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data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Indice</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">sposta nella barra laterale</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">nascondi</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">Inizio</div> </a> </li> <li id="toc-Energia_di_legame_ed_energia_di_dissociazione" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Energia_di_legame_ed_energia_di_dissociazione"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Energia di legame ed energia di dissociazione</span> </div> </a> <ul id="toc-Energia_di_legame_ed_energia_di_dissociazione-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Tipi_di_energie_di_legame" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Tipi_di_energie_di_legame"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Tipi di energie di legame</span> </div> </a> <ul id="toc-Tipi_di_energie_di_legame-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Difetto_di_massa" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Difetto_di_massa"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Difetto di massa</span> </div> </a> <ul id="toc-Difetto_di_massa-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Energia_di_legame_nucleare" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Energia_di_legame_nucleare"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Energia di legame nucleare</span> </div> </a> <button aria-controls="toc-Energia_di_legame_nucleare-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>Attiva/disattiva la sottosezione Energia di legame nucleare</span> </button> <ul id="toc-Energia_di_legame_nucleare-sublist" class="vector-toc-list"> <li id="toc-Formula_semiempirica_di_Bethe-Weizsäcker" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Formula_semiempirica_di_Bethe-Weizsäcker"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Formula semiempirica di Bethe-Weizsäcker</span> </div> </a> <ul id="toc-Formula_semiempirica_di_Bethe-Weizsäcker-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Masse_ed_energie_atomiche_e_nucleari" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Masse_ed_energie_atomiche_e_nucleari"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Masse ed energie atomiche e nucleari</span> </div> </a> <ul id="toc-Masse_ed_energie_atomiche_e_nucleari-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Note" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Note"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Note</span> </div> </a> <ul id="toc-Note-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Altri_progetti" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Altri_progetti"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Altri progetti</span> </div> </a> <ul id="toc-Altri_progetti-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Collegamenti_esterni" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Collegamenti_esterni"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Collegamenti esterni</span> </div> </a> <ul id="toc-Collegamenti_esterni-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="Indice" 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="Mostra/Nascondi l'indice" > <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">Mostra/Nascondi l'indice</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">Energia di legame</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="Vai a una voce in un'altra lingua. Disponibile in 38 lingue" > <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-38" 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">38 lingue</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/Bindingsenergie" title="Bindingsenergie - afrikaans" lang="af" hreflang="af" data-title="Bindingsenergie" data-language-autonym="Afrikaans" data-language-local-name="afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%B7%D8%A7%D9%82%D8%A9_%D8%A7%D9%84%D8%A7%D8%B1%D8%AA%D8%A8%D8%A7%D8%B7" title="طاقة الارتباط - arabo" lang="ar" hreflang="ar" data-title="طاقة الارتباط" data-language-autonym="العربية" data-language-local-name="arabo" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%AD%D0%BD%D0%B5%D1%80%D0%B3%D1%96%D1%8F_%D1%81%D1%83%D0%B2%D1%8F%D0%B7%D1%96" title="Энергія сувязі - bielorusso" lang="be" hreflang="be" data-title="Энергія сувязі" data-language-autonym="Беларуская" data-language-local-name="bielorusso" 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%AD%D0%BD%D1%8D%D1%80%D0%B3%D1%96%D1%8F_%D1%81%D1%83%D0%B2%D1%8F%D0%B7%D1%96" title="Энэргія сувязі - Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Энэргія сувязі" 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%95%D0%BD%D0%B5%D1%80%D0%B3%D0%B8%D1%8F_%D0%BD%D0%B0_%D1%81%D0%B2%D1%8A%D1%80%D0%B7%D0%B2%D0%B0%D0%BD%D0%B5" title="Енергия на свързване - bulgaro" lang="bg" hreflang="bg" data-title="Енергия на свързване" data-language-autonym="Български" data-language-local-name="bulgaro" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Energia_de_lligadura" title="Energia de lligadura - catalano" lang="ca" hreflang="ca" data-title="Energia de lligadura" data-language-autonym="Català" data-language-local-name="catalano" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-ce mw-list-item"><a href="https://ce.wikipedia.org/wiki/%D0%97%D3%80%D0%B5%D0%BD_%D1%8D%D0%BD%D0%B5%D1%80%D0%B3%D0%B8" title="ЗӀен энерги - ceceno" lang="ce" hreflang="ce" data-title="ЗӀен энерги" data-language-autonym="Нохчийн" data-language-local-name="ceceno" class="interlanguage-link-target"><span>Нохчийн</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Bindingsenergi" title="Bindingsenergi - danese" lang="da" hreflang="da" data-title="Bindingsenergi" data-language-autonym="Dansk" data-language-local-name="danese" 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/Bindungsenergie" title="Bindungsenergie - tedesco" lang="de" hreflang="de" data-title="Bindungsenergie" data-language-autonym="Deutsch" data-language-local-name="tedesco" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Binding_energy" title="Binding energy - inglese" lang="en" hreflang="en" data-title="Binding energy" data-language-autonym="English" data-language-local-name="inglese" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Energ%C3%ADa_de_uni%C3%B3n" title="Energía de unión - spagnolo" lang="es" hreflang="es" data-title="Energía de unión" data-language-autonym="Español" data-language-local-name="spagnolo" 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/Seoseenergia" title="Seoseenergia - estone" lang="et" hreflang="et" data-title="Seoseenergia" data-language-autonym="Eesti" data-language-local-name="estone" 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/Lotze-energia" title="Lotze-energia - basco" lang="eu" hreflang="eu" data-title="Lotze-energia" data-language-autonym="Euskara" data-language-local-name="basco" 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/%D8%A7%D9%86%D8%B1%DA%98%DB%8C_%D8%A8%D8%B3%D8%AA%DA%AF%DB%8C" title="انرژی بستگی - persiano" lang="fa" hreflang="fa" data-title="انرژی بستگی" data-language-autonym="فارسی" data-language-local-name="persiano" 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/Sidosenergia" title="Sidosenergia - finlandese" lang="fi" hreflang="fi" data-title="Sidosenergia" data-language-autonym="Suomi" data-language-local-name="finlandese" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/%C3%89nergie_de_liaison" title="Énergie de liaison - francese" lang="fr" hreflang="fr" data-title="Énergie de liaison" data-language-autonym="Français" data-language-local-name="francese" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%AC%E0%A4%82%E0%A4%A7%E0%A4%A8_%E0%A4%8A%E0%A4%B0%E0%A5%8D%E0%A4%9C%E0%A4%BE" title="बंधन ऊर्जा - hindi" lang="hi" hreflang="hi" data-title="बंधन ऊर्जा" 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/Energija_vezanja" title="Energija vezanja - croato" lang="hr" hreflang="hr" data-title="Energija vezanja" data-language-autonym="Hrvatski" data-language-local-name="croato" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/K%C3%B6t%C3%A9si_energia" title="Kötési energia - ungherese" lang="hu" hreflang="hu" data-title="Kötési energia" data-language-autonym="Magyar" data-language-local-name="ungherese" 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/%D4%BF%D5%A1%D5%BA%D5%AB_%D5%A7%D5%B6%D5%A5%D6%80%D5%A3%D5%AB%D5%A1" title="Կապի էներգիա - armeno" lang="hy" hreflang="hy" data-title="Կապի էներգիա" data-language-autonym="Հայերեն" data-language-local-name="armeno" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Energi_pengikatan" title="Energi pengikatan - indonesiano" lang="id" hreflang="id" data-title="Energi pengikatan" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonesiano" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E7%B5%90%E5%90%88%E3%82%A8%E3%83%8D%E3%83%AB%E3%82%AE%E3%83%BC" title="結合エネルギー - giapponese" lang="ja" hreflang="ja" data-title="結合エネルギー" data-language-autonym="日本語" data-language-local-name="giapponese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%AC%E0%B4%A8%E0%B5%8D%E0%B4%A7%E0%B4%A8%E0%B5%8B%E0%B5%BC%E0%B4%9C%E0%B5%8D%E0%B4%9C%E0%B4%82" title="ബന്ധനോർജ്ജം - malayalam" lang="ml" hreflang="ml" data-title="ബന്ധനോർജ്ജം" data-language-autonym="മലയാളം" data-language-local-name="malayalam" 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%A5%D0%BE%D0%BB%D0%B1%D0%BE%D0%B3%D0%B4%D0%BE%D1%85_%D1%8D%D0%BD%D0%B5%D1%80%D0%B3%D0%B8" title="Холбогдох энерги - mongolo" lang="mn" hreflang="mn" data-title="Холбогдох энерги" data-language-autonym="Монгол" data-language-local-name="mongolo" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Tenaga_pengikatan" title="Tenaga pengikatan - malese" lang="ms" hreflang="ms" data-title="Tenaga pengikatan" data-language-autonym="Bahasa Melayu" data-language-local-name="malese" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Bindingsenergie" title="Bindingsenergie - olandese" lang="nl" hreflang="nl" data-title="Bindingsenergie" data-language-autonym="Nederlands" data-language-local-name="olandese" 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/Bindingsenergi" title="Bindingsenergi - norvegese nynorsk" lang="nn" hreflang="nn" data-title="Bindingsenergi" data-language-autonym="Norsk nynorsk" data-language-local-name="norvegese 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/Bindingsenergi" title="Bindingsenergi - norvegese bokmål" lang="nb" hreflang="nb" data-title="Bindingsenergi" data-language-autonym="Norsk bokmål" data-language-local-name="norvegese bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Energia_wi%C4%85zania" title="Energia wiązania - polacco" lang="pl" hreflang="pl" data-title="Energia wiązania" data-language-autonym="Polski" data-language-local-name="polacco" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%AD%D0%BD%D0%B5%D1%80%D0%B3%D0%B8%D1%8F_%D1%81%D0%B2%D1%8F%D0%B7%D0%B8" title="Энергия связи - russo" lang="ru" hreflang="ru" data-title="Энергия связи" data-language-autonym="Русский" data-language-local-name="russo" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Vezavna_energija" title="Vezavna energija - sloveno" lang="sl" hreflang="sl" data-title="Vezavna energija" data-language-autonym="Slovenščina" data-language-local-name="sloveno" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/Energija_vezanja" title="Energija vezanja - serbo" lang="sr" hreflang="sr" data-title="Energija vezanja" data-language-autonym="Српски / srpski" data-language-local-name="serbo" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Bindningsenergi" title="Bindningsenergi - svedese" lang="sv" hreflang="sv" data-title="Bindningsenergi" data-language-autonym="Svenska" data-language-local-name="svedese" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%AA%E0%AE%BF%E0%AE%A3%E0%AF%88_%E0%AE%86%E0%AE%B1%E0%AF%8D%E0%AE%B1%E0%AE%B2%E0%AF%8D" title="பிணை ஆற்றல் - tamil" lang="ta" hreflang="ta" data-title="பிணை ஆற்றல்" data-language-autonym="தமிழ்" data-language-local-name="tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%9E%E0%B8%A5%E0%B8%B1%E0%B8%87%E0%B8%87%E0%B8%B2%E0%B8%99%E0%B8%A2%E0%B8%B6%E0%B8%94%E0%B9%80%E0%B8%AB%E0%B8%99%E0%B8%B5%E0%B9%88%E0%B8%A2%E0%B8%A7" title="พลังงานยึดเหนี่ยว - thailandese" lang="th" hreflang="th" data-title="พลังงานยึดเหนี่ยว" data-language-autonym="ไทย" data-language-local-name="thailandese" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Ba%C4%9Flanma_enerjisi" title="Bağlanma enerjisi - turco" lang="tr" hreflang="tr" data-title="Bağlanma enerjisi" data-language-autonym="Türkçe" data-language-local-name="turco" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%95%D0%BD%D0%B5%D1%80%D0%B3%D1%96%D1%8F_%D0%B7%D0%B2%27%D1%8F%D0%B7%D0%BA%D1%83" title="Енергія зв'язку - ucraino" lang="uk" hreflang="uk" data-title="Енергія зв'язку" data-language-autonym="Українська" data-language-local-name="ucraino" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E7%BB%93%E5%90%88%E8%83%BD" title="结合能 - cinese" lang="zh" hreflang="zh" data-title="结合能" data-language-autonym="中文" data-language-local-name="cinese" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q420754#sitelinks-wikipedia" title="Modifica collegamenti interlinguistici" class="wbc-editpage">Modifica collegamenti</a></span></div> </div> </div> </div> </header> <div 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id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">Da Wikipedia, l'enciclopedia libera.</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="it" dir="ltr"><style data-mw-deduplicate="TemplateStyles:r130658281">body:not(.skin-minerva) .mw-parser-output .hatnote.nota-disambigua{clear:both;margin-top:0;padding:.05em .5em}</style> <style data-mw-deduplicate="TemplateStyles:r139142988">.mw-parser-output .hatnote-content{align-items:center;display:flex}.mw-parser-output .hatnote-icon{flex-shrink:0}.mw-parser-output .hatnote-icon img{display:flex}.mw-parser-output .hatnote-text{font-style:italic}body:not(.skin-minerva) .mw-parser-output .hatnote{border:1px solid #CCC;display:flex;margin:.5em 0;padding:.2em .5em}body:not(.skin-minerva) .mw-parser-output .hatnote-text{padding-left:.5em}body.skin-minerva .mw-parser-output .hatnote-icon{padding-right:8px}body.skin-minerva .mw-parser-output .hatnote-icon img{height:auto;width:16px}body.skin--responsive .mw-parser-output .hatnote a.new{color:#d73333}body.skin--responsive .mw-parser-output .hatnote a.new:visited{color:#a55858}</style> <div class="hatnote noprint nota-disambigua"> <div class="hatnote-content"><span class="noviewer hatnote-icon" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/bc/Nota_disambigua.svg/18px-Nota_disambigua.svg.png" decoding="async" width="18" height="18" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/bc/Nota_disambigua.svg/27px-Nota_disambigua.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/bc/Nota_disambigua.svg/36px-Nota_disambigua.svg.png 2x" data-file-width="200" data-file-height="200" /></span></span> <span class="hatnote-text"><a 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//upload.wikimedia.org/wikipedia/commons/thumb/b/bc/Nota_disambigua.svg/36px-Nota_disambigua.svg.png 2x" data-file-width="200" data-file-height="200" /></span></span> <span class="hatnote-text"><a href="/wiki/Aiuto:Disambiguazione" title="Aiuto:Disambiguazione">Disambiguazione</a> – Se stai cercando in riferimento all'<a href="/wiki/Energia_di_dissociazione_di_legame" title="Energia di dissociazione di legame">energia di dissociazione di legame</a> chimico, vedi <b><a href="/wiki/Energia_di_dissociazione_di_legame" title="Energia di dissociazione di legame">Energia di dissociazione di legame</a></b>.</span></div> </div> <p>In <a href="/wiki/Fisica" title="Fisica">fisica</a> e in <a href="/wiki/Chimica" title="Chimica">chimica</a>, l'<b>energia di legame</b> è l'<a href="/wiki/Energia" title="Energia">energia</a> necessaria per tenere aggregate le parti di un sistema composto. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Energia_di_legame_ed_energia_di_dissociazione">Energia di legame ed energia di dissociazione</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Energia_di_legame&veaction=edit&section=1" title="Modifica la sezione Energia di legame ed energia di dissociazione" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Energia_di_legame&action=edit&section=1" title="Edit section's source code: Energia di legame ed energia di dissociazione"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In un sistema legato, l'energia totale è inferiore rispetto a quella degli elementi che lo compongono e quindi l'energia di legame <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/2b71d40b28612bb3f7578929558cccef2bb5798d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.195ex; height:2.509ex;" alt="{\displaystyle E_{B}}"></span> (dall'inglese: <i>Binding Energy</i>) è per definizione negativa (<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}<0}"> <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> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{B}<0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c430d46ee4d83f7ef67d98f137ecc31b9004a448" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.456ex; height:2.509ex;" alt="{\displaystyle E_{B}<0}"></span>). L'energia di dissociazione è invece l'energia che deve essere fornita al sistema per vincere le forze che lo tengono unito (<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_{D}>0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>D</mi> </mrow> </msub> <mo>></mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{D}>0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d6763223e93d33dd5f1f66f63090768e3ada88e5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.569ex; height:2.509ex;" alt="{\displaystyle E_{D}>0}"></span>). L'energia di legame e quella di dissociazione sono quindi uguali in modulo, ma opposte di segno: <sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p> <dl><dd><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_{D}=-\,E_{B}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>D</mi> </mrow> </msub> <mo>=</mo> <mo>−</mo> <mspace width="thinmathspace" /> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{D}=-\,E_{B}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/38437291464118e2c1fcc648fd436700a663a86b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:11.797ex; height:2.509ex;" alt="{\displaystyle E_{D}=-\,E_{B}}"></span></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Tipi_di_energie_di_legame">Tipi di energie di legame</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Energia_di_legame&veaction=edit&section=2" title="Modifica la sezione Tipi di energie di legame" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Energia_di_legame&action=edit&section=2" title="Edit section's source code: Tipi di energie di legame"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Ogni corpo ha la propria energia di legame <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/2b71d40b28612bb3f7578929558cccef2bb5798d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.195ex; height:2.509ex;" alt="{\displaystyle E_{B}}"></span>, calcolabile a partire da quella di dissociazione <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_{D}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>D</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{D}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2f282f669829b6adcbfcfdb7da10cc64535f6c11" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.308ex; height:2.509ex;" alt="{\displaystyle E_{D}}"></span> cambiata di segno. L'energia di dissociazione si valuta calcolando l'energia necessaria per allontanare all'infinito (quindi con energia di legame nulla) tutte le particelle che lo compongono. Il valore di tale energia dipende dalla forza che lega tra loro le particelle. </p><p>In successione, dalla forza più debole alla più forte, si ha: </p> <ol><li><b>Gravitazionale</b>. In <a href="/wiki/Astrofisica" title="Astrofisica">astrofisica</a>, l'energia di legame di un <a href="/wiki/Corpo_celeste" class="mw-redirect" title="Corpo celeste">corpo celeste</a> è l'energia necessaria a tenerne aggregate le parti. Tale energia è data dall'<a href="/wiki/Interazione_gravitazionale" title="Interazione gravitazionale">interazione gravitazionale</a> e prende il nome di <i>energia di legame gravitazionale</i>. Se un corpo con la massa e il raggio della <a href="/wiki/Terra" title="Terra">Terra</a> fosse composto solo da idrogeno atomico, l'energia di legame gravitazionale sarebbe di -0,392 eV per atomo. Se invece l'astro formato di solo idrogeno atomico avesse la massa e il raggio del <a href="/wiki/Sole" title="Sole">Sole</a>, l'energia di legame raggiungerebbe i -1.195,586 eV per atomo.</li> <li><b>Molecolare</b>. In una <a href="/wiki/Molecola" title="Molecola">molecola</a>, l'energia di legame tiene uniti gli <a href="/wiki/Atomo" title="Atomo">atomi</a> costituenti mediante dei <a href="/wiki/Legame_chimico" title="Legame chimico">legami chimici</a>. L'<a href="/wiki/Energia_chimica" title="Energia chimica">energia chimica</a> si manifesta nel corso della dissociazione di molecole con la produzione di <a href="/wiki/Calore" title="Calore">calore</a>, come nei fenomeni di <a href="/wiki/Combustione" title="Combustione">combustione</a>, nelle <a href="/wiki/Esplosivo" title="Esplosivo">esplosioni</a> o anche nei processi <a href="/wiki/Biologia" title="Biologia">biologici</a>. Le energie coinvolte sono tipicamente di pochi <a href="/wiki/Elettronvolt" title="Elettronvolt">elettronvolt</a> per ogni legame chimico (il legame carbonio-carbonio è di circa -3,6 eV).</li> <li><b>Atomica</b>. Per un <a href="/wiki/Atomo" title="Atomo">atomo</a> l'energia di legame è data dall'<a href="/wiki/Interazione_elettromagnetica" title="Interazione elettromagnetica">interazione elettromagnetica</a> e prende il nome di <i>energia di legame atomico</i>. L'energia di dissociazione è l'<a href="/wiki/Energia_di_ionizzazione" title="Energia di ionizzazione">energia di ionizzazione</a> necessaria a separare il <a href="/wiki/Nucleo_atomico" title="Nucleo atomico">nucleo atomico</a> dagli <a href="/wiki/Elettrone" title="Elettrone">elettroni</a>, ponendoli a distanza tale che non interferiscano tra loro. L'energia di dissociazione per un atomo di <a href="/wiki/Idrogeno" title="Idrogeno">idrogeno</a> nello <a href="/wiki/Stato_fondamentale" title="Stato fondamentale">stato fondamentale</a> è di 13,598 eV. L'intervallo delle energie di ionizzazione degli <a href="/wiki/Elemento_chimico" title="Elemento chimico">elementi chimici</a> varia dai 3,894 eV per l'elettrone più esterno del <a href="/wiki/Cesio" title="Cesio">cesio</a> agli 11.567,617 eV per l'elettrone più interno dell'atomo di <a href="/wiki/Rame" title="Rame">rame</a>.</li> <li><b>Nucleare</b>. Per un <a href="/wiki/Nucleo_atomico" title="Nucleo atomico">nucleo atomico</a> l'energia di legame è l'energia necessaria a comporre il nucleo a partire dai singoli <a href="/wiki/Protone" title="Protone">protoni</a> e <a href="/wiki/Neutrone" title="Neutrone">neutroni</a>. Tale energia è data dall'<a href="/wiki/Interazione_nucleare_forte" class="mw-redirect" title="Interazione nucleare forte">forza nucleare forte</a>, mediata dai <a href="/wiki/Pione" title="Pione">pioni</a>, e prende il nome di <i>energia di legame nucleare</i>. L'energia di dissociazione è l'energia necessaria a separare i costituenti del <a href="/wiki/Nucleo_atomico" title="Nucleo atomico">nucleo</a>, portandoli a distanza tale che non vi sia interazione tra loro. L'energia di legame per <a href="/wiki/Nucleone" title="Nucleone">nucleone</a> varia da -2,2245 MeV per il <a href="/wiki/Deuterio" title="Deuterio">deuterio</a> (<sup>2</sup>H o H–2) (2 <a href="/wiki/Nucleoni" class="mw-redirect" title="Nucleoni">nucleoni</a>) a -8,7945 MeV per il <a href="/wiki/Nichel" title="Nichel">nichel</a>–62 (62 <a href="/wiki/Nucleoni" class="mw-redirect" title="Nucleoni">nucleoni</a>).</li> <li><b>Subnucleare</b>. È l'energia che lega i vari <a href="/wiki/Quark_(particella)" title="Quark (particella)">quark</a> all'interno di un <a href="/wiki/Adrone" title="Adrone">adrone</a>. Come previsto dalla QCD (<a href="/wiki/Cromodinamica_quantistica" title="Cromodinamica quantistica">cromodinamica quantistica</a>), è generata dall'<a href="/wiki/Interazione_nucleare_forte" class="mw-redirect" title="Interazione nucleare forte">interazione nucleare forte</a>, mediata dai <a href="/wiki/Gluone" title="Gluone">gluoni</a>. Questa energia di legame è responsabile per il 99% della massa dei <a href="/wiki/Nucleone" title="Nucleone">nucleoni</a>.</li></ol> <div class="mw-heading mw-heading2"><h2 id="Difetto_di_massa">Difetto di massa</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Energia_di_legame&veaction=edit&section=3" title="Modifica la sezione Difetto di massa" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Energia_di_legame&action=edit&section=3" title="Edit section's source code: Difetto di massa"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In un sistema legato, l'energia totale è inferiore rispetto a quella degli elementi che lo compongono. Durante la formazione di un sistema legato, la differenza d'energia viene rilasciata o sotto forma di <a href="/wiki/Energia_cinetica" title="Energia cinetica">energia cinetica</a> o trasportata da <a href="/wiki/Onda" title="Onda">onde</a> (solitamente <a href="/wiki/Onde_elettromagnetiche" class="mw-redirect" title="Onde elettromagnetiche">elettromagnetiche</a>; <a href="/wiki/Onde_gravitazionali" class="mw-redirect" title="Onde gravitazionali">gravitazionali</a> nel caso del collasso di <a href="/wiki/Buco_nero" title="Buco nero">buchi neri</a>). </p><p>Per la <a href="/wiki/E%3Dmc%C2%B2" title="E=mc²">legge di conservazione della massa-energia</a> di <a href="/wiki/Albert_Einstein" title="Albert Einstein">Albert Einstein</a>, la sua massa deve di conseguenza essere minore della somma delle masse dei componenti. Il motivo di tale differenza di massa, che prende il nome di <i>difetto di massa</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 \Delta M}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">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/3c33157113b395199ed668d8295fbb6a075c7f1d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.378ex; height:2.176ex;" alt="{\displaystyle \Delta M}"></span>, dipende dal fatto che il sistema necessita di un'energia di legame (negativa) per mantenere coese le sue parti. Se </p> <dl><dd><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+B\to C}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>+</mo> <mi>B</mi> <mo stretchy="false">→</mo> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A+B\to C}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/28a2a2041923516c02cb7c178099710abda93284" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:11.728ex; height:2.343ex;" alt="{\displaystyle A+B\to C}"></span></dd></dl> <p>allora </p> <dl><dd><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_{C}<M_{A}+M_{B}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> <mo><</mo> <msub> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle M_{C}<M_{A}+M_{B}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/76bd15ef9b3ef982edb815197b74ee634d5703c0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:17.127ex; height:2.509ex;" alt="{\displaystyle M_{C}<M_{A}+M_{B}}"></span></dd></dl> <p>e </p> <dl><dd><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=M_{C}-M_{A}-M_{B}<0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>M</mi> <mo>=</mo> <msub> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> <mo>−</mo> <msub> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> <mo>−</mo> <msub> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mo><</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta M=M_{C}-M_{A}-M_{B}<0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d7860137e5a70736d820067820469578414ff723" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:28.606ex; height:2.509ex;" alt="{\displaystyle \Delta M=M_{C}-M_{A}-M_{B}<0}"></span></dd></dl> <p>L'energia di legame (atomico, molecolare, nucleare, subnucleare, gravitazionale) è data dal prodotto tra il difetto di 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 \Delta M}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">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/3c33157113b395199ed668d8295fbb6a075c7f1d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.378ex; height:2.176ex;" alt="{\displaystyle \Delta M}"></span> per il quadrato della <a href="/wiki/Velocit%C3%A0_della_luce" title="Velocità della luce">velocità della luce</a> nel vuoto: <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> </p> <dl><dd><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 B_{E}=\Delta M\cdot c^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>E</mi> </mrow> </msub> <mo>=</mo> <mi mathvariant="normal">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 B_{E}=\Delta M\cdot c^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f010e8c2b8871ea91498b99b27cfe913b66aba2d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:14.469ex; height:3.009ex;" alt="{\displaystyle B_{E}=\Delta M\cdot c^{2}}"></span></dd></dl> <p>Si noti che entrambe le quantità <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 B_{E}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>E</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B_{E}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f216a044c34d0bf07b69ef46a6df141032c6e035" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.252ex; height:2.509ex;" alt="{\displaystyle B_{E}}"></span> e <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 mathvariant="normal">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/3c33157113b395199ed668d8295fbb6a075c7f1d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.378ex; height:2.176ex;" alt="{\displaystyle \Delta M}"></span> sono negative. </p><p>Nei <a href="/wiki/Radioattivit%C3%A0" title="Radioattività">decadimenti radioattivi</a> spontanei: </p> <dl><dd><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\to A+B}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>C</mi> <mo stretchy="false">→</mo> <mi>A</mi> <mo>+</mo> <mi>B</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C\to A+B}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6a4f51b531c3946232fcbb7122d873fda568096a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:11.728ex; height:2.343ex;" alt="{\displaystyle C\to A+B}"></span></dd></dl> <p>deve valere </p> <dl><dd><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_{C}>M_{A}+M_{B}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> <mo>></mo> <msub> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle M_{C}>M_{A}+M_{B}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/da2f088fbca410094689035949a23ba33a6120d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:17.127ex; height:2.509ex;" alt="{\displaystyle M_{C}>M_{A}+M_{B}}"></span></dd></dl> <p>e il difetto di massa risulta essere </p> <dl><dd><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=M_{A}+M_{B}-M_{C}<0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>M</mi> <mo>=</mo> <msub> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mo>−</mo> <msub> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> <mo><</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta M=M_{A}+M_{B}-M_{C}<0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6bebd71f0c119c660117fe5132ab45851fb4f304" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:28.606ex; height:2.509ex;" alt="{\displaystyle \Delta M=M_{A}+M_{B}-M_{C}<0}"></span></dd></dl> <p>L'energia di dissociazione spontanea (<i><a href="/wiki/Q_valore" title="Q valore">Q valore</a></i>) si trasforma in <a href="/wiki/Energia_cinetica" title="Energia cinetica">energia cinetica</a> <i>K</i> dei prodotti di decadimento: </p> <dl><dd><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=E_{D}=-E_{B}=-\Delta M\cdot c^{2}=(M_{C}-M_{A}-M_{B})\cdot c^{2}=K_{A}+K_{B}>0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Q</mi> <mo>=</mo> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>D</mi> </mrow> </msub> <mo>=</mo> <mo>−</mo> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mo>=</mo> <mo>−</mo> <mi mathvariant="normal">Δ</mi> <mi>M</mi> <mo>⋅</mo> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mo stretchy="false">(</mo> <msub> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> <mo>−</mo> <msub> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> <mo>−</mo> <msub> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mo>⋅</mo> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mo>></mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Q=E_{D}=-E_{B}=-\Delta M\cdot c^{2}=(M_{C}-M_{A}-M_{B})\cdot c^{2}=K_{A}+K_{B}>0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f8b64b0cce987d822bfbb89674c247da0bfa3bdf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:71.978ex; height:3.176ex;" alt="{\displaystyle Q=E_{D}=-E_{B}=-\Delta M\cdot c^{2}=(M_{C}-M_{A}-M_{B})\cdot c^{2}=K_{A}+K_{B}>0}"></span></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Energia_di_legame_nucleare">Energia di legame nucleare</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Energia_di_legame&veaction=edit&section=4" title="Modifica la sezione Energia di legame nucleare" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Energia_di_legame&action=edit&section=4" title="Edit section's source code: Energia di legame nucleare"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Binding_energy.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a6/Binding_energy.png/220px-Binding_energy.png" decoding="async" width="220" height="176" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a6/Binding_energy.png/330px-Binding_energy.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a6/Binding_energy.png/440px-Binding_energy.png 2x" data-file-width="600" data-file-height="480" /></a><figcaption>Energia di legame per nucleone. I nuclei più stabili sono quelli del picco (curva rossa). Quelli troppo pesanti (oltre la linea blu) subiscono decadimenti alfa spontanei, fino al raggiungimento della linea di demarcazione per l'emissione alfa. I valori riportati sono positivi perché viene rappresentato la quantità <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"> <mo>−</mo> <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> <mo>.</mo> </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/dbd8629d17e1b2c5a633b13e35d54db602901ed0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.555ex; height:2.843ex;" alt="{\displaystyle -E_{B}/A.}"></span></figcaption></figure> <p>L'energia di legame nucleare è l'energia responsabile della stabilità del nucleo, che dipende dal numero di protoni in relazione al numero di neutroni: se il numero di neutroni è troppo piccolo o troppo grande, il nucleo risulta instabile e <a href="/wiki/Radioattivit%C3%A0" title="Radioattività">decade radioattivamente</a>. </p><p>Per un nucleo atomico la massa misurata è minore della somma delle masse dei suoi protoni e neutroni: detti <i>Z</i> e <i>N</i> rispettivamente il numero di protoni e neutroni presenti, si ha: </p> <dl><dd><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_{nucleo}<Z\cdot m_{protone}+N\cdot m_{neutrone}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mi>u</mi> <mi>c</mi> <mi>l</mi> <mi>e</mi> <mi>o</mi> </mrow> </msub> <mo><</mo> <mi>Z</mi> <mo>⋅</mo> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> <mi>r</mi> <mi>o</mi> <mi>t</mi> <mi>o</mi> <mi>n</mi> <mi>e</mi> </mrow> </msub> <mo>+</mo> <mi>N</mi> <mo>⋅</mo> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mi>e</mi> <mi>u</mi> <mi>t</mi> <mi>r</mi> <mi>o</mi> <mi>n</mi> <mi>e</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle M_{nucleo}<Z\cdot m_{protone}+N\cdot m_{neutrone}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/10ac584a040b66da105ce324820a9082a34b6b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:36.851ex; height:2.843ex;" alt="{\displaystyle M_{nucleo}<Z\cdot m_{protone}+N\cdot m_{neutrone}}"></span></dd></dl> <p>Come detto, l'energia di legame è data dal prodotto tra il difetto di massa ed il quadrato della velocità della luce nel vuoto: </p> <dl><dd><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 B_{E}=\Delta M\cdot \,c^{2}=(M_{nucleo}-\sum _{k=1}^{A}m_{k})\cdot c^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>E</mi> </mrow> </msub> <mo>=</mo> <mi mathvariant="normal">Δ</mi> <mi>M</mi> <mo>⋅</mo> <mspace width="thinmathspace" /> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mo stretchy="false">(</mo> <msub> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mi>u</mi> <mi>c</mi> <mi>l</mi> <mi>e</mi> <mi>o</mi> </mrow> </msub> <mo>−</mo> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </munderover> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mo>⋅</mo> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B_{E}=\Delta M\cdot \,c^{2}=(M_{nucleo}-\sum _{k=1}^{A}m_{k})\cdot c^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0f26d13b885ce4b101e62deb25ae44991b8e640e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:40.394ex; height:7.343ex;" alt="{\displaystyle B_{E}=\Delta M\cdot \,c^{2}=(M_{nucleo}-\sum _{k=1}^{A}m_{k})\cdot c^{2}}"></span></dd></dl> <p>Nella <a href="/wiki/Tavola_periodica" class="mw-redirect" title="Tavola periodica">tavola periodica degli elementi</a> l'energia di legame cresce (in <a href="/wiki/Valore_assoluto" title="Valore assoluto">valore assoluto</a>) all'aumentare della massa atomica fino ad arrivare alla regione più stabile, nella sequenza tra il <a href="/wiki/Magnesio" title="Magnesio">magnesio</a> e lo <a href="/wiki/Xeno" title="Xeno">xeno</a>: con l'ulteriore crescere delle dimensioni nucleari l'energia di legame decresce. Dividendo il valore assoluto l'energia di legame del nucleo per il numero di nucleoni (<i>A</i> = <i>Z</i> + <i>N</i>) si ottiene l'energia di legame media per ogni nucleone, il cui massimo valore si trova nel <a href="/wiki/Nichel" title="Nichel">nichel</a> 62.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Formula_semiempirica_di_Bethe-Weizsäcker"><span id="Formula_semiempirica_di_Bethe-Weizs.C3.A4cker"></span>Formula semiempirica di Bethe-Weizsäcker</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Energia_di_legame&veaction=edit&section=5" title="Modifica la sezione Formula semiempirica di Bethe-Weizsäcker" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Energia_di_legame&action=edit&section=5" title="Edit section's source code: Formula semiempirica di Bethe-Weizsäcker"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r130657691">body:not(.skin-minerva) .mw-parser-output .vedi-anche{font-size:95%}</style><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r139142988"> <div class="hatnote noprint vedi-anche"> <div class="hatnote-content"><span class="noviewer hatnote-icon" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/87/Magnifying_glass_icon_mgx2.svg/18px-Magnifying_glass_icon_mgx2.svg.png" decoding="async" width="18" height="18" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/87/Magnifying_glass_icon_mgx2.svg/27px-Magnifying_glass_icon_mgx2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/87/Magnifying_glass_icon_mgx2.svg/36px-Magnifying_glass_icon_mgx2.svg.png 2x" data-file-width="286" data-file-height="280" /></span></span> <span class="hatnote-text">Lo stesso argomento in dettaglio: <b><a href="/wiki/Formula_di_Weizs%C3%A4cker" title="Formula di Weizsäcker">Formula di Weizsäcker</a></b>.</span></div> </div> <p>Per un nucleo contenente A nucleoni, di cui Z protoni, esiste una formula semiempirica per l'energia di legame, dovuta al fisico <a href="/wiki/Carl_Friedrich_von_Weizs%C3%A4cker" title="Carl Friedrich von Weizsäcker">Carl Friedrich von Weizsäcker</a>: </p> <dl><dd><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\,A-b\,A^{2/3}-c\,{\frac {Z(Z-1)}{A^{1/3}}}-d\,{\frac {(A-2Z)^{2}}{A}}\pm {\frac {e}{A^{3/4}}}}"> <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>a</mi> <mspace width="thinmathspace" /> <mi>A</mi> <mo>−</mo> <mi>b</mi> <mspace width="thinmathspace" /> <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> <mi>c</mi> <mspace width="thinmathspace" /> <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> <mi>d</mi> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo stretchy="false">(</mo> <mi>A</mi> <mo>−</mo> <mn>2</mn> <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> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>e</mi> <msup> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>4</mn> </mrow> </msup> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{B}=a\,A-b\,A^{2/3}-c\,{\frac {Z(Z-1)}{A^{1/3}}}-d\,{\frac {(A-2Z)^{2}}{A}}\pm {\frac {e}{A^{3/4}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cbfabc24650f8369bc861153ac0adf704d1c3e19" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:56.25ex; height:6.176ex;" alt="{\displaystyle E_{B}=a\,A-b\,A^{2/3}-c\,{\frac {Z(Z-1)}{A^{1/3}}}-d\,{\frac {(A-2Z)^{2}}{A}}\pm {\frac {e}{A^{3/4}}}}"></span></dd></dl> <p>dove l'energia di legame <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}>0}"> <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> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{B}>0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/33dc3e8f2c6527ac649e523cdd19b607a68ca0d2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.456ex; height:2.509ex;" alt="{\displaystyle E_{B}>0}"></span> (vedi nota successiva) è misurata in <a href="/wiki/MeV" class="mw-redirect" title="MeV">MeV</a> per i seguenti valori delle costanti:<br /> </p> <dl><dd><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=14.0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mo>=</mo> <mn>14.0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a=14.0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c3982295d6eae0880a111b4b0486349d5f989440" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:8.462ex; height:2.176ex;" alt="{\displaystyle a=14.0}"></span> <br /></dd> <dd><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 b=13.0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>b</mi> <mo>=</mo> <mn>13.0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b=13.0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9b4e35310b0a83a79dce56c1ac044f4f1654a1ec" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:8.23ex; height:2.176ex;" alt="{\displaystyle b=13.0}"></span> <br /></dd> <dd><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=0.585}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>c</mi> <mo>=</mo> <mn>0.585</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c=0.585}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/78e8d5861e9bc461cc56837577ccdd4587a8f7ea" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:9.402ex; height:2.176ex;" alt="{\displaystyle c=0.585}"></span> <br /></dd> <dd><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 d=19.3}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mo>=</mo> <mn>19.3</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d=19.3}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af8a06f8b3484197877214fb735309fcd4805406" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:8.449ex; height:2.176ex;" alt="{\displaystyle d=19.3}"></span> <br /></dd> <dd><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=12.0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>e</mi> <mo>=</mo> <mn>12.0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle e=12.0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/78bf68dac4c83edebdbd2ae9d6c6438d19520e8d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:8.316ex; height:2.176ex;" alt="{\displaystyle e=12.0}"></span></dd></dl> <p>Il primo termine rappresenta l'energia dovuta all'interazione tra due nucleoni vicini, il secondo termine, proporzionale alla superficie del nucleo, è una correzione al primo, il terzo è dovuto alla repulsione elettrostatica, il quarto tiene conto della stabilità del nucleo dovuta alla simmetria tra protoni e neutroni, mentre l'ultimo termine è dato dal "pairing" degli spin, ed è dato da: </p> <dl><dd><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 _{o}={\frac {e}{A^{3/4}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>o</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>e</mi> <msup> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>4</mn> </mrow> </msup> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \delta _{o}={\frac {e}{A^{3/4}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9720cb3e01316d74a0e5c0ced7071a2e2fed63b7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:10.438ex; height:5.009ex;" alt="{\displaystyle \delta _{o}={\frac {e}{A^{3/4}}}}"></span></dd></dl> <p>con </p> <dl><dd><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 (A,Z)={\begin{cases}+\delta _{o}&Z,N{\mbox{ pari }}(A{\mbox{ pari }})\\~~~0&A{\mbox{ dispari }}\\-\delta _{o}&Z,N{\mbox{ dispari }}(A{\mbox{ pari }})\end{cases}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>δ</mi> <mo stretchy="false">(</mo> <mi>A</mi> <mo>,</mo> <mi>Z</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>{</mo> <mtable columnalign="left left" rowspacing=".2em" columnspacing="1em" displaystyle="false"> <mtr> <mtd> <mo>+</mo> <msub> <mi>δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>o</mi> </mrow> </msub> </mtd> <mtd> <mi>Z</mi> <mo>,</mo> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext> pari </mtext> </mstyle> </mrow> <mo stretchy="false">(</mo> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext> pari </mtext> </mstyle> </mrow> <mo stretchy="false">)</mo> </mtd> </mtr> <mtr> <mtd> <mtext> </mtext> <mtext> </mtext> <mtext> </mtext> <mn>0</mn> </mtd> <mtd> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext> dispari </mtext> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mo>−</mo> <msub> <mi>δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>o</mi> </mrow> </msub> </mtd> <mtd> <mi>Z</mi> <mo>,</mo> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext> dispari </mtext> </mstyle> </mrow> <mo stretchy="false">(</mo> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext> pari </mtext> </mstyle> </mrow> <mo stretchy="false">)</mo> </mtd> </mtr> </mtable> <mo fence="true" stretchy="true" symmetric="true"></mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \delta (A,Z)={\begin{cases}+\delta _{o}&Z,N{\mbox{ pari }}(A{\mbox{ pari }})\\~~~0&A{\mbox{ dispari }}\\-\delta _{o}&Z,N{\mbox{ dispari }}(A{\mbox{ pari }})\end{cases}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/148ff68c09e3c6388540b710301cd2687d4df6d4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.671ex; width:40.959ex; height:8.509ex;" alt="{\displaystyle \delta (A,Z)={\begin{cases}+\delta _{o}&Z,N{\mbox{ pari }}(A{\mbox{ pari }})\\~~~0&A{\mbox{ dispari }}\\-\delta _{o}&Z,N{\mbox{ dispari }}(A{\mbox{ pari }})\end{cases}}}"></span></dd></dl> <p>Secondo una convenzione usata in <a href="/wiki/Fisica_nucleare" title="Fisica nucleare">fisica nucleare</a>, la formula di Bethe-Weizsäcker calcola un <i>valore positivo</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 E_{B}>0}"> <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> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{B}>0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/33dc3e8f2c6527ac649e523cdd19b607a68ca0d2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.456ex; height:2.509ex;" alt="{\displaystyle E_{B}>0}"></span>) dell'energia di legame <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/2b71d40b28612bb3f7578929558cccef2bb5798d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.195ex; height:2.509ex;" alt="{\displaystyle E_{B}}"></span>. La massa di un nucleo atomico è in questo caso data da: </p> <dl><dd><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_{nucleo}=Z\cdot m_{protone}+N\cdot m_{neutrone}-{\frac {E_{B}}{c^{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mi>u</mi> <mi>c</mi> <mi>l</mi> <mi>e</mi> <mi>o</mi> </mrow> </msub> <mo>=</mo> <mi>Z</mi> <mo>⋅</mo> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> <mi>r</mi> <mi>o</mi> <mi>t</mi> <mi>o</mi> <mi>n</mi> <mi>e</mi> </mrow> </msub> <mo>+</mo> <mi>N</mi> <mo>⋅</mo> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mi>e</mi> <mi>u</mi> <mi>t</mi> <mi>r</mi> <mi>o</mi> <mi>n</mi> <mi>e</mi> </mrow> </msub> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle M_{nucleo}=Z\cdot m_{protone}+N\cdot m_{neutrone}-{\frac {E_{B}}{c^{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f66565c1418e6fc0445eda71cac993b1e364a06c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:43.723ex; height:5.509ex;" alt="{\displaystyle M_{nucleo}=Z\cdot m_{protone}+N\cdot m_{neutrone}-{\frac {E_{B}}{c^{2}}}}"></span></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Masse_ed_energie_atomiche_e_nucleari">Masse ed energie atomiche e nucleari</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Energia_di_legame&veaction=edit&section=6" title="Modifica la sezione Masse ed energie atomiche e nucleari" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Energia_di_legame&action=edit&section=6" title="Edit section's source code: Masse ed energie atomiche e nucleari"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Sperimentalmente, dati i valori </p> <ul><li>m<sub>p</sub> = 938,2723 MeV/c<sup>2</sup></li> <li>m<sub>e</sub> = 0,5110 MeV/c<sup>2</sup></li> <li>m<sub>n</sub> = 939,5656 MeV/c<sup>2</sup></li> <li>1 u = 1 <a href="/wiki/Unit%C3%A0_di_massa_atomica" title="Unità di massa atomica">uma</a> = 931,494028(±0.000023) MeV/c<sup>2</sup></li></ul> <p>per i nuclei la cui energia di legame è maggiore si sono trovati i seguenti risultati: </p> <table class="wikitable"> <tbody><tr> <th>nucleo</th> <th>P</th> <th>N</th> <th>eccesso di massa<sup id="cite_ref-me_4-0" class="reference"><a href="#cite_note-me-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup></th> <th>massa totale</th> <th>massa totale / A</th> <th>energia di legame totale / A</th> <th>difetto di massa</th> <th>energia di legame</th> <th>energia di legame / A </th></tr> <tr> <td><a href="/wiki/Ferro" title="Ferro"><sup>56</sup>Fe</a></td> <td>26</td> <td>30</td> <td>-60.6054 MeV</td> <td>55.934937 u</td> <td>0.9988382 u</td> <td>9.1538 MeV</td> <td>0.528479 u</td> <td>492.275 MeV</td> <td>8.7906 MeV </td></tr> <tr> <td><sup>58</sup>Fe</td> <td>26</td> <td>32</td> <td>-62.1534 MeV</td> <td>57.933276 u</td> <td>0.9988496 u</td> <td>9.1432 MeV</td> <td>0.547471 u</td> <td>509.966 MeV</td> <td>8.7925 MeV </td></tr> <tr> <td><a href="/wiki/Nichel" title="Nichel"><sup>60</sup>Ni</a></td> <td>28</td> <td>32</td> <td>-64.4721 MeV</td> <td>59.930786 u</td> <td>0.9988464 u</td> <td>9.1462 MeV</td> <td>0.565612 u</td> <td>526.864 MeV</td> <td>8.7811 MeV </td></tr> <tr> <td><sup>62</sup>Ni</td> <td>28</td> <td>34</td> <td>-66.7461 MeV</td> <td>61.928345 u</td> <td>0.9988443 u</td> <td>9.1481 MeV</td> <td>0.585383 u</td> <td>545.281 MeV</td> <td>8.7948 MeV </td></tr></tbody></table> <p>Per alcuni nuclei leggeri, inoltre, si ha: </p> <table class="wikitable"> <tbody><tr> <th>nucleo</th> <th>P</th> <th>N</th> <th>eccesso di massa<sup id="cite_ref-me_4-1" class="reference"><a href="#cite_note-me-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup></th> <th>massa totale</th> <th>massa totale / A</th> <th>energia di legame totale / A</th> <th>difetto di massa</th> <th>energia di legame</th> <th>energia di legame / A </th></tr> <tr> <td><a href="/wiki/Neutrone" title="Neutrone">n</a></td> <td>0</td> <td>1</td> <td>8.0716 MeV</td> <td>1.008665 u</td> <td>1.008665 u</td> <td>0.0000 MeV</td> <td>0 u</td> <td>0 MeV</td> <td>0 MeV </td></tr> <tr> <td><a href="/wiki/Idrogeno" title="Idrogeno"><sup>1</sup>H</a></td> <td>1</td> <td>0</td> <td>7.2890 MeV</td> <td>1.007825 u</td> <td>1.007825 u</td> <td>0.7826 MeV</td> <td>0.0000000146 u</td> <td>0.0000136 MeV</td> <td>13.6 eV </td></tr> <tr> <td><a href="/wiki/Deuterio" title="Deuterio"><sup>2</sup>H</a></td> <td>1</td> <td>1</td> <td>13.13572 MeV</td> <td>2.014102 u</td> <td>1.007051 u</td> <td>1.50346 MeV</td> <td>0.002388 u</td> <td>2.22452 MeV</td> <td>1.11226 MeV </td></tr> <tr> <td><a href="/wiki/Trizio" title="Trizio"><sup>3</sup>H</a></td> <td>1</td> <td>2</td> <td>14.9498 MeV</td> <td>3.016049 u</td> <td>1.005350 u</td> <td>3.08815 MeV</td> <td>0.0091058 u</td> <td>8.4820 MeV</td> <td>2.8273 MeV </td></tr> <tr> <td><a href="/wiki/Elio" title="Elio"><sup>3</sup>He</a></td> <td>2</td> <td>1</td> <td>14.9312 MeV</td> <td>3.016029 u</td> <td>1.005343 u</td> <td>3.09433 MeV</td> <td>0.0082857 u</td> <td>7.7181 MeV</td> <td>2.5727 MeV </td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="Note">Note</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Energia_di_legame&veaction=edit&section=7" title="Modifica la sezione Note" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Energia_di_legame&action=edit&section=7" title="Edit section's source code: Note"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><a href="#cite_ref-1"><b>^</b></a> <span class="reference-text"><cite class="citation web" style="font-style:normal"> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20200411221513/https://www.chimicamo.org/chimica-fisica/energia-di-legame.html"><span style="font-style:italic;">Energia di legame</span></a>, su <span style="font-style:italic;">chimicamo.org</span>. <small>URL consultato l'11 aprile 2020</small> <small>(archiviato dall'<abbr title="https://www.chimicamo.org/chimica-fisica/energia-di-legame.html">url originale</abbr> l'11 aprile 2020)</small>.</cite></span> </li> <li id="cite_note-2"><a href="#cite_ref-2"><b>^</b></a> <span class="reference-text"><cite class="citation libro" style="font-style:normal"> R. Eisberg, R. Resnick, <a rel="nofollow" class="external text" href="https://archive.org/details/quantumphysicsof0000eisb"><span style="font-style:italic;">Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles</span></a>, John Wiley & Sons, New York 1985<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"> <msup> <mi></mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </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/3abccdd2a8344117c797bb9b8cb39fe082fdf14b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.171ex; width:1.054ex; height:2.509ex;" alt="{\displaystyle ^{2}}"></span>, p. 524, <a href="/wiki/ISBN" title="ISBN">ISBN</a> <a href="/wiki/Speciale:RicercaISBN/047187373X" title="Speciale:RicercaISBN/047187373X">047187373X</a>.</cite></span> </li> <li id="cite_note-3"><a href="#cite_ref-3"><b>^</b></a> <span class="reference-text"><cite class="citation pubblicazione" style="font-style:normal"> M. P. Fewell, <a rel="nofollow" class="external text" href="http://adsabs.harvard.edu/abs/1995AmJPh..63..653F"><span style="font-style:italic;">The atomic nuclide with the highest mean binding energy</span></a>, in <span style="font-style:italic;">American Journal of Physics</span>, vol. 63, n. 7, 1995, pp. 653–658, <a href="/wiki/Digital_object_identifier" title="Digital object identifier">DOI</a>:<a rel="nofollow" class="external text" href="https://dx.doi.org/10.1119%2F1.17828">10.1119/1.17828</a>.</cite></span> </li> <li id="cite_note-me-4"><span class="mw-cite-backlink"><b>^</b> <sup><i><a href="#cite_ref-me_4-0">a</a></i></sup> <sup><i><a href="#cite_ref-me_4-1">b</a></i></sup></span> <span class="reference-text">Jagdish K. Tuli, Nuclear Wallet Cards, 7th edition, April 2005, Brookhaven National Laboratory, US National Nuclear Data Center.</span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="Altri_progetti">Altri progetti</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Energia_di_legame&veaction=edit&section=8" title="Modifica la sezione Altri progetti" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Energia_di_legame&action=edit&section=8" title="Edit section's source code: Altri progetti"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <div id="interProject" class="toccolours" style="display: none; clear: both; margin-top: 2em"><p id="sisterProjects" style="background-color: #efefef; color: black; font-weight: bold; margin: 0"><span>Altri progetti</span></p><ul title="Collegamenti verso gli altri progetti Wikimedia"> <li class="" title=""><a href="https://it.wiktionary.org/wiki/energia_di_legame" class="extiw" title="wikt:energia di legame">Wikizionario</a></li></ul></div> <ul><li><span typeof="mw:File"><a href="https://it.wiktionary.org/wiki/" title="Collabora a Wikizionario"><img alt="Collabora a Wikizionario" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f9/Wiktionary_small.svg/18px-Wiktionary_small.svg.png" decoding="async" width="18" height="18" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f9/Wiktionary_small.svg/27px-Wiktionary_small.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f9/Wiktionary_small.svg/36px-Wiktionary_small.svg.png 2x" data-file-width="350" data-file-height="350" /></a></span> <a href="https://it.wiktionary.org/wiki/" class="extiw" title="wikt:">Wikizionario</a> contiene il lemma di dizionario «<b><a href="https://it.wiktionary.org/wiki/energia_di_legame" class="extiw" title="wikt:energia di legame">energia di legame</a></b>»</li></ul> <div class="mw-heading mw-heading2"><h2 id="Collegamenti_esterni">Collegamenti esterni</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Energia_di_legame&veaction=edit&section=9" title="Modifica la sezione Collegamenti esterni" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Energia_di_legame&action=edit&section=9" title="Edit section's source code: Collegamenti esterni"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li class="mw-empty-elt"></li> <li><cite id="CITEREFBritannica.com" class="citation web" style="font-style:normal">(<span style="font-weight:bolder; font-size:80%"><abbr title="inglese">EN</abbr></span>) <a rel="nofollow" class="external text" href="https://www.britannica.com/science/binding-energy"><span style="font-style:italic;">binding energy</span></a>, su <span style="font-style:italic;"><a href="/wiki/Enciclopedia_Britannica" title="Enciclopedia Britannica">Enciclopedia Britannica</a></span>, Encyclopædia Britannica, Inc.</cite> <span class="mw-valign-text-top noprint" typeof="mw:File/Frameless"><a href="https://www.wikidata.org/wiki/Q420754#P1417" title="Modifica su Wikidata"><img alt="Modifica su Wikidata" src="//upload.wikimedia.org/wikipedia/commons/thumb/7/73/Blue_pencil.svg/10px-Blue_pencil.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/73/Blue_pencil.svg/15px-Blue_pencil.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/73/Blue_pencil.svg/20px-Blue_pencil.svg.png 2x" data-file-width="600" data-file-height="600" /></a></span></li> <li><cite class="citation web" style="font-style:normal"> <a rel="nofollow" class="external text" href="http://goldbook.iupac.org/BT07002.html"><span style="font-style:italic;">IUPAC Gold Book, "bond energy in theoretical chemistry"</span></a>, su <span style="font-style:italic;">goldbook.iupac.org</span>.</cite></li></ul> <style data-mw-deduplicate="TemplateStyles:r141815314">.mw-parser-output .navbox{border:1px solid #aaa;clear:both;margin:auto;padding:2px;width:100%}.mw-parser-output .navbox th{padding-left:1em;padding-right:1em;text-align:center}.mw-parser-output .navbox>tbody>tr:first-child>th{background:#ccf;font-size:90%;width:100%;color:var(--color-base,black)}.mw-parser-output .navbox_navbar{float:left;margin:0;padding:0 10px 0 0;text-align:left;width:6em}.mw-parser-output .navbox_title{font-size:110%}.mw-parser-output .navbox_abovebelow{background:#ddf;font-size:90%;font-weight:normal}.mw-parser-output .navbox_group{background:#ddf;font-size:90%;padding:0 10px;white-space:nowrap}.mw-parser-output .navbox_list{font-size:90%;width:100%}.mw-parser-output .navbox_list a{white-space:nowrap}html:not(.vector-feature-night-mode-enabled) .mw-parser-output .navbox_odd{background:#fdfdfd;color:var(--color-base,black)}html:not(.vector-feature-night-mode-enabled) .mw-parser-output .navbox_even{background:#f7f7f7;color:var(--color-base,black)}.mw-parser-output .navbox a.mw-selflink{color:var(--color-base,black)}.mw-parser-output .navbox_center{text-align:center}.mw-parser-output .navbox .navbox_image{padding-left:7px;vertical-align:middle;width:0}.mw-parser-output .navbox+.navbox{margin-top:-1px}.mw-parser-output .navbox .mw-collapsible-toggle{font-weight:normal;text-align:right;width:7em}body.skin--responsive .mw-parser-output .navbox_image img{max-width:none!important}.mw-parser-output .subnavbox{margin:-3px;width:100%}.mw-parser-output .subnavbox_group{background:#e6e6ff;padding:0 10px}@media screen{html.skin-theme-clientpref-night .mw-parser-output .navbox>tbody>tr:first-child>th{background:var(--background-color-interactive)!important}html.skin-theme-clientpref-night .mw-parser-output .navbox th{color:var(--color-base)!important}html.skin-theme-clientpref-night .mw-parser-output .navbox_abovebelow,html.skin-theme-clientpref-night .mw-parser-output .navbox_group{background:var(--background-color-interactive-subtle)!important}html.skin-theme-clientpref-night .mw-parser-output .subnavbox_group{background:var(--background-color-neutral-subtle)!important}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbox>tbody>tr:first-child>th{background:var(--background-color-interactive)!important}html.skin-theme-clientpref-os .mw-parser-output .navbox th{color:var(--color-base)!important}html.skin-theme-clientpref-os .mw-parser-output .navbox_abovebelow,html.skin-theme-clientpref-os .mw-parser-output .navbox_group{background:var(--background-color-interactive-subtle)!important}html.skin-theme-clientpref-os .mw-parser-output .subnavbox_group{background:var(--background-color-neutral-subtle)!important}}</style><table class="navbox mw-collapsible mw-collapsed noprint metadata" id="navbox-Legami_chimici"><tbody><tr><th colspan="2"><div class="navbox_navbar"><div class="noprint plainlinks" style="background-color:transparent; 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