <a href="/wiki/DOI" title="DOI">DOI</a>: <a rel="nofollow" class="external text" href="https://dx.doi.org/10.1098%2Frspa.1920.0040">10.1098/rspa.1920.0040</a>.</span></span> </li> <li id="cite_note-Chad1932-25"><span class="mw-cite-backlink"><a href="#cite_ref-Chad1932_25-0">↑</a></span> <span class="reference-text"><span class="citation" style="font-style:normal" id="CITEREFChadwick1932"><span style="font-variant: small-caps;">Chadwick</span>, James «Possible Existence of a Neutron». <i><a href="/wiki/Nature" title="Nature">Nature</a></i>, 129, 3252, 1932, pàg. 312. <a href="/wiki/Bibcode" title="Bibcode">Bibcode</a>: <a rel="nofollow" class="external text" href="http://adsabs.harvard.edu/abs/1932Natur.129Q.312C">1932Natur.129Q.312C</a>. <a href="/wiki/DOI" title="DOI">DOI</a>: <a rel="nofollow" class="external text" href="https://dx.doi.org/10.1038%2F129312a0">10.1038/129312a0</a>.</span></span> </li> <li id="cite_note-26"><span class="mw-cite-backlink"><a href="#cite_ref-26">↑</a></span> <span class="reference-text"><span class="citation" style="font-style:normal" id="CITEREFChadwick1933"><span style="font-variant: small-caps;">Chadwick</span>, J. «Bakerian Lecture. The Neutron». <i>Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences</i>, 142, 846, 1933, pàg. 1. <a href="/wiki/Bibcode" title="Bibcode">Bibcode</a>: <a rel="nofollow" class="external text" href="http://adsabs.harvard.edu/abs/1933RSPSA.142....1C">1933RSPSA.142....1C</a>. <a href="/wiki/DOI" title="DOI">DOI</a>: <a rel="nofollow" class="external text" href="https://dx.doi.org/10.1098%2Frspa.1933.0152">10.1098/rspa.1933.0152</a>.</span></span> </li> <li id="cite_note-:1-27"><span class="mw-cite-backlink">↑ <sup><a href="#cite_ref-:1_27-0">27,0</a></sup> <sup><a href="#cite_ref-:1_27-1">27,1</a></sup></span> <span class="reference-text"><span class="citation book" style="font-style:normal" id="CITEREFMittalVernaGupta2014"><span style="font-variant: small-caps;">Mittal</span>, V.K.; <span style="font-variant: small-caps;">Verna</span>, R.C.; <span style="font-variant: small-caps;">Gupta</span>, S.C.. <a rel="nofollow" class="external text" href="https://books.google.cat/books?id=hOgTSXNxZ-sC&dq=liquid+drop+model+Bohr+Weizs%C3%A4cker&hl=ca&source=gbs_navlinks_s"><i>Introduction to Nuclear and Particle Physics</i></a> (en anglès).  PHI Learning Pvt. Ltd., 2014, p. 47. <span style="font-size:90%; white-space:nowrap;"><a href="/wiki/Especial:Fonts_bibliogr%C3%A0fiques/9788120343115" title="Especial:Fonts bibliogràfiques/9788120343115">ISBN 9788120343115</a></span>.</span><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Introduction+to+Nuclear+and+Particle+Physics&rft.aulast=Mittal&rft.aufirst=V.K.&rft.date=2014&rft.pub=PHI+Learning+Pvt.+Ltd.&rft.pages=47&rft.isbn=9788120343115&rft_id=https%3A%2F%2Fbooks.google.cat%2Fbooks%3Fid%3DhOgTSXNxZ-sC%26dq%3Dliquid%2Bdrop%2Bmodel%2BBohr%2BWeizs%25C3%25A4cker%26hl%3Dca%26source%3Dgbs_navlinks_s"><span style="display: none;"> </span></span></span> </li> <li id="cite_note-28"><span class="mw-cite-backlink"><a href="#cite_ref-28">↑</a></span> <span class="reference-text"><span class="citation book" style="font-style:normal" id="CITEREFFerrer_Soria2006"><span style="font-variant: small-caps;">Ferrer Soria</span>, A. <a rel="nofollow" class="external text" href="https://books.google.cat/books?id=zn0vUDrayO0C&dq=el+nucleo+at%C3%B3mico&hl=ca&source=gbs_navlinks_s"><i>Física nuclear y de partículas</i></a> (en castellà). 2a.  Universitat de València, 2006, p. 107. <span style="font-size:90%; white-space:nowrap;"><a href="/wiki/Especial:Fonts_bibliogr%C3%A0fiques/9788437065687" title="Especial:Fonts bibliogràfiques/9788437065687">ISBN 9788437065687</a></span>.</span><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=F%C3%ADsica+nuclear+y+de+part%C3%ADculas&rft.aulast=Ferrer+Soria&rft.aufirst=A&rft.date=2006&rft.edition=2a&rft.pub=Universitat+de+Val%C3%A8ncia&rft.pages=107&rft.isbn=9788437065687&rft_id=https%3A%2F%2Fbooks.google.cat%2Fbooks%3Fid%3Dzn0vUDrayO0C%26dq%3Del%2Bnucleo%2Bat%25C3%25B3mico%26hl%3Dca%26source%3Dgbs_navlinks_s"><span style="display: none;"> </span></span></span> </li> <li id="cite_note-29"><span class="mw-cite-backlink"><a href="#cite_ref-29">↑</a></span> <span class="reference-text"><span class="citation book" style="font-style:normal" id="CITEREFFlügge2012"><span style="font-variant: small-caps;">Flügge</span>, S. <a rel="nofollow" class="external text" href="https://books.google.cat/books?id=8aP1CAAAQBAJ&dq=atomic+nucleus+theory&hl=ca&source=gbs_navlinks_s"><i>Structure of Atomic Nuclei / Bau der Atomkerne</i></a> (en anglès).  Springer Science & Business Media, 2012. <span style="font-size:90%; white-space:nowrap;"><a href="/wiki/Especial:Fonts_bibliogr%C3%A0fiques/9783642458729" title="Especial:Fonts bibliogràfiques/9783642458729">ISBN 9783642458729</a></span>.</span><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Structure+of+Atomic+Nuclei+%2F+Bau+der+Atomkerne&rft.aulast=Fl%C3%BCgge&rft.aufirst=S.&rft.date=2012&rft.pub=Springer+Science+%26+Business+Media&rft.isbn=9783642458729&rft_id=https%3A%2F%2Fbooks.google.cat%2Fbooks%3Fid%3D8aP1CAAAQBAJ%26dq%3Datomic%2Bnucleus%2Btheory%26hl%3Dca%26source%3Dgbs_navlinks_s"><span style="display: none;"> </span></span></span> </li> <li id="cite_note-:4-30"><span class="mw-cite-backlink">↑ <sup><a href="#cite_ref-:4_30-0">30,0</a></sup> <sup><a href="#cite_ref-:4_30-1">30,1</a></sup></span> <span class="reference-text"><span class="citation book" style="font-style:normal" id="CITEREFSitenkoTartakovskii2014"><span style="font-variant: small-caps;">Sitenko</span>, A.G.; <span style="font-variant: small-caps;">Tartakovskii</span>, V.K.. <a rel="nofollow" class="external text" href="https://books.google.cat/books?id=BCiLBQAAQBAJ&pg=PA106&dq=shell+nucleus&hl=ca&sa=X&ved=0ahUKEwj_4pPT2cLRAhWDOBQKHd9pDGo4FBDoAQguMAE#v=onepage&q=shell%20nucleus&f=false"><i>Lectures on the Theory of the Nucleus</i></a> (en anglès).  Elsevier, 2014, p. 113. <span style="font-size:90%; white-space:nowrap;"><a href="/wiki/Especial:Fonts_bibliogr%C3%A0fiques/9781483295411" title="Especial:Fonts bibliogràfiques/9781483295411">ISBN 9781483295411</a></span>.</span><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Lectures+on+the+Theory+of+the+Nucleus&rft.aulast=Sitenko&rft.aufirst=A.G.&rft.date=2014&rft.pub=Elsevier&rft.pages=113&rft.isbn=9781483295411&rft_id=https%3A%2F%2Fbooks.google.cat%2Fbooks%3Fid%3DBCiLBQAAQBAJ%26pg%3DPA106%26dq%3Dshell%2Bnucleus%26hl%3Dca%26sa%3DX%26ved%3D0ahUKEwj_4pPT2cLRAhWDOBQKHd9pDGo4FBDoAQguMAE%23v%3Donepage%26q%3Dshell%2520nucleus%26f%3Dfalse"><span style="display: none;"> </span></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="Vegeu_també"><span id="Vegeu_tamb.C3.A9"></span>Vegeu també</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Nucli_at%C3%B2mic&action=edit&section=14" title="Modifica la secció: Vegeu també"><span>modifica</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Estabilitat_del_nucli_at%C3%B2mic" title="Estabilitat del nucli atòmic">Estabilitat del nucli atòmic</a></li> <li><a href="/wiki/Escor%C3%A7a_at%C3%B2mica" class="mw-redirect" title="Escorça atòmica">Escorça atòmica</a></li></ul> <div role="navigation" class="navbox" aria-label="Navbox" style="padding:3px"><table class="nowraplinks hlist navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Control_d%27autoritats" title="Control d'autoritats">Registres d'autoritat</a></th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/Gemeinsame_Normdatei" title="Gemeinsame Normdatei">GND</a> <span class="uid"> (<a rel="nofollow" class="external text" href="http://d-nb.info/gnd/4068924-4">1</a>)</span></li> <li><a href="/wiki/National_Diet_Library" class="mw-redirect" title="National Diet Library">NDL</a> <span class="uid"> (<a rel="nofollow" class="external text" href="http://id.ndl.go.jp/auth/ndlna/00562376">1</a>)</span></li> <li><a href="/wiki/Biblioteca_Nacional_de_la_Rep%C3%BAblica_Txeca" title="Biblioteca Nacional de la República Txeca">NKC</a> <span class="uid"> (<a rel="nofollow" class="external text" href="http://aleph.nkp.cz/F/?func=find-c&local_base=aut&ccl_term=ica=ph170603&CON_LNG=ENG">1</a>)</span></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Bases d'informació</th><td class="navbox-list navbox-even" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/GEC" class="mw-redirect" title="GEC">GEC</a> <span class="uid"> (<a rel="nofollow" class="external text" href="https://www.enciclopedia.cat/gran-enciclopedia-catalana/nucli-mirall">1</a>)</span></li></ul> </div></td></tr></tbody></table></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; 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