Efecte Compton - Viquipèdia, l'enciclopèdia lliure

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class="vector-dropdown-label-text">Aparença</span> </label> <div class="vector-dropdown-content"> <div id="vector-appearance-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <div id="p-vector-user-menu-notifications" 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-overflow" class="vector-menu mw-portlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" 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" 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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-Descobriment_i_rellevància_històrica" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Descobriment_i_rellevància_històrica"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Descobriment i rellevància històrica</span> </div> </a> <ul id="toc-Descobriment_i_rellevància_històrica-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Formulació_de_l'efecte_Compton" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Formulació_de_l'efecte_Compton"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Formulació de l'efecte Compton</span> </div> </a> <button aria-controls="toc-Formulació_de_l'efecte_Compton-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 Formulació de l'efecte Compton</span> </button> <ul id="toc-Formulació_de_l'efecte_Compton-sublist" class="vector-toc-list"> <li id="toc-Derivació" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Derivació"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Derivació</span> </div> </a> <ul id="toc-Derivació-sublist" class="vector-toc-list"> <li id="toc-Solució_(part_1)" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Solució_(part_1)"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1.1</span> <span>Solució (part 1)</span> </div> </a> <ul id="toc-Solució_(part_1)-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Solució_(part_2)" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Solució_(part_2)"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1.2</span> <span>Solució (part 2)</span> </div> </a> <ul id="toc-Solució_(part_2)-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Ajuntem" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Ajuntem"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1.3</span> <span>Ajuntem</span> </div> </a> <ul id="toc-Ajuntem-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> </ul> </li> <li id="toc-Efecte_Compton_invers" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Efecte_Compton_invers"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Efecte Compton invers</span> </div> </a> <ul id="toc-Efecte_Compton_invers-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Aplicacions" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Aplicacions"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Aplicacions</span> </div> </a> <button aria-controls="toc-Aplicacions-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 Aplicacions</span> </button> <ul id="toc-Aplicacions-sublist" class="vector-toc-list"> <li id="toc-Dispersió_Compton" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Dispersió_Compton"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Dispersió Compton</span> </div> </a> <ul id="toc-Dispersió_Compton-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Dispersió_magnètica_Compton" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Dispersió_magnètica_Compton"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>Dispersió magnètica Compton</span> </div> </a> <ul id="toc-Dispersió_magnètica_Compton-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Dispersió_Compton_inversa" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Dispersió_Compton_inversa"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.3</span> <span>Dispersió Compton inversa</span> </div> </a> <ul id="toc-Dispersió_Compton_inversa-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Dispersió_Compton_inversa_no_lineal" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Dispersió_Compton_inversa_no_lineal"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.4</span> <span>Dispersió Compton inversa no lineal</span> </div> </a> <ul id="toc-Dispersió_Compton_inversa_no_lineal-sublist" class="vector-toc-list"> </ul> </li> </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">5</span> <span>Vegeu també</span> </div> </a> <ul id="toc-Vegeu_també-sublist" class="vector-toc-list"> </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">6</span> <span>Referències</span> </div> </a> <ul id="toc-Referències-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Bibliografia" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Bibliografia"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Bibliografia</span> </div> </a> <ul id="toc-Bibliografia-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Enllaços_externs" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Enllaços_externs"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Enllaços externs</span> </div> </a> <ul id="toc-Enllaços_externs-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">Efecte Compton</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 59 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-59" 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">59 llengües</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%B8%D8%A7%D9%87%D8%B1%D8%A9_%D9%83%D9%88%D9%85%D8%A8%D8%AA%D9%88%D9%86" title="ظاهرة كومبتون - àrab" lang="ar" hreflang="ar" data-title="ظاهرة كومبتون" data-language-autonym="العربية" data-language-local-name="àrab" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Efeutu_Compton" title="Efeutu Compton - asturià" lang="ast" hreflang="ast" data-title="Efeutu Compton" 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/Kompton_effekti" title="Kompton effekti - azerbaidjanès" lang="az" hreflang="az" data-title="Kompton effekti" data-language-autonym="Azərbaycanca" data-language-local-name="azerbaidjanès" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%AD%D1%84%D0%B5%D0%BA%D1%82_%D0%9A%D0%BE%D0%BC%D0%BF%D1%82%D0%B0%D0%BD%D0%B0" title="Эфект Комптана - belarús" lang="be" hreflang="be" data-title="Эфект Комптана" data-language-autonym="Беларуская" data-language-local-name="belarús" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%95%D1%84%D0%B5%D0%BA%D1%82_%D0%BD%D0%B0_%D0%9A%D0%BE%D0%BC%D0%BF%D1%82%D1%8A%D0%BD" title="Ефект на Комптън - búlgar" lang="bg" hreflang="bg" data-title="Ефект на Комптън" data-language-autonym="Български" data-language-local-name="búlgar" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D8%AF%DB%8C%D8%A7%D8%B1%D8%AF%DB%95%DB%8C_%D9%BE%DB%95%D8%B1%D8%B4%D8%A8%D9%88%D9%88%D9%86%DB%95%D9%88%DB%95%DB%8C_%DA%A9%DB%86%D9%85%D9%BE%D8%AA%D9%86" title="دیاردەی پەرشبوونەوەی کۆمپتن - kurd central" lang="ckb" hreflang="ckb" data-title="دیاردەی پەرشبوونەوەی کۆمپتن" data-language-autonym="کوردی" data-language-local-name="kurd central" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Compton%C5%AFv_jev" title="Comptonův jev - txec" lang="cs" hreflang="cs" data-title="Comptonův jev" data-language-autonym="Čeština" data-language-local-name="txec" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Compton-Effekt" title="Compton-Effekt - alemany" lang="de" hreflang="de" data-title="Compton-Effekt" data-language-autonym="Deutsch" data-language-local-name="alemany" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el badge-Q70894304 mw-list-item" title=""><a href="https://el.wikipedia.org/wiki/%CE%A6%CE%B1%CE%B9%CE%BD%CF%8C%CE%BC%CE%B5%CE%BD%CE%BF_%CE%9A%CF%8C%CE%BC%CF%80%CF%84%CE%BF%CE%BD" title="Φαινόμενο Κόμπτον - grec" lang="el" hreflang="el" data-title="Φαινόμενο Κόμπτον" data-language-autonym="Ελληνικά" data-language-local-name="grec" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en badge-Q70894304 mw-list-item" title=""><a href="https://en.wikipedia.org/wiki/Compton_Effect" title="Compton Effect - anglès" lang="en" hreflang="en" data-title="Compton Effect" 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/Kompton-efiko" title="Kompton-efiko - esperanto" lang="eo" hreflang="eo" data-title="Kompton-efiko" 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/Efecto_Compton" title="Efecto Compton - espanyol" lang="es" hreflang="es" data-title="Efecto Compton" data-language-autonym="Español" data-language-local-name="espanyol" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et badge-Q70894304 mw-list-item" title=""><a href="https://et.wikipedia.org/wiki/Comptoni_efekt" title="Comptoni efekt - estonià" lang="et" hreflang="et" data-title="Comptoni efekt" 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/Compton_efektua" title="Compton efektua - basc" lang="eu" hreflang="eu" data-title="Compton efektua" 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/%D8%A7%D8%AB%D8%B1_%DA%A9%D8%A7%D9%85%D9%BE%D8%AA%D9%88%D9%86" title="اثر کامپتون - persa" lang="fa" hreflang="fa" data-title="اثر کامپتون" 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/Comptonin_ilmi%C3%B6" title="Comptonin ilmiö - finès" lang="fi" hreflang="fi" data-title="Comptonin ilmiö" data-language-autonym="Suomi" data-language-local-name="finès" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr badge-Q70894304 mw-list-item" title=""><a href="https://fr.wikipedia.org/wiki/Effet_Compton" title="Effet Compton - francès" lang="fr" hreflang="fr" data-title="Effet Compton" data-language-autonym="Français" data-language-local-name="francès" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Efecto_Compton" title="Efecto Compton - gallec" lang="gl" hreflang="gl" data-title="Efecto Compton" 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%90%D7%A4%D7%A7%D7%98_%D7%A7%D7%95%D7%9E%D7%A4%D7%98%D7%95%D7%9F" title="אפקט קומפטון - hebreu" lang="he" hreflang="he" data-title="אפקט קומפטון" 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%95%E0%A5%89%E0%A4%AE%E0%A5%8D%E0%A4%AA%E0%A4%9F%E0%A4%A8_%E0%A4%AA%E0%A5%8D%E0%A4%B0%E0%A4%AD%E0%A4%BE%E0%A4%B5" title="कॉम्पटन प्रभाव - hindi" lang="hi" hreflang="hi" data-title="कॉम्पटन प्रभाव" 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/Comptonov_u%C4%8Dinak" title="Comptonov učinak - croat" lang="hr" hreflang="hr" data-title="Comptonov učinak" data-language-autonym="Hrvatski" data-language-local-name="croat" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-hu badge-Q70894304 mw-list-item" title=""><a href="https://hu.wikipedia.org/wiki/Compton-hat%C3%A1s" title="Compton-hatás - hongarès" lang="hu" hreflang="hu" data-title="Compton-hatás" 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%94%D5%B8%D5%B4%D6%83%D5%A9%D5%B8%D5%B6%D5%AB_%D5%A7%D6%86%D5%A5%D5%AF%D5%BF" title="Քոմփթոնի էֆեկտ - armeni" lang="hy" hreflang="hy" data-title="Քոմփթոնի էֆեկտ" data-language-autonym="Հայերեն" data-language-local-name="armeni" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-id badge-Q70894304 mw-list-item" title=""><a href="https://id.wikipedia.org/wiki/Efek_Compton" title="Efek Compton - indonesi" lang="id" hreflang="id" data-title="Efek Compton" 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-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Effetto_Compton" title="Effetto Compton - italià" lang="it" hreflang="it" data-title="Effetto Compton" 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/%E3%82%B3%E3%83%B3%E3%83%97%E3%83%88%E3%83%B3%E5%8A%B9%E6%9E%9C" title="コンプトン効果 - japonès" lang="ja" hreflang="ja" data-title="コンプトン効果" 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-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%99%E1%83%9D%E1%83%9B%E1%83%9E%E1%83%A2%E1%83%9D%E1%83%9C%E1%83%98%E1%83%A1_%E1%83%94%E1%83%A4%E1%83%94%E1%83%A5%E1%83%A2%E1%83%98" title="კომპტონის ეფექტი - georgià" lang="ka" hreflang="ka" data-title="კომპტონის ეფექტი" data-language-autonym="ქართული" data-language-local-name="georgià" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%9A%D0%BE%D0%BC%D0%BF%D1%82%D0%BE%D0%BD_%D1%8D%D1%84%D1%84%D0%B5%D0%BA%D1%82%D1%96%D1%81%D1%96" title="Комптон эффектісі - kazakh" lang="kk" hreflang="kk" data-title="Комптон эффектісі" data-language-autonym="Қазақша" data-language-local-name="kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ko badge-Q70894304 mw-list-item" title=""><a href="https://ko.wikipedia.org/wiki/%EC%BD%A4%ED%94%84%ED%84%B4_%ED%9A%A8%EA%B3%BC" title="콤프턴 효과 - coreà" lang="ko" hreflang="ko" data-title="콤프턴 효과" data-language-autonym="한국어" data-language-local-name="coreà" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-lt badge-Q70894304 mw-list-item" title=""><a href="https://lt.wikipedia.org/wiki/Komptono_efektas" title="Komptono efektas - lituà" lang="lt" hreflang="lt" data-title="Komptono efektas" 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/Komptona_efekts" title="Komptona efekts - letó" lang="lv" hreflang="lv" data-title="Komptona efekts" data-language-autonym="Latviešu" data-language-local-name="letó" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%9A%D0%BE%D0%BC%D0%BF%D1%82%D0%BE%D0%BD%D0%BE%D0%B2_%D0%B5%D1%84%D0%B5%D0%BA%D1%82" title="Комптонов ефект - macedoni" lang="mk" hreflang="mk" data-title="Комптонов ефект" 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%95%E0%B5%8B%E0%B4%82%E2%80%8C%E0%B4%AA%E0%B5%8D%E0%B4%B1%E0%B5%8D%E0%B4%B1%E0%B5%BA_%E0%B4%AA%E0%B5%8D%E0%B4%B0%E0%B4%A4%E0%B4%BF%E0%B4%AD%E0%B4%BE%E0%B4%B8%E0%B4%82" title="കോം‌പ്റ്റൺ പ്രതിഭാസം - malaiàlam" lang="ml" hreflang="ml" data-title="കോം‌പ്റ്റൺ പ്രതിഭാസം" data-language-autonym="മലയാളം" data-language-local-name="malaiàlam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Compton-effect" title="Compton-effect - neerlandès" lang="nl" hreflang="nl" data-title="Compton-effect" 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/Comptoneffekt" title="Comptoneffekt - noruec nynorsk" lang="nn" hreflang="nn" data-title="Comptoneffekt" 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 badge-Q70894304 mw-list-item" title=""><a href="https://no.wikipedia.org/wiki/Comptoneffekten" title="Comptoneffekten - noruec bokmål" lang="nb" hreflang="nb" data-title="Comptoneffekten" 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-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Zjawisko_Comptona" title="Zjawisko Comptona - polonès" lang="pl" hreflang="pl" data-title="Zjawisko Comptona" data-language-autonym="Polski" data-language-local-name="polonès" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/Efet_Compton" title="Efet Compton - piemontès" lang="pms" hreflang="pms" data-title="Efet Compton" data-language-autonym="Piemontèis" data-language-local-name="piemontès" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%D8%A7%D8%AB%D8%B1_%DA%A9%D9%88%D9%85%D9%BE%D9%B9%D9%86" title="اثر کومپٹن - Western Punjabi" lang="pnb" hreflang="pnb" data-title="اثر کومپٹن" 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/Efeito_Compton" title="Efeito Compton - portuguès" lang="pt" hreflang="pt" data-title="Efeito Compton" data-language-autonym="Português" data-language-local-name="portuguès" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro badge-Q70894304 mw-list-item" title=""><a href="https://ro.wikipedia.org/wiki/Efectul_Compton" title="Efectul Compton - romanès" lang="ro" hreflang="ro" data-title="Efectul Compton" 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%AD%D1%84%D1%84%D0%B5%D0%BA%D1%82_%D0%9A%D0%BE%D0%BC%D0%BF%D1%82%D0%BE%D0%BD%D0%B0" title="Эффект Комптона - rus" lang="ru" hreflang="ru" data-title="Эффект Комптона" data-language-autonym="Русский" data-language-local-name="rus" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Comptonov_efekat" title="Comptonov efekat - serbocroat" lang="sh" hreflang="sh" data-title="Comptonov efekat" 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 badge-Q70894304 mw-list-item" title=""><a href="https://simple.wikipedia.org/wiki/Compton_effect" title="Compton effect - Simple English" lang="en-simple" hreflang="en-simple" data-title="Compton effect" 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/Comptonov_jav" title="Comptonov jav - eslovac" lang="sk" hreflang="sk" data-title="Comptonov jav" data-language-autonym="Slovenčina" data-language-local-name="eslovac" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-skr mw-list-item"><a href="https://skr.wikipedia.org/wiki/%DA%A9%D9%88%D9%85%D9%BE%D9%B9%D9%86_%D8%A7%DB%8C%D9%81%DB%8C%DA%A9%D9%B9" title="کومپٹن ایفیکٹ - Saraiki" lang="skr" hreflang="skr" data-title="کومپٹن ایفیکٹ" data-language-autonym="سرائیکی" data-language-local-name="Saraiki" class="interlanguage-link-target"><span>سرائیکی</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Comptonov_pojav" title="Comptonov pojav - eslovè" lang="sl" hreflang="sl" data-title="Comptonov pojav" 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/Efekti_i_Komptonit" title="Efekti i Komptonit - albanès" lang="sq" hreflang="sq" data-title="Efekti i Komptonit" 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%9A%D0%BE%D0%BC%D0%BF%D1%82%D0%BE%D0%BD%D0%BE%D0%B2_%D0%B5%D1%84%D0%B5%D0%BA%D0%B0%D1%82" title="Комптонов ефекат - serbi" lang="sr" hreflang="sr" data-title="Комптонов ефекат" 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-sv badge-Q70894304 mw-list-item" title=""><a href="https://sv.wikipedia.org/wiki/Comptoneffekt" title="Comptoneffekt - suec" lang="sv" hreflang="sv" data-title="Comptoneffekt" data-language-autonym="Svenska" data-language-local-name="suec" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta badge-Q70894304 mw-list-item" title=""><a href="https://ta.wikipedia.org/wiki/%E0%AE%95%E0%AE%BE%E0%AE%AE%E0%AF%8D%E0%AE%AA%E0%AF%8D%E0%AE%9F%E0%AE%A9%E0%AF%8D_%E0%AE%B5%E0%AE%BF%E0%AE%B3%E0%AF%88%E0%AE%B5%E0%AF%81" title="காம்ப்டன் விளைவு - tàmil" lang="ta" hreflang="ta" data-title="காம்ப்டன் விளைவு" data-language-autonym="தமிழ்" data-language-local-name="tàmil" 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%9B%E0%B8%A3%E0%B8%B2%E0%B8%81%E0%B8%8F%E0%B8%81%E0%B8%B2%E0%B8%A3%E0%B8%93%E0%B9%8C%E0%B8%84%E0%B8%AD%E0%B8%A1%E0%B8%9B%E0%B9%8C%E0%B8%95%E0%B8%B1%E0%B8%99" title="ปรากฏการณ์คอมป์ตัน - tai" lang="th" hreflang="th" data-title="ปรากฏการณ์คอมป์ตัน" data-language-autonym="ไทย" data-language-local-name="tai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr badge-Q70894304 mw-list-item" title=""><a href="https://tr.wikipedia.org/wiki/Compton_olay%C4%B1" title="Compton olayı - turc" lang="tr" hreflang="tr" data-title="Compton olayı" data-language-autonym="Türkçe" data-language-local-name="turc" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/%D0%9A%D0%BE%D0%BC%D0%BF%D1%82%D0%BE%D0%BD_%D1%8D%D1%84%D1%84%D0%B5%D0%BA%D1%82%D1%8B" title="Комптон эффекты - tàtar" lang="tt" hreflang="tt" data-title="Комптон эффекты" data-language-autonym="Татарча / tatarça" data-language-local-name="tàtar" class="interlanguage-link-target"><span>Татарча / tatarça</span></a></li><li class="interlanguage-link interwiki-uk badge-Q70894304 mw-list-item" title=""><a href="https://uk.wikipedia.org/wiki/%D0%95%D1%84%D0%B5%D0%BA%D1%82_%D0%9A%D0%BE%D0%BC%D0%BF%D1%82%D0%BE%D0%BD%D0%B0" title="Ефект Комптона - ucraïnès" lang="uk" hreflang="uk" data-title="Ефект Комптона" 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/%DA%A9%D8%A7%D9%85%D9%BE%D9%B9%D9%86_%D8%A7%D8%AB%D8%B1" title="کامپٹن اثر - urdú" lang="ur" hreflang="ur" data-title="کامپٹن اثر" 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/Kompton_effekti" title="Kompton effekti - uzbek" lang="uz" hreflang="uz" data-title="Kompton effekti" 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/Hi%E1%BB%87u_%E1%BB%A9ng_Compton" title="Hiệu ứng Compton - vietnamita" lang="vi" hreflang="vi" data-title="Hiệu ứng Compton" 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-zh badge-Q70894304 mw-list-item" title=""><a href="https://zh.wikipedia.org/wiki/%E5%BA%B7%E6%99%AE%E9%A0%93%E6%95%88%E6%87%89" title="康普頓效應 - xinès" lang="zh" hreflang="zh" data-title="康普頓效應" data-language-autonym="中文" data-language-local-name="xinès" 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/Q171516#sitelinks-wikipedia" title="Modifica enllaços interlingües" class="wbc-editpage">Modifica els enllaços</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Espais de noms"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Efecte_Compton" title="Vegeu el contingut de la pàgina [c]" accesskey="c"><span>Pàgina</span></a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a href="/wiki/Discussi%C3%B3:Efecte_Compton" 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</nav> </div> </div> <div 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">De la Viquipèdia, l'enciclopèdia lliure</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="ca" dir="ltr"><figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Fitxer:Compton-effekt1.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Compton-effekt1.png/220px-Compton-effekt1.png" decoding="async" width="220" height="184" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Compton-effekt1.png/330px-Compton-effekt1.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Compton-effekt1.png/440px-Compton-effekt1.png 2x" data-file-width="600" data-file-height="502" /></a><figcaption>Efecte Compton d'un fotó sobre un electró lligat a un nucli</figcaption></figure> <p>En <a href="/wiki/Mec%C3%A0nica_qu%C3%A0ntica" title="Mecànica quàntica">mecànica quàntica</a>, l'<b>efecte Compton</b> és l'augment de la <a href="/wiki/Longitud_d%27ona" title="Longitud d'ona">longitud d'ona</a>, que comporta una disminució de la serva <a href="/wiki/Energia" title="Energia">energia</a>, d'un fotó en col·lidir amb un <a href="/wiki/Electr%C3%B3" title="Electró">electró</a>. És a dir, l'augment de la longitud d'ona de la radiació electromagnètica de les bandes dels <a href="/wiki/Raigs_X" class="mw-redirect" title="Raigs X">raigs X</a> i <a href="/wiki/Raigs_gamma" class="mw-redirect" title="Raigs gamma">raigs gamma</a> de l'<a href="/wiki/Espectre" title="Espectre">espectre</a> en ser dispersats en xocar amb els electrons menys lligats als <a href="/wiki/%C3%80tom" title="Àtom">àtoms</a>. Va ser observat per primer cop l'any 1923 pel físic estatunidenc <a href="/wiki/Arthur_Holly_Compton" title="Arthur Holly Compton">Arthur Holly Compton</a> (1892 - 1962) i independentment pel també estatunidenc d'origen neerlandès <a href="/wiki/Peter_Debye" title="Peter Debye">Peter Debye</a> (1884 - 1966).<sup id="cite_ref-GEC8_1-0" class="reference"><a href="#cite_note-GEC8-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> Comptom seria guardonat amb el <a href="/wiki/Premi_Nobel" title="Premi Nobel">premi Nobel</a> de física del <a href="/wiki/1927" title="1927">1927</a> per aquest descobriment.<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><p>El fenomen es pot observar si es fa incidir un feix de radiació de <a href="/wiki/Freq%C3%BC%C3%A8ncia" title="Freqüència">freqüència</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 f}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/132e57acb643253e7810ee9702d9581f159a1c61" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.279ex; height:2.509ex;" alt="{\displaystyle f}"></span> sobre una làmina de material, la radiació difosa tindrà una freqüència menor (<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 f'<f}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>f</mi> <mo>′</mo> </msup> <mo><</mo> <mi>f</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f'<f}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f5748c061f9ee88b6e936294e86ac00577e835f5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.382ex; height:2.843ex;" alt="{\displaystyle f'<f}"></span>). La teoria clàssica de la difusió de la radiació electromagnètica, la <a href="/wiki/Dispersi%C3%B3_de_Thomson" title="Dispersió de Thomson">dispersió de Thomson</a> en particular, no pot explicar aquesta observació, els àtoms de la làmina haurien d'oscil·lar a la freqüència incident <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 f}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/132e57acb643253e7810ee9702d9581f159a1c61" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.279ex; height:2.509ex;" alt="{\displaystyle f}"></span> i, per tant, reemetre radiació a la mateixa freqüència. És a dir, l'efecte Compton demostra que la llum no es pot explicar exclusivament com una <a href="/wiki/Ona" title="Ona">ona</a>, d'aquí la seva gran importància.<sup id="cite_ref-GEC8_1-1" class="reference"><a href="#cite_note-GEC8-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><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> És la manera principal en què la <a href="/wiki/Mat%C3%A8ria" title="Matèria">matèria</a> absorbeix energia radiant.<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> </p><p>La interacció entre els electrons i els fotons d'alta <a href="/wiki/Energia" title="Energia">energia</a> produeix que el fotó cedeixi part de la seva energia a l'electró (fent-lo retrocedir), i el fotó que conté l'energia romanent sigui emès en una direcció diferent de l'original, per tal que el <a href="/wiki/Moment" title="Moment">moment</a> del sistema es conservi. Si el fotó encara té prou energia, el procés es pot repetir. En aquest cas, l'electró es tracta com a lliure. Si el fotó és de baixa energia, però encara té prou energia (en general uns pocs <a href="/wiki/Electr%C3%B3-volt" title="Electró-volt">eV</a>, al voltant de l'energia de la <a href="/wiki/Llum_visible" class="mw-redirect" title="Llum visible">llum visible</a>), pot ejectar l'electró del seu àtom hoste completament (un procés conegut com a <i><a href="/wiki/Efecte_fotoel%C3%A8ctric" title="Efecte fotoelèctric">efecte fotoelèctric</a></i>), en comptes de seguir l'efecte Compton. </p><p>També existeix l'<a href="/wiki/Efecte_Compton_invers" class="mw-redirect" title="Efecte Compton invers">efecte Compton invers</a>, en aquest cas el fotó guanya energia (decreix en longitud d'ona) en interaccionar amb la matèria. Encara que la dispersió nuclear Compton existeix, normalment ens referim a dispersió Compton a la interacció en la qual es relacionen només els electrons d'un àtom. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Descobriment_i_rellevància_històrica"><span id="Descobriment_i_rellev.C3.A0ncia_hist.C3.B2rica"></span>Descobriment i rellevància històrica</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Efecte_Compton&action=edit&section=1" title="Modifica la secció: Descobriment i rellevància històrica"><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:Compton-en.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c2/Compton-en.svg/220px-Compton-en.svg.png" decoding="async" width="220" height="155" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c2/Compton-en.svg/330px-Compton-en.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c2/Compton-en.svg/440px-Compton-en.svg.png 2x" data-file-width="656" data-file-height="461" /></a><figcaption>Fig. 1: Diagrama esquemàtic de l'experiment de Compton. La dispersió Compton es produeix al blanc de <a href="/wiki/Grafit" title="Grafit">grafit</a> de l'esquerra. L'escletxa fa passar fotons de raigs X dispersats en un angle seleccionat. L'energia d'un fotó dispers es mesura utilitzant <a href="/w/index.php?title=Dispersi%C3%B3_de_Bragg&action=edit&redlink=1" class="new" title="Dispersió de Bragg (encara no existeix)">dispersió de Bragg</a> al vidre de la dreta juntament amb una càmera d'ionització; la càmera podria mesurar l'energia total dipositada al llarg del temps, no l'energia de fotons dispersos individuals.</figcaption></figure> <p>L'efecte Compton va ser estudiat pel físic <a href="/wiki/Arthur_Compton" class="mw-redirect" title="Arthur Compton">Arthur Compton</a> en 1923, qui va poder explicar-ho utilitzant la noció quàntica de la radiació electromagnètica com quants d'energia i la mecànica relativista d'<a href="/wiki/Albert_Einstein" title="Albert Einstein">Einstein</a>. L'efecte Compton va constituir la demostració final de la naturalesa quàntica de la llum després dels estudis de <a href="/wiki/Planck" class="mw-redirect" title="Planck">Planck</a> sobre el <a href="/wiki/Cos_negre" title="Cos negre">cos negre</a> i l'explicació d'<a href="/wiki/Albert_Einstein" title="Albert Einstein">Albert Einstein</a> de l'<a href="/wiki/Efecte_fotoel%C3%A8ctric" title="Efecte fotoelèctric">efecte fotoelèctric</a>. </p><p>Compton va descobrir aquest efecte en experimentar amb <a href="/wiki/Raigs_X" class="mw-redirect" title="Raigs X">raigs X</a>, els quals van ser dirigits contra una de les cares d'un bloc de carbó. En xocar els raigs X amb el bloc es van difondre en diverses direccions; a mesura que l'angle dels raigs difosos augmentava, també se n'incrementava la longitud d'ona. Amb base en la <a href="/wiki/Mec%C3%A0nica_qu%C3%A0ntica" title="Mecànica quàntica">teoria quàntica</a>, Compton va afirmar que l'efecte es devia al fet que el <a href="/w/index.php?title=Quant&action=edit&redlink=1" class="new" title="Quant (encara no existeix)">quant</a> de raigs X actua com una partícula material en xocar contra l'electró, per la qual cosa l'<a href="/wiki/Energia_cin%C3%A8tica" title="Energia cinètica">energia cinètica</a>, que el que comunica a l'electró, representa una pèrdua en la seva energia original.<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>A conseqüència d'aquests estudis, Compton va guanyar el <a href="/wiki/Llista_de_guardonats_amb_el_Premi_Nobel_de_F%C3%ADsica" title="Llista de guardonats amb el Premi Nobel de Física">Premi Nobel de Física</a> en 1927. </p><p>Aquest efecte és d'especial rellevància científica, ja que no es pot explicar a través de la naturalesa ondulatòria de la llum. Aquesta ha de comportar-se com a partícula per poder explicar aquestes observacions, per la qual cosa adquireix una <a href="/wiki/Dualitat_ona_corpuscle" class="mw-redirect" title="Dualitat ona corpuscle">dualitat ona corpuscle</a> característica de la <a href="/wiki/Mec%C3%A0nica_qu%C3%A0ntica" title="Mecànica quàntica">mecànica quàntica</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Formulació_de_l'efecte_Compton"><span id="Formulaci.C3.B3_de_l.27efecte_Compton"></span>Formulació de l'efecte Compton</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Efecte_Compton&action=edit&section=2" title="Modifica la secció: Formulació de l'efecte Compton"><span>modifica</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Frame"><a href="/wiki/Fitxer:Compton-scattering.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e3/Compton-scattering.svg/239px-Compton-scattering.svg.png" decoding="async" width="239" height="141" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e3/Compton-scattering.svg/359px-Compton-scattering.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e3/Compton-scattering.svg/478px-Compton-scattering.svg.png 2x" data-file-width="239" data-file-height="141" /></a><figcaption>Un fotó de longitud d'ona <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 \lambda \,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>λ</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lambda \,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/988b7b8a22b11081bc97378c30391f573535c21c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.742ex; height:2.176ex;" alt="{\displaystyle \lambda \,}"></span> arriba de l'esquerra, col·lideix amb l'objectiu en repòs, i un nou fotó de longitud d'ona <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 \lambda '\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>λ</mi> <mo>′</mo> </msup> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lambda '\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c5d71f0e2299a780c52436caec725013f75e7b63" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.427ex; height:2.509ex;" alt="{\displaystyle \lambda '\,}"></span>emergeix a un angle <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 \theta \,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>θ</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \theta \,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/228647b7d4a18b6c8c0c390b439a61da8fafec76" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.478ex; height:2.176ex;" alt="{\displaystyle \theta \,}"></span></figcaption></figure> <p>Compton va utilitzar una combinació de tres fórmules fonamentals que representen els diferents aspectes de la física moderna i la clàssica, combinant-los per a descriure el comportament quàntic de la llum. </p> <ul><li>La llum com a partícula, com es descriu en l'<a href="/wiki/Efecte_fotoel%C3%A8ctric" title="Efecte fotoelèctric">efecte fotoelèctric</a>.</li> <li>Dinàmica relativista: <a href="/wiki/Relativitat_especial" title="Relativitat especial">teoria de la relativitat especial</a>.</li> <li>Trigonometria: <a href="/wiki/Teorema_del_cosinus" title="Teorema del cosinus">teorema del cosinus</a>.</li></ul> <p>El resultat final ens dona l'equació de l'<b>efecte Compton</b>: </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 \lambda '-\lambda ={\frac {h}{m_{e}c}}(1-\cos {\theta })}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>λ</mi> <mo>′</mo> </msup> <mo>−</mo> <mi>λ</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>h</mi> <mrow> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> </mrow> </msub> <mi>c</mi> </mrow> </mfrac> </mrow> <mo stretchy="false">(</mo> <mn>1</mn> <mo>−</mo> <mi>cos</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>θ</mi> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lambda '-\lambda ={\frac {h}{m_{e}c}}(1-\cos {\theta })}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c522e893cdba4c0399b2425862cab950e4b611fb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:24.617ex; height:5.676ex;" alt="{\displaystyle \lambda '-\lambda ={\frac {h}{m_{e}c}}(1-\cos {\theta })}"></span></dd></dl> <p>en què: </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 \lambda \,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>λ</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lambda \,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/988b7b8a22b11081bc97378c30391f573535c21c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.742ex; height:2.176ex;" alt="{\displaystyle \lambda \,}"></span> és la longitud d'ona del fotó <b>abans</b> de la dispersió,</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 \lambda '\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>λ</mi> <mo>′</mo> </msup> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lambda '\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c5d71f0e2299a780c52436caec725013f75e7b63" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.427ex; height:2.509ex;" alt="{\displaystyle \lambda '\,}"></span> és la longitud d'ona del fotó <b>després</b> de la dispersió,</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 m_{e}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m_{e}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8303b668e94e02d8f3db8c5b3ebd069ca5da9ba5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.039ex; height:2.009ex;" alt="{\displaystyle m_{e}}"></span> és la massa de l'<a href="/wiki/Electr%C3%B3" title="Electró">electró</a>,</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 \theta \,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>θ</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \theta \,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/228647b7d4a18b6c8c0c390b439a61da8fafec76" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.478ex; height:2.176ex;" alt="{\displaystyle \theta \,}"></span> és l'angle en què el fotó canvia,</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 h}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>h</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle h}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b26be3e694314bc90c3215047e4a2010c6ee184a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.339ex; height:2.176ex;" alt="{\displaystyle h}"></span> és la <a href="/wiki/Constant_de_Planck" title="Constant de Planck">constant de Planck</a>, i</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}"> <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 <a href="/wiki/Velocitat_de_la_llum" title="Velocitat de la llum">velocitat de la llum</a>.</dd></dl> <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 {\frac {h}{m_{e}c}}=2.43\times 10^{-12}\,m}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>h</mi> <mrow> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> </mrow> </msub> <mi>c</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mn>2.43</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>12</mn> </mrow> </msup> <mspace width="thinmathspace" /> <mi>m</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {h}{m_{e}c}}=2.43\times 10^{-12}\,m}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/15ecd517a9053ce6c188262362c788f383b61492" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:22.862ex; height:5.676ex;" alt="{\displaystyle {\frac {h}{m_{e}c}}=2.43\times 10^{-12}\,m}"></span> és coneguda com la <i><a href="/wiki/Longitud_d%27ona_Compton" title="Longitud d'ona Compton">longitud d'ona de Compton</a></i>.</dd></dl> <div class="mw-heading mw-heading3"><h3 id="Derivació"><span id="Derivaci.C3.B3"></span>Derivació</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Efecte_Compton&action=edit&section=3" title="Modifica la secció: Derivació"><span>modifica</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Començant amb la conservació de l'energia i la conservació del moment: </p> <dl><dd><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_{\gamma }+E_{e}=E_{\gamma ^{\prime }}+E_{e^{\prime }}\quad \quad (1)\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>γ</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>γ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msup> </mrow> </msub> <mo>+</mo> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msup> </mrow> </msub> <mspace width="1em" /> <mspace width="1em" /> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{\gamma }+E_{e}=E_{\gamma ^{\prime }}+E_{e^{\prime }}\quad \quad (1)\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/92e40725e2c0da15b73b5d08b4a23dbd81c148e0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:28.966ex; height:3.009ex;" alt="{\displaystyle E_{\gamma }+E_{e}=E_{\gamma ^{\prime }}+E_{e^{\prime }}\quad \quad (1)\,}"></span></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 {\vec {p}}_{\gamma }={\vec {p}}_{\gamma ^{\prime }}+{\vec {p}}_{e^{\prime }}\quad \quad \quad \quad \quad (2)\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>p</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>γ</mi> </mrow> </msub> <mo>=</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>p</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>γ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msup> </mrow> </msub> <mo>+</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>p</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msup> </mrow> </msub> <mspace width="1em" /> <mspace width="1em" /> <mspace width="1em" /> <mspace width="1em" /> <mspace width="1em" /> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {p}}_{\gamma }={\vec {p}}_{\gamma ^{\prime }}+{\vec {p}}_{e^{\prime }}\quad \quad \quad \quad \quad (2)\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e80d209804543f43b6cc0959575bca030c2260df" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; margin-left: -0.089ex; width:29.299ex; height:3.176ex;" alt="{\displaystyle {\vec {p}}_{\gamma }={\vec {p}}_{\gamma ^{\prime }}+{\vec {p}}_{e^{\prime }}\quad \quad \quad \quad \quad (2)\,}"></span></dd></dl></dd></dl> <dl><dd>en què: <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_{\gamma }\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>γ</mi> </mrow> </msub> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{\gamma }\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fe61438dd3b96fa1e51443bfb747e5be276c038d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.227ex; height:2.843ex;" alt="{\displaystyle E_{\gamma }\,}"></span> and <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 p_{\gamma }\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>γ</mi> </mrow> </msub> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p_{\gamma }\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/821a54f7270a4a354202cc110e337713211b492d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; margin-left: -0.089ex; width:2.771ex; height:2.343ex;" alt="{\displaystyle p_{\gamma }\,}"></span> és l'energia i el moment del fotó i</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_{e}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> </mrow> </msub> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{e}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5ad91ce98556ec49ea53f313061d3942661825f3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.101ex; height:2.509ex;" alt="{\displaystyle E_{e}\,}"></span> and <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 p_{e}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> </mrow> </msub> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p_{e}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/48c4761e475c6b83344ce20bd2b3a3dc4d74cd5d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:2.644ex; height:2.009ex;" alt="{\displaystyle p_{e}\,}"></span> és l'energia i el moment de l'electró.</dd></dl></dd></dl> <div class="mw-heading mw-heading4"><h4 id="Solució_(part_1)"><span id="Soluci.C3.B3_.28part_1.29"></span>Solució (part 1)</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Efecte_Compton&action=edit&section=4" title="Modifica la secció: Solució (part 1)"><span>modifica</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Ara omplim per la part de l'energia:<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 E_{\gamma }+E_{e}=E_{\gamma '}+E_{e'}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>γ</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>γ</mi> <mo>′</mo> </msup> </mrow> </msub> <mo>+</mo> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>e</mi> <mo>′</mo> </msup> </mrow> </msub> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{\gamma }+E_{e}=E_{\gamma '}+E_{e'}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/269664ebc9b88e4b722734e248d1176c206c5669" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:21.349ex; height:2.843ex;" alt="{\displaystyle E_{\gamma }+E_{e}=E_{\gamma '}+E_{e'}\,}"></span></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 hf+mc^{2}=hf'+{\sqrt {(p_{e'}c)^{2}+(mc^{2})^{2}}}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>h</mi> <mi>f</mi> <mo>+</mo> <mi>m</mi> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mi>h</mi> <msup> <mi>f</mi> <mo>′</mo> </msup> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mo stretchy="false">(</mo> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>e</mi> <mo>′</mo> </msup> </mrow> </msub> <mi>c</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mo stretchy="false">(</mo> <mi>m</mi> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mrow> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle hf+mc^{2}=hf'+{\sqrt {(p_{e'}c)^{2}+(mc^{2})^{2}}}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87b58c1fd2095da04b44cec062b53b6751c1ae71" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.671ex; width:37.929ex; height:4.843ex;" alt="{\displaystyle hf+mc^{2}=hf'+{\sqrt {(p_{e'}c)^{2}+(mc^{2})^{2}}}\,}"></span></dd></dl> <p>Solucionem per p<sub>e'</sub>: </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 (hf+mc^{2}-hf')^{2}=(p_{e'}c)^{2}+(mc^{2})^{2}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>h</mi> <mi>f</mi> <mo>+</mo> <mi>m</mi> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mi>h</mi> <msup> <mi>f</mi> <mo>′</mo> </msup> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mo stretchy="false">(</mo> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>e</mi> <mo>′</mo> </msup> </mrow> </msub> <mi>c</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mo stretchy="false">(</mo> <mi>m</mi> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (hf+mc^{2}-hf')^{2}=(p_{e'}c)^{2}+(mc^{2})^{2}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9b1e36effbcc59d65820424f4ef828cc0b4c20ce" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:38.468ex; height:3.176ex;" alt="{\displaystyle (hf+mc^{2}-hf')^{2}=(p_{e'}c)^{2}+(mc^{2})^{2}\,}"></span></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 {\frac {(hf+mc^{2}-hf')^{2}-m^{2}c^{4}}{c^{2}}}=p_{e'}^{2}\quad \quad \quad \quad \quad (3)\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo stretchy="false">(</mo> <mi>h</mi> <mi>f</mi> <mo>+</mo> <mi>m</mi> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mi>h</mi> <msup> <mi>f</mi> <mo>′</mo> </msup> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <msup> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> </mrow> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mo>=</mo> <msubsup> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>e</mi> <mo>′</mo> </msup> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mspace width="1em" /> <mspace width="1em" /> <mspace width="1em" /> <mspace width="1em" /> <mspace width="1em" /> <mo stretchy="false">(</mo> <mn>3</mn> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {(hf+mc^{2}-hf')^{2}-m^{2}c^{4}}{c^{2}}}=p_{e'}^{2}\quad \quad \quad \quad \quad (3)\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0b4c9f8311afd5a807303da3d588e55af4ce44bd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:48.209ex; height:6.176ex;" alt="{\displaystyle {\frac {(hf+mc^{2}-hf')^{2}-m^{2}c^{4}}{c^{2}}}=p_{e'}^{2}\quad \quad \quad \quad \quad (3)\,}"></span></dd></dl> <div class="mw-heading mw-heading4"><h4 id="Solució_(part_2)"><span id="Soluci.C3.B3_.28part_2.29"></span>Solució (part 2)</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Efecte_Compton&action=edit&section=5" title="Modifica la secció: Solució (part 2)"><span>modifica</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Reajustem l'equació (2) </p> <dl><dd><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 {\vec {p}}_{e'}={\vec {p}}_{\gamma }-{\vec {p}}_{\gamma '}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>p</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>e</mi> <mo>′</mo> </msup> </mrow> </msub> <mo>=</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>p</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>γ</mi> </mrow> </msub> <mo>−</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>p</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>γ</mi> <mo>′</mo> </msup> </mrow> </msub> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {p}}_{e'}={\vec {p}}_{\gamma }-{\vec {p}}_{\gamma '}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/42a58b79621e51908b88b1287856ddd0cce9d17e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; margin-left: -0.089ex; width:14.715ex; height:3.176ex;" alt="{\displaystyle {\vec {p}}_{e'}={\vec {p}}_{\gamma }-{\vec {p}}_{\gamma '}\,}"></span></dd></dl></dd></dl> <p>I elevem al quadrat </p> <dl><dd><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 p_{e'}^{2}=({\vec {p}}_{\gamma }-{\vec {p}}_{\gamma '})\cdot ({\vec {p}}_{\gamma }-{\vec {p}}_{\gamma '})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>e</mi> <mo>′</mo> </msup> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>=</mo> <mo stretchy="false">(</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>p</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>γ</mi> </mrow> </msub> <mo>−</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>p</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>γ</mi> <mo>′</mo> </msup> </mrow> </msub> <mo stretchy="false">)</mo> <mo>⋅</mo> <mo stretchy="false">(</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>p</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>γ</mi> </mrow> </msub> <mo>−</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>p</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>γ</mi> <mo>′</mo> </msup> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p_{e'}^{2}=({\vec {p}}_{\gamma }-{\vec {p}}_{\gamma '})\cdot ({\vec {p}}_{\gamma }-{\vec {p}}_{\gamma '})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c79eae2387f89133b0f0fcf7b266a8490b66478b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; margin-left: -0.089ex; width:27.754ex; height:3.343ex;" alt="{\displaystyle p_{e'}^{2}=({\vec {p}}_{\gamma }-{\vec {p}}_{\gamma '})\cdot ({\vec {p}}_{\gamma }-{\vec {p}}_{\gamma '})}"></span></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 p_{e'}^{2}=p_{\gamma }^{2}+p_{\gamma '}^{2}-2{\vec {p_{\gamma }}}\cdot {\vec {p_{\gamma '}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>e</mi> <mo>′</mo> </msup> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>=</mo> <msubsup> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>γ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>+</mo> <msubsup> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>γ</mi> <mo>′</mo> </msup> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>−</mo> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>γ</mi> </mrow> </msub> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>γ</mi> <mo>′</mo> </msup> </mrow> </msub> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p_{e'}^{2}=p_{\gamma }^{2}+p_{\gamma '}^{2}-2{\vec {p_{\gamma }}}\cdot {\vec {p_{\gamma '}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f7e1701dc60ceb2e8fc69a2bd01aaaebf216b440" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.505ex; margin-left: -0.089ex; width:24.704ex; height:4.176ex;" alt="{\displaystyle p_{e'}^{2}=p_{\gamma }^{2}+p_{\gamma '}^{2}-2{\vec {p_{\gamma }}}\cdot {\vec {p_{\gamma '}}}}"></span></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 p_{e'}^{2}=p_{\gamma }^{2}+p_{\gamma '}^{2}-2|p_{\gamma }||p_{\gamma '}|\cos(\theta )\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>e</mi> <mo>′</mo> </msup> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>=</mo> <msubsup> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>γ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>+</mo> <msubsup> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>γ</mi> <mo>′</mo> </msup> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>−</mo> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>γ</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>γ</mi> <mo>′</mo> </msup> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>θ</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p_{e'}^{2}=p_{\gamma }^{2}+p_{\gamma '}^{2}-2|p_{\gamma }||p_{\gamma '}|\cos(\theta )\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8aaf532c4fa067c2220612a004c54e3076890904" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.505ex; margin-left: -0.089ex; width:32.368ex; height:3.676ex;" alt="{\displaystyle p_{e'}^{2}=p_{\gamma }^{2}+p_{\gamma '}^{2}-2|p_{\gamma }||p_{\gamma '}|\cos(\theta )\,}"></span></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 p_{e'}^{2}=\left({\frac {hf}{c}}\right)^{2}+\left({\frac {hf'}{c}}\right)^{2}-2\left({\frac {hf}{c}}\right)\left({\frac {hf'}{c}}\right)\cos {\theta }\quad \quad \quad (4)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>e</mi> <mo>′</mo> </msup> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>=</mo> <msup> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>h</mi> <mi>f</mi> </mrow> <mi>c</mi> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>h</mi> <msup> <mi>f</mi> <mo>′</mo> </msup> </mrow> <mi>c</mi> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mn>2</mn> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>h</mi> <mi>f</mi> </mrow> <mi>c</mi> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>h</mi> <msup> <mi>f</mi> <mo>′</mo> </msup> </mrow> <mi>c</mi> </mfrac> </mrow> <mo>)</mo> </mrow> <mi>cos</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>θ</mi> </mrow> <mspace width="1em" /> <mspace width="1em" /> <mspace width="1em" /> <mo stretchy="false">(</mo> <mn>4</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p_{e'}^{2}=\left({\frac {hf}{c}}\right)^{2}+\left({\frac {hf'}{c}}\right)^{2}-2\left({\frac {hf}{c}}\right)\left({\frac {hf'}{c}}\right)\cos {\theta }\quad \quad \quad (4)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e9bade32cd76408c0f6afa741580aeb9f7ed31ef" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; margin-left: -0.089ex; width:59.481ex; height:6.676ex;" alt="{\displaystyle p_{e'}^{2}=\left({\frac {hf}{c}}\right)^{2}+\left({\frac {hf'}{c}}\right)^{2}-2\left({\frac {hf}{c}}\right)\left({\frac {hf'}{c}}\right)\cos {\theta }\quad \quad \quad (4)}"></span></dd></dl></dd></dl> <div class="mw-heading mw-heading4"><h4 id="Ajuntem">Ajuntem</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Efecte_Compton&action=edit&section=6" title="Modifica la secció: Ajuntem"><span>modifica</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Ara tenim dues equacions <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 p_{e'}^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>e</mi> <mo>′</mo> </msup> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p_{e'}^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ace0d8369712b834386df7c2046c661a5ef3d78b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; margin-left: -0.089ex; width:2.789ex; height:3.343ex;" alt="{\displaystyle p_{e'}^{2}}"></span> (eq 3 & 4): </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 \left({\frac {hf}{c}}\right)^{2}+\left({\frac {hf'}{c}}\right)^{2}-{\frac {2h^{2}ff'\cos {\theta }}{c^{2}}}={\frac {(hf+mc^{2}-hf')^{2}-m^{2}c^{4}}{c^{2}}}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>h</mi> <mi>f</mi> </mrow> <mi>c</mi> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>h</mi> <msup> <mi>f</mi> <mo>′</mo> </msup> </mrow> <mi>c</mi> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>2</mn> <msup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>f</mi> <msup> <mi>f</mi> <mo>′</mo> </msup> <mi>cos</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>θ</mi> </mrow> </mrow> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo stretchy="false">(</mo> <mi>h</mi> <mi>f</mi> <mo>+</mo> <mi>m</mi> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mi>h</mi> <msup> <mi>f</mi> <mo>′</mo> </msup> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <msup> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> </mrow> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left({\frac {hf}{c}}\right)^{2}+\left({\frac {hf'}{c}}\right)^{2}-{\frac {2h^{2}ff'\cos {\theta }}{c^{2}}}={\frac {(hf+mc^{2}-hf')^{2}-m^{2}c^{4}}{c^{2}}}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/445c1f4964c358bdfaee61d41c88411421ed7370" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:65.842ex; height:6.676ex;" alt="{\displaystyle \left({\frac {hf}{c}}\right)^{2}+\left({\frac {hf'}{c}}\right)^{2}-{\frac {2h^{2}ff'\cos {\theta }}{c^{2}}}={\frac {(hf+mc^{2}-hf')^{2}-m^{2}c^{4}}{c^{2}}}\,}"></span></dd></dl> <p>Ara, simplifiquem. Primer multiplicant els dos costats per <i>c</i>²: </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 h^{2}f^{2}+h^{2}f'^{2}-2h^{2}ff'\cos \theta =(hf+mc^{2}-hf')^{2}-m^{2}c^{4}.\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>f</mi> <mrow> <mo class="MJX-variant">′</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </mrow> </msup> <mo>−</mo> <mn>2</mn> <msup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>f</mi> <msup> <mi>f</mi> <mo>′</mo> </msup> <mi>cos</mi> <mo>⁡</mo> <mi>θ</mi> <mo>=</mo> <mo stretchy="false">(</mo> <mi>h</mi> <mi>f</mi> <mo>+</mo> <mi>m</mi> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mi>h</mi> <msup> <mi>f</mi> <mo>′</mo> </msup> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <msup> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> <mo>.</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle h^{2}f^{2}+h^{2}f'^{2}-2h^{2}ff'\cos \theta =(hf+mc^{2}-hf')^{2}-m^{2}c^{4}.\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9a8a8df9e927459dd3bbb839b02e6cf53e5cc266" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:58.22ex; height:3.176ex;" alt="{\displaystyle h^{2}f^{2}+h^{2}f'^{2}-2h^{2}ff'\cos \theta =(hf+mc^{2}-hf')^{2}-m^{2}c^{4}.\,}"></span></dd></dl> <p>Després: </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 h^{2}f^{2}+h^{2}f'^{2}-2h^{2}ff'\cos {\theta }=h^{2}f^{2}+m^{2}c^{4}+h^{2}f'^{2}-2h^{2}ff'+2h(f-f')mc^{2}-m^{2}c^{4}.\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>f</mi> <mrow> <mo class="MJX-variant">′</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </mrow> </msup> <mo>−</mo> <mn>2</mn> <msup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>f</mi> <msup> <mi>f</mi> <mo>′</mo> </msup> <mi>cos</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>θ</mi> </mrow> <mo>=</mo> <msup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>f</mi> <mrow> <mo class="MJX-variant">′</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </mrow> </msup> <mo>−</mo> <mn>2</mn> <msup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>f</mi> <msup> <mi>f</mi> <mo>′</mo> </msup> <mo>+</mo> <mn>2</mn> <mi>h</mi> <mo stretchy="false">(</mo> <mi>f</mi> <mo>−</mo> <msup> <mi>f</mi> <mo>′</mo> </msup> <mo stretchy="false">)</mo> <mi>m</mi> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <msup> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> <mo>.</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle h^{2}f^{2}+h^{2}f'^{2}-2h^{2}ff'\cos {\theta }=h^{2}f^{2}+m^{2}c^{4}+h^{2}f'^{2}-2h^{2}ff'+2h(f-f')mc^{2}-m^{2}c^{4}.\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fd32447fbbd2c7e4b9f2ec50f8dd2d18552ef144" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:87.494ex; height:3.176ex;" alt="{\displaystyle h^{2}f^{2}+h^{2}f'^{2}-2h^{2}ff'\cos {\theta }=h^{2}f^{2}+m^{2}c^{4}+h^{2}f'^{2}-2h^{2}ff'+2h(f-f')mc^{2}-m^{2}c^{4}.\,}"></span></dd></dl> <p>Simplificant, tindrem </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 -2h^{2}ff'\cos {\theta }=-2h^{2}ff'+2h(f-f')mc^{2}.\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>−</mo> <mn>2</mn> <msup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>f</mi> <msup> <mi>f</mi> <mo>′</mo> </msup> <mi>cos</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>θ</mi> </mrow> <mo>=</mo> <mo>−</mo> <mn>2</mn> <msup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>f</mi> <msup> <mi>f</mi> <mo>′</mo> </msup> <mo>+</mo> <mn>2</mn> <mi>h</mi> <mo stretchy="false">(</mo> <mi>f</mi> <mo>−</mo> <msup> <mi>f</mi> <mo>′</mo> </msup> <mo stretchy="false">)</mo> <mi>m</mi> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>.</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle -2h^{2}ff'\cos {\theta }=-2h^{2}ff'+2h(f-f')mc^{2}.\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d575c9f1cf181e7936f0fbe662c987acd8598349" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:43.78ex; height:3.176ex;" alt="{\displaystyle -2h^{2}ff'\cos {\theta }=-2h^{2}ff'+2h(f-f')mc^{2}.\,}"></span></dd></dl> <p>Dividim els dos costats 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 -2h}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>−</mo> <mn>2</mn> <mi>h</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle -2h}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8a275937630e6e459ea523f8f8aa7dcef05b0d42" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:4.31ex; height:2.343ex;" alt="{\displaystyle -2h}"></span>' </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 hff'\cos {\theta }=hff'-(f-f')mc^{2}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>h</mi> <mi>f</mi> <msup> <mi>f</mi> <mo>′</mo> </msup> <mi>cos</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>θ</mi> </mrow> <mo>=</mo> <mi>h</mi> <mi>f</mi> <msup> <mi>f</mi> <mo>′</mo> </msup> <mo>−</mo> <mo stretchy="false">(</mo> <mi>f</mi> <mo>−</mo> <msup> <mi>f</mi> <mo>′</mo> </msup> <mo stretchy="false">)</mo> <mi>m</mi> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle hff'\cos {\theta }=hff'-(f-f')mc^{2}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3773544f4cf377740441feac99bc52e2c95cfe06" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:32.582ex; height:3.176ex;" alt="{\displaystyle hff'\cos {\theta }=hff'-(f-f')mc^{2}\,}"></span></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 (f-f')mc^{2}=hff'(1-\cos {\theta }).\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>f</mi> <mo>−</mo> <msup> <mi>f</mi> <mo>′</mo> </msup> <mo stretchy="false">)</mo> <mi>m</mi> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mi>h</mi> <mi>f</mi> <msup> <mi>f</mi> <mo>′</mo> </msup> <mo stretchy="false">(</mo> <mn>1</mn> <mo>−</mo> <mi>cos</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>θ</mi> </mrow> <mo stretchy="false">)</mo> <mo>.</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (f-f')mc^{2}=hff'(1-\cos {\theta }).\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/999fd32fc3d5c5c97a254279bf850eeb2c9e4199" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:31.191ex; height:3.176ex;" alt="{\displaystyle (f-f')mc^{2}=hff'(1-\cos {\theta }).\,}"></span></dd></dl> <p>Ara dividim els dos costats 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 mc^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle mc^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/68e4e95f7216bad6eab483ef0072d531a965962b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.101ex; height:2.676ex;" alt="{\displaystyle mc^{2}}"></span> i llavors 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 ff^{\prime }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <msup> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ff^{\prime }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/46a990f678886e38b335b60d37bc426408446969" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.284ex; height:2.843ex;" alt="{\displaystyle ff^{\prime }}"></span>: </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 {\frac {f-f^{\prime }}{ff^{\prime }}}={\frac {h}{mc^{2}}}\left(1-\cos \theta \right).\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>f</mi> <mo>−</mo> <msup> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msup> </mrow> <mrow> <mi>f</mi> <msup> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>h</mi> <mrow> <mi>m</mi> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>−</mo> <mi>cos</mi> <mo>⁡</mo> <mi>θ</mi> </mrow> <mo>)</mo> </mrow> <mo>.</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {f-f^{\prime }}{ff^{\prime }}}={\frac {h}{mc^{2}}}\left(1-\cos \theta \right).\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6a48ad20bfa9c67699c8e0a8e61c4e503b156cff" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:27.205ex; height:6.009ex;" alt="{\displaystyle {\frac {f-f^{\prime }}{ff^{\prime }}}={\frac {h}{mc^{2}}}\left(1-\cos \theta \right).\,}"></span></dd></dl> <p>Ara la part esquerra es pot reescriure simplement com: </p> <dl><dd><dl><dd><table cellpadding="2" style="border:2px solid #ccccff"> <tbody><tr> <td><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 {1}{f^{\prime }}}-{\frac {1}{f}}={\frac {h}{mc^{2}}}\left(1-\cos \theta \right)\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msup> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msup> </mfrac> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>f</mi> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>h</mi> <mrow> <mi>m</mi> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>−</mo> <mi>cos</mi> <mo>⁡</mo> <mi>θ</mi> </mrow> <mo>)</mo> </mrow> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {1}{f^{\prime }}}-{\frac {1}{f}}={\frac {h}{mc^{2}}}\left(1-\cos \theta \right)\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dd8fed633fea9ce1e08015857e2c95af885cf24d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:27.008ex; height:5.843ex;" alt="{\displaystyle {\frac {1}{f^{\prime }}}-{\frac {1}{f}}={\frac {h}{mc^{2}}}\left(1-\cos \theta \right)\,}"></span> </td></tr></tbody></table></dd></dl></dd></dl> <p>Això és equivalent a l'equació de l'<b>efecte Compton</b>, però normalment s'escriu usant <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 \lambda }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>λ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lambda }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b43d0ea3c9c025af1be9128e62a18fa74bedda2a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.355ex; height:2.176ex;" alt="{\displaystyle \lambda }"></span> en lloc 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 f}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/132e57acb643253e7810ee9702d9581f159a1c61" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.279ex; height:2.509ex;" alt="{\displaystyle f}"></span>. Per a fer el canvi s'usa: </p> <dl><dd><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 f={\frac {c}{\lambda }}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>c</mi> <mi>λ</mi> </mfrac> </mrow> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f={\frac {c}{\lambda }}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/48fd093473ed22b7b99bd7e4914c7b9500819208" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:6.956ex; height:4.843ex;" alt="{\displaystyle f={\frac {c}{\lambda }}\,}"></span></dd></dl></dd></dl> <p>i finalment: </p> <dl><dd><dl><dd><table cellpadding="2" style="border:2px solid #ccccff"> <tbody><tr> <td><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 \lambda '-\lambda ={\frac {h}{mc}}(1-\cos {\theta })\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>λ</mi> <mo>′</mo> </msup> <mo>−</mo> <mi>λ</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>h</mi> <mrow> <mi>m</mi> <mi>c</mi> </mrow> </mfrac> </mrow> <mo stretchy="false">(</mo> <mn>1</mn> <mo>−</mo> <mi>cos</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>θ</mi> </mrow> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lambda '-\lambda ={\frac {h}{mc}}(1-\cos {\theta })\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/54f49ba37293baf1ef3f698272c56d763bbcf3f1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:24.005ex; height:5.343ex;" alt="{\displaystyle \lambda '-\lambda ={\frac {h}{mc}}(1-\cos {\theta })\,}"></span> </td></tr></tbody></table></dd></dl></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Efecte_Compton_invers">Efecte Compton invers</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Efecte_Compton&action=edit&section=7" title="Modifica la secció: Efecte Compton invers"><span>modifica</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>L'efecte Compton invers succeeix quan els fotons disminueixen la seva longitud d'ona en xocar amb electrons. Però, perquè això succeeixi, és necessari que els electrons viatgin a velocitats properes a la <a href="/wiki/Velocitat_de_la_llum" title="Velocitat de la llum">velocitat de la llum</a> i que els fotons tinguin altes energies. La principal diferència entre els dos fenòmens és que durant l'efecte Compton "convencional", els fotons lliuren energia als electrons, i durant l'invers succeeix el contrari. </p><p>Aquest efecte pot ser una de les explicacions de l'emissió de <a href="/wiki/Raigs_X" class="mw-redirect" title="Raigs X">raigs X</a> en <a href="/wiki/Supernova" title="Supernova">supernoves</a>, <a href="/wiki/Qu%C3%A0sar" title="Quàsar">quàsars</a> i altres objectes <a href="/wiki/Astrof%C3%ADsica" title="Astrofísica">astrofísics</a> d'alta energia. </p> <div class="mw-heading mw-heading2"><h2 id="Aplicacions">Aplicacions</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Efecte_Compton&action=edit&section=8" title="Modifica la secció: Aplicacions"><span>modifica</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Dispersió_Compton"><span id="Dispersi.C3.B3_Compton"></span>Dispersió Compton</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Efecte_Compton&action=edit&section=9" title="Modifica la secció: Dispersió Compton"><span>modifica</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>La dispersió Compton és de primordial importància per a la <a href="/wiki/Radiobiologia" title="Radiobiologia">radiobiologia</a>, ja que és la interacció més probable dels raigs gamma i els raigs X d'alta energia amb els àtoms dels éssers vius i s'aplica a <a href="/wiki/Radioter%C3%A0pia" title="Radioteràpia">radioteràpia</a>.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup><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> </p><p>La dispersió Compton és un efecte important en <a href="/wiki/Espectrosc%C3%B2pia_gamma" title="Espectroscòpia gamma">espectroscòpia gamma</a> que dóna lloc a la <a href="/w/index.php?title=Vora_Compton&action=edit&redlink=1" class="new" title="Vora Compton (encara no existeix)">vora Compton</a>, ja que és possible que els raigs gamma es dispersin fora dels detectors utilitzats. La supressió Compton s'utilitza per detectar els raigs gamma dispersos per contrarestar aquest efecte. </p> <div class="mw-heading mw-heading3"><h3 id="Dispersió_magnètica_Compton"><span id="Dispersi.C3.B3_magn.C3.A8tica_Compton"></span>Dispersió magnètica Compton</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Efecte_Compton&action=edit&section=10" title="Modifica la secció: Dispersió magnètica Compton"><span>modifica</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>La dispersió magnètica Compton és una extensió de la tècnica esmentada anteriorment que implica la magnetització d'una mostra de vidre assolida per fotons d'alta energia polaritzats circularment. Mesurant l'energia dels fotons dispersats i invertint la magnetització de la mostra, es generen dos perfils Compton diferents (un per als moments d'espí cap amunt i un altre per als moments d'espí cap avall). Prenent la diferència entre aquests dos perfils s'obté el perfil magnètic Compton (MCP), donat 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 J_{\text{mag}}(\mathbf {p} _{z})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>J</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>mag</mtext> </mrow> </msub> <mo stretchy="false">(</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">p</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle J_{\text{mag}}(\mathbf {p} _{z})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/148b4fa698849af41d382ac433448991abadf1e0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:8.832ex; height:3.009ex;" alt="{\displaystyle J_{\text{mag}}(\mathbf {p} _{z})}"></span> - una projecció unidimensional de la densitat d'espí de l'electró. </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 J_{\text{mag}}(\mathbf {p} _{z})={\frac {1}{\mu }}\iint _{-\infty }^{\infty }(n_{\uparrow }(\mathbf {p} )-n_{\downarrow }(\mathbf {p} ))d\mathbf {p} _{x}d\mathbf {p} _{y}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>J</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>mag</mtext> </mrow> </msub> <mo stretchy="false">(</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">p</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>μ</mi> </mfrac> </mrow> <msubsup> <mo>∬</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mi mathvariant="normal">∞</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </msubsup> <mo stretchy="false">(</mo> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">↑</mo> </mrow> </msub> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">p</mi> </mrow> <mo stretchy="false">)</mo> <mo>−</mo> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">↓</mo> </mrow> </msub> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">p</mi> </mrow> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> <mi>d</mi> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">p</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> <mi>d</mi> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">p</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle J_{\text{mag}}(\mathbf {p} _{z})={\frac {1}{\mu }}\iint _{-\infty }^{\infty }(n_{\uparrow }(\mathbf {p} )-n_{\downarrow }(\mathbf {p} ))d\mathbf {p} _{x}d\mathbf {p} _{y}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aea290bbb2138f127ac1b6a510250df732428dda" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:43.989ex; height:6.009ex;" alt="{\displaystyle J_{\text{mag}}(\mathbf {p} _{z})={\frac {1}{\mu }}\iint _{-\infty }^{\infty }(n_{\uparrow }(\mathbf {p} )-n_{\downarrow }(\mathbf {p} ))d\mathbf {p} _{x}d\mathbf {p} _{y}}"></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 \mu }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>μ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mu }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9fd47b2a39f7a7856952afec1f1db72c67af6161" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.402ex; height:2.176ex;" alt="{\displaystyle \mu }"></span> és el nombre d'electrons d'espí no aparellat al sistema, <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_{\uparrow }(\mathbf {p} )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">↑</mo> </mrow> </msub> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">p</mi> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n_{\uparrow }(\mathbf {p} )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e53f311bc1323a0a0ea238c4624da428d069fa32" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:5.744ex; height:3.009ex;" alt="{\displaystyle n_{\uparrow }(\mathbf {p} )}"></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 n_{\downarrow }(\mathbf {p} )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">↓</mo> </mrow> </msub> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">p</mi> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n_{\downarrow }(\mathbf {p} )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fe8b17eedc88980cc49d2fc4488cd69d4d2df9e7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:5.744ex; height:3.009ex;" alt="{\displaystyle n_{\downarrow }(\mathbf {p} )}"></span> són les distribucions tridimensionals del moment electrònic per als electrons d'espín majoritari i espín minoritari respectivament. </p><p>Com que aquest procés de dispersió és <a href="/wiki/Coher%C3%A8ncia_(f%C3%ADsica)" title="Coherència (física)">incoherent</a> (no hi ha relació de fase entre els fotons dispersats), la MCP és representativa de les propietats del gruix de la mostra i és una sonda de l'estat bàsic. Això significa que la MCP és ideal per a la comparació amb tècniques teòriques com la <a href="/wiki/Teoria_del_funcional_de_la_densitat" title="Teoria del funcional de la densitat">teoria del funcional de la densitat</a>. L'àrea sota la MCP és directament proporcional al moment d'espín del sistema i, per tant, quan es combina amb mètodes de mesura del moment total (com la magnetometria <a href="/wiki/SQUID" title="SQUID">SQUID</a>), es pot utilitzar per aïllar les contribucions orbitals i d'espín al moment total d'un sistema. La forma del MCP també permet comprendre l'origen del magnetisme al sistema.<sup id="cite_ref-Cooper2004_8-0" class="reference"><a href="#cite_note-Cooper2004-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Dispersió_Compton_inversa"><span id="Dispersi.C3.B3_Compton_inversa"></span>Dispersió Compton inversa</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Efecte_Compton&action=edit&section=11" title="Modifica la secció: Dispersió Compton inversa"><span>modifica</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>La dispersió Compton inversa és important en <a href="/wiki/Astrof%C3%ADsica" title="Astrofísica">astrofísica</a>. En <a href="/wiki/Astronomia_de_raigs_X" title="Astronomia de raigs X">astronomia de raigs X</a>, se suposa que el disc d'acreció que envolta un <a href="/wiki/Forat_negre" title="Forat negre">forat negre</a> produeix un espectre tèrmic. Els electrons relativistes de la <a href="/wiki/Corona_estel%C2%B7lar" class="mw-redirect" title="Corona estel·lar">corona estel·lar</a> circumdant dispersen els fotons de menor energia produïts per aquest espectre. Se suposa que això causa el component de llei de potència als espectres de raigs X (0,2-10 keV) dels forats negres en acreció.<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> </p><p>L'efecte també s'observa quan els fotons del <a href="/wiki/Radiaci%C3%B3_c%C3%B2smica_de_fons_de_microones" class="mw-redirect" title="Radiació còsmica de fons de microones">fons còsmic de microones</a> (CMB) es mouen a través del gas calent que envolta un <a href="/wiki/C%C3%BAmul_de_gal%C3%A0xies" title="Cúmul de galàxies">cúmul de galàxies</a>. Els fotons del CMB són dispersats a energies més altes pels electrons d'aquest gas, donant lloc a l'<a href="/w/index.php?title=Efecte_Sunyaev-Zel%27dovich&action=edit&redlink=1" class="new" title="Efecte Sunyaev-Zel'dovich (encara no existeix)">efecte Sunyaev-Zel'dovich</a>. Les observacions de l'efecte Sunyaev-Zel'dovich proporcionen un mitjà gairebé independent del desplaçament al vermell per detectar cúmuls de galàxies. </p><p>Algunes instal·lacions de radiació sincrotró dispersen la llum làser del feix d'electrons emmagatzemat. Aquesta retrodispersió Compton produeix fotons d'alta energia al rang de MeV a GeV<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><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> utilitzat posteriorment per a experiments de física nuclear. </p> <div class="mw-heading mw-heading3"><h3 id="Dispersió_Compton_inversa_no_lineal"><span id="Dispersi.C3.B3_Compton_inversa_no_lineal"></span>Dispersió Compton inversa no lineal</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Efecte_Compton&action=edit&section=12" title="Modifica la secció: Dispersió Compton inversa no lineal"><span>modifica</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>La dispersió Compton inversa no lineal (NICS) és la dispersió de múltiples fotons de baixa energia, donada per un camp electromagnètic intens, en un fotó d'alta energia (raigs X o raigs gamma) durant la interacció amb una partícula carregada, com un electró.<sup id="cite_ref-:0_12-0" class="reference"><a href="#cite_note-:0-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> També s'anomena dispersió Compton no lineal i dispersió Compton multifotó. És la versió no lineal de la dispersió Compton inversa en què les condicions per a l'absorció multifotònica per la partícula carregada s'assoleixen a causa d'un camp electromagnètic molt intens, per exemple el produït per un <a href="/wiki/L%C3%A0ser" title="Làser">làser</a>.<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>La dispersió Compton inversa no-lineal és un fenomen interessant per a totes les aplicacions que requereixen fotons d'alta energia, ja que la NICS és capaç de produir fotons amb energia comparable a l'energia de repòs de les partícules carregades i superiors.<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> Com a conseqüència, els fotons NICS poden utilitzar-se per desencadenar altres fenòmens com la producció de parells, la dispersió Compton, <a href="/wiki/Reacci%C3%B3_nuclear" title="Reacció nuclear">reaccions nuclears</a>, i poden utilitzar-se per sondejar efectes quàntics no lineals i <a href="/wiki/Electrodin%C3%A0mica_qu%C3%A0ntica" title="Electrodinàmica quàntica">QED</a> no lineal.<sup id="cite_ref-:0_12-1" class="reference"><a href="#cite_note-:0-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> </p> <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=Efecte_Compton&action=edit&section=13" title="Modifica la secció: Vegeu també"><span>modifica</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Dispersi%C3%B3_de_Thomson" title="Dispersió de Thomson">Dispersió de Thomson</a></li> <li><a href="/wiki/F%C3%B3rmula_de_Klein-Nishina" title="Fórmula de Klein-Nishina">Fórmula de Klein-Nishina</a></li> <li><a href="/wiki/Observatori_de_raigs_gamma_Compton" title="Observatori de raigs gamma Compton">Observatori de raigs gamma Compton</a></li></ul> <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=Efecte_Compton&action=edit&section=14" 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-GEC8-1"><span class="mw-cite-backlink">↑ <sup><a href="#cite_ref-GEC8_1-0">1,0</a></sup> <sup><a href="#cite_ref-GEC8_1-1">1,1</a></sup></span> <span class="reference-text"><span class="citation book" style="font-style:normal"> <i>Gran Enciclopèdia Catalana</i>. Volum 8. Reimpressió d'octubre de 1992.  Barcelona: Gran Enciclopèdia Catalana, 1992, p. 26. <span style="font-size:90%; white-space:nowrap;"><a href="/wiki/Especial:Fonts_bibliogr%C3%A0fiques/84-85194-96-9" title="Especial:Fonts bibliogràfiques/84-85194-96-9">ISBN 84-85194-96-9</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=Gran+Enciclop%C3%A8dia+Catalana&rft.date=1992&rft.edition=Reimpressi%C3%B3+d%27octubre+de+1992&rft.pub=Gran+Enciclop%C3%A8dia+Catalana&rft.place=Barcelona&rft.pages=26&rft.isbn=84-85194-96-9"><span style="display: none;"> </span></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">«<a rel="nofollow" class="external text" href="https://www.nobelprize.org/prizes/physics/1927/compton/facts/">Arthur H. Compton Facts</a>» (en anglès). <i>The Nobel Foundation. The Nobel Prize</i>. [Consulta: 12 octubre 2021].</span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><a href="#cite_ref-3">↑</a></span> <span class="reference-text"><span class="citation" style="font-style:normal" id="CITEREFCompton1923"><span style="font-variant: small-caps;">Compton</span>, Arthur H. «<a rel="nofollow" class="external text" href="https://journals.aps.org/pr/pdf/10.1103/PhysRev.21.483">A Quantum Theory of the Scattering of X-rays by Light Elements</a>» (PDF). <i>Physical Review</i>, vol. 21, núm. 5, 5-1923, pàg. 483-502. <a href="/wiki/DOI" title="DOI">DOI</a>: <a rel="nofollow" class="external text" href="https://dx.doi.org/doi%3A10.1103%2FPhysRev.21.483">doi:10.1103/PhysRev.21.483</a>.</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">«<a rel="nofollow" class="external text" href="https://www.britannica.com/science/Compton-effect">Compton effect</a>» (en anglès). <i>Encyclopædia Britannica</i>.  Encyclopædia Britannica, Inc.. [Consulta: 12 octubre 2021].</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 book" style="font-style:normal" id="CITEREFPérez_Montiel2011"><span style="font-variant: small-caps;">Pérez Montiel</span>, Héctor. «17». A: <i>Física general</i>.  Grupo Editorial Patria, 2011.</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+general&rft.atitle=17&rft.aulast=P%C3%A9rez+Montiel&rft.aufirst=H%C3%A9ctor&rft.date=2011&rft.pub=Grupo+Editorial+Patria"><span style="display: none;"> </span></span></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><a href="#cite_ref-6">↑</a></span> <span class="reference-text">Camphausen KA, Lawrence RC. <a rel="nofollow" class="external text" href="http://www.cancernetwork.com/cancer-management-11/chapter02/article/10165/1399960">"Principios de radioterapia"</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20090515031929/http://www.cancernetwork.com/cancer-management-11/chapter02/article/10165/1399960">Arxivat</a> 2009-maig-15 a la <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>. en Pazdur R, Wagman LD, Camphausen KA, Hoskins WJ (Eds) <a rel="nofollow" class="external text" href="http://www.cancernetwork.com/cancer-management-11/">Cancer Management: A Multidisciplinary Approach</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20100228072652/http://www.cancernetwork.com/cancer-management-11/">Arxivat</a> 2010-febrer-28 a la <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>.. 11 ed. 2008.</span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><a href="#cite_ref-7">↑</a></span> <span class="reference-text">Ridwan, S. M., El-Tayyeb, F., Hainfeld, J. F., & Smilowitz, H. M. (2020). Distributions of intravenous injected iodine nanoparticles in orthotopic U87 human glioma xenografts over time and tumor therapy. Nanomedicine, 15(24), 2369-2383. <a rel="nofollow" class="external free" href="https://doi.org/10.2217/nnm-2020-0178">https://doi.org/10.2217/nnm-2020-0178</a> </span> </li> <li id="cite_note-Cooper2004-8"><span class="mw-cite-backlink"><a href="#cite_ref-Cooper2004_8-0">↑</a></span> <span class="reference-text"><span class="citation book" style="font-style:normal">Malcolm Cooper. <a rel="nofollow" class="external text" href="https://books.google.com/books?id=m58jXIJDs3QC"><i>X-Ray Compton Scattering</i></a>.  <a href="/w/index.php?title=OUP_Oxford&action=edit&redlink=1" class="new" title="OUP Oxford (encara no existeix)">OUP Oxford</a>, 2004-10-14. <span style="font-size:90%; white-space:nowrap;"><a href="/wiki/Especial:Fonts_bibliogr%C3%A0fiques/978-0-19-850168-8" title="Especial:Fonts bibliogràfiques/978-0-19-850168-8">ISBN 978-0-19-850168-8</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=X-Ray+Compton+Scattering&rft.au=Malcolm+Cooper&rft.date=2004-10-14&rft.pub=%5B%5BOUP+Oxford%5D%5D&rft.isbn=978-0-19-850168-8&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3Dm58jXIJDs3QC"><span style="display: none;"> </span></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"><span style="font-variant: small-caps;">Dr. Tortosa</span>, Alessia. «<a rel="nofollow" class="external text" href="http://www.matfis.uniroma3.it/Allegati/Dottorato/TESI/tortosa/tesi_PhD_Tortosa_Alessia.pdf">Mecanismos de comptonización en coronas calientes en AGN. The NuSTAR view</a>».  DIPARTIMENTO DI MATEMATICA E FISICA.</span></span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><a href="#cite_ref-10">↑</a></span> <span class="reference-text"><span class="citation" style="font-style:normal">«<a rel="nofollow" class="external text" href="http://www.lnf.infn.it/~levisand/graal/graal.html">Página principal de GRAAL</a>».  Lnf.infn. it. [Consulta: 8 novembre 2011].</span></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">«<a rel="nofollow" class="external text" href="https://tunl.duke.edu/research/our-facilities">Duke University TUNL HIGS Facility</a>». [Consulta: 31 gener 2021].</span></span> </li> <li id="cite_note-:0-12"><span class="mw-cite-backlink">↑ <sup><a href="#cite_ref-:0_12-0">12,0</a></sup> <sup><a href="#cite_ref-:0_12-1">12,1</a></sup></span> <span class="reference-text"><span class="citation" style="font-style:normal"><span style="font-variant: small-caps;">Di Piazza</span>, A.; <span style="font-variant: small-caps;">Müller</span>, C.; <span style="font-variant: small-caps;">Hatsagortsyan</span>, K. Z.; <span style="font-variant: small-caps;">Keitel</span>, C. H. «<a rel="nofollow" class="external text" href="https://link.aps.org/doi/10.1103/RevModPhys.84.1177">Interacciones láser de altísima intensidad con sistemas cuánticos fundamentales</a>» (en anglès). <i>Reviews of Modern Physics</i>, vol. 84, 3, 16-08-2012, pàg. 1177-1228. <a href="/wiki/ArXiv" title="ArXiv">arXiv</a>: <a rel="nofollow" class="external text" href="http://arxiv.org/abs/1111.3886">1111.3886</a>. <a href="/wiki/Bibcode" title="Bibcode">Bibcode</a>: <a rel="nofollow" class="external text" href="http://adsabs.harvard.edu/abs/2012RvMP...84.1177D">2012RvMP...84.1177D</a>. <a href="/wiki/DOI" title="DOI">DOI</a>: <a rel="nofollow" class="external text" href="https://dx.doi.org/10.1103%2FRevModPhys.84.1177">10.1103/RevModPhys.84.1177</a>. <a href="/wiki/ISSN" title="ISSN">ISSN</a>: <a rel="nofollow" class="external text" href="//www.worldcat.org/issn/0034-6861">0034-6861</a>.</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"><span style="font-variant: small-caps;">Meyerhofer</span>, D. D. «<a rel="nofollow" class="external text" href="https://ieeexplore.ieee.org/document/641308">Dispersión de electrones de alta intensidad por láser</a>». <i>IEEE Journal of Quantum Electronics</i>. <a href="/wiki/Bibcode" title="Bibcode">Bibcode</a>: <a rel="nofollow" class="external text" href="http://adsabs.harvard.edu/abs/1997IJQE...33.1935M">1997IJQE...33.1935M</a>. <a href="/wiki/DOI" title="DOI">DOI</a>: <a rel="nofollow" class="external text" href="https://dx.doi.org/10.1109%2F3.641308">10.1109/3.641308</a>.</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"><span style="font-variant: small-caps;">Ritus</span>, V. I. «<a rel="nofollow" class="external text" href="http://link.springer.com/10.1007/BF01120220">Efectos cuánticos de la interacción de partículas elementales con un campo electromagnético intenso</a>» (en anglès). <i>Journal of Soviet Laser Research</i>, vol. 6, 5, 1985, pàg. 497-617. <a href="/wiki/DOI" title="DOI">DOI</a>: <a rel="nofollow" class="external text" href="https://dx.doi.org/10.1007%2FBF01120220">10.1007/BF01120220</a>. <a href="/wiki/ISSN" title="ISSN">ISSN</a>: <a rel="nofollow" class="external text" href="//www.worldcat.org/issn/0270-2010">0270-2010</a>.</span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="Bibliografia">Bibliografia</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Efecte_Compton&action=edit&section=15" title="Modifica la secció: Bibliografia"><span>modifica</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><span class="citation" style="font-style:normal">S. Chen; <span style="font-variant: small-caps;">Ambrozewicz</span>; <span style="font-variant: small-caps;">Anghinolfi</span>; <span style="font-variant: small-caps;">Asryan</span> «Measurement of Deeply Virtual Compton Scattering with a Polarized Proton Target». <i><a href="/wiki/Physical_Review_Letters" title="Physical Review Letters">Physical Review Letters</a></i>, vol. 97, 7, 2006, pàg. 072002. <a href="/wiki/ArXiv" title="ArXiv">arXiv</a>: <a rel="nofollow" class="external text" href="http://arxiv.org/abs/hep-ex/0605012">hep-ex/0605012</a>. <a href="/wiki/Bibcode" title="Bibcode">Bibcode</a>: <a rel="nofollow" class="external text" href="http://adsabs.harvard.edu/abs/2006PhRvL..97g2002C">2006PhRvL..97g2002C</a>. <a href="/wiki/DOI" title="DOI">DOI</a>: <a rel="nofollow" class="external text" href="https://dx.doi.org/10.1103%2FPhysRevLett.97.072002">10.1103/PhysRevLett.97.072002</a>. <a href="/wiki/PubMed" title="PubMed">PMID</a>: <a href="https://www.ncbi.nlm.nih.gov/pubmed/17026221?dopt=Abstract" class="extiw" title="pmid:17026221">17026221</a>.</span></li> <li><span class="citation" style="font-style:normal">Compton, Arthur H. «A Quantum Theory of the Scattering of X-Rays by Light Elements». <i><a href="/wiki/Physical_Review" title="Physical Review">Physical Review</a></i>, vol. 21, 5, 5-1923, pàg. 483–502. <a href="/wiki/Bibcode" title="Bibcode">Bibcode</a>: <a rel="nofollow" class="external text" href="http://adsabs.harvard.edu/abs/1923PhRv...21..483C">1923PhRv...21..483C</a>. <a href="/wiki/DOI" title="DOI">DOI</a>: <a rel="nofollow" class="external text" href="https://dx.doi.org/10.1103%2FPhysRev.21.483">10.1103/PhysRev.21.483</a>.</span> (trabajo original de 1923 en el sitio web de la American Physical Society)</li> <li>Stuewer, Roger H. (1975), The Compton Effect: Turning Point in Physics (New York: Science History Publications)</li></ul> <div class="mw-heading mw-heading2"><h2 id="Enllaços_externs"><span id="Enlla.C3.A7os_externs"></span>Enllaços externs</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Efecte_Compton&action=edit&section=16" title="Modifica la secció: Enllaços externs"><span>modifica</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r33663753">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:#f9f9f9;display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 2px 0;text-align:center}@media(min-width:500px){.mw-parser-output .side-box-flex{display:flex;align-items:center}.mw-parser-output .side-box-text{flex:1;min-width:0}}@media(min-width:720px){.mw-parser-output .side-box{width:238px}.mw-parser-output .side-box-right{clear:right;float:right;margin-left:1em}.mw-parser-output .side-box-left{margin-right:1em}.mw-parser-output .side-box-center{clear:both;margin:auto}}</style><div class="side-box metadata side-box-right plainlinks"> <div class="side-box-flex"> <div class="side-box-image"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png" decoding="async" width="30" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/45px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/59px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></span></span></div> <div class="side-box-text plainlist">A <span class="plainlinks"><a class="external text" href="https://commons.wikimedia.org/wiki/P%C3%A0gina_principal?uselang=ca">Wikimedia Commons</a></span> hi ha contingut multimèdia relatiu a: <i><b><a href="https://commons.wikimedia.org/wiki/Category:Compton_scattering" class="extiw" title="commons:Category:Compton scattering">Efecte Compton</a></b></i></div></div> </div> <ul><li><a rel="nofollow" class="external text" href="http://prola.aps.org/abstract/PR/v21/i5/p483_1"><i>A Quantum Theory of the Scattering of X-Rays by Light Elements</i></a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20170127201624/http://prola.aps.org/abstract/PR/v21/i5/p483_1">Arxivat</a> 2017-01-27 a <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>. - the original 1923 <i><a href="/wiki/Physical_Review" title="Physical Review">Physical Review</a></i> paper by Arthur H. 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