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id="toc-Discovery_and_initial_characterization" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Discovery_and_initial_characterization"> <div class="vector-toc-text"> 2.1 Discovery and initial characterization </div> </a> <ul id="toc-Discovery_and_initial_characterization-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Neutrinos" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Neutrinos"> <div class="vector-toc-text"> 2.2 Neutrinos </div> </a> <ul id="toc-Neutrinos-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-β+_decay_and_electron_capture" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#β+_decay_and_electron_capture"> <div class="vector-toc-text"> 2.3 β+ decay and electron capture </div> </a> <ul id="toc-β+_decay_and_electron_capture-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Non-conservation_of_parity" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Non-conservation_of_parity"> <div class="vector-toc-text"> 2.4 Non-conservation of parity </div> </a> <ul id="toc-Non-conservation_of_parity-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-β−_decay" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#β−_decay"> <div class="vector-toc-text"> 3 β− decay </div> </a> <ul id="toc-β−_decay-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-β+_decay" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#β+_decay"> <div class="vector-toc-text"> 4 β+ decay </div> </a> <ul id="toc-β+_decay-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Electron_capture_(K-capture/L-capture)" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Electron_capture_(K-capture/L-capture)"> <div class="vector-toc-text"> 5 Electron capture (K-capture/L-capture) </div> </a> <ul id="toc-Electron_capture_(K-capture/L-capture)-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Nuclear_transmutation" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Nuclear_transmutation"> <div class="vector-toc-text"> 6 Nuclear transmutation </div> </a> <button aria-controls="toc-Nuclear_transmutation-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> Toggle Nuclear transmutation subsection </button> <ul id="toc-Nuclear_transmutation-sublist" class="vector-toc-list"> <li id="toc-Competition_of_beta_decay_types" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Competition_of_beta_decay_types"> <div class="vector-toc-text"> 6.1 Competition of beta decay types </div> </a> <ul id="toc-Competition_of_beta_decay_types-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Stability_of_naturally_occurring_nuclides" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Stability_of_naturally_occurring_nuclides"> <div class="vector-toc-text"> 6.2 Stability of naturally occurring nuclides </div> </a> <ul id="toc-Stability_of_naturally_occurring_nuclides-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Conservation_rules_for_beta_decay" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Conservation_rules_for_beta_decay"> <div class="vector-toc-text"> 7 Conservation rules for beta decay </div> </a> <button aria-controls="toc-Conservation_rules_for_beta_decay-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> Toggle Conservation rules for beta decay subsection </button> <ul id="toc-Conservation_rules_for_beta_decay-sublist" class="vector-toc-list"> <li id="toc-Baryon_number_is_conserved" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Baryon_number_is_conserved"> <div class="vector-toc-text"> 7.1 Baryon number is conserved </div> </a> <ul id="toc-Baryon_number_is_conserved-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Lepton_number_is_conserved" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Lepton_number_is_conserved"> <div class="vector-toc-text"> 7.2 Lepton number is conserved </div> </a> <ul id="toc-Lepton_number_is_conserved-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Angular_momentum" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Angular_momentum"> <div class="vector-toc-text"> 7.3 Angular momentum </div> </a> <ul id="toc-Angular_momentum-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Energy_release" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Energy_release"> <div class="vector-toc-text"> 8 Energy release </div> </a> <button aria-controls="toc-Energy_release-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> Toggle Energy release subsection </button> <ul id="toc-Energy_release-sublist" class="vector-toc-list"> <li id="toc-β−_decay_2" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#β−_decay_2"> <div class="vector-toc-text"> 8.1 β− decay </div> </a> <ul id="toc-β−_decay_2-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-β+_decay_2" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#β+_decay_2"> <div class="vector-toc-text"> 8.2 β+ decay </div> </a> <ul id="toc-β+_decay_2-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Electron_capture" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Electron_capture"> <div class="vector-toc-text"> 8.3 Electron capture </div> </a> <ul id="toc-Electron_capture-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Beta_emission_spectrum" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Beta_emission_spectrum"> <div class="vector-toc-text"> 9 Beta emission spectrum </div> </a> <button aria-controls="toc-Beta_emission_spectrum-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> Toggle Beta emission spectrum subsection </button> <ul id="toc-Beta_emission_spectrum-sublist" class="vector-toc-list"> <li id="toc-Fermi_function" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Fermi_function"> <div class="vector-toc-text"> 9.1 Fermi function </div> </a> <ul id="toc-Fermi_function-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Kurie_plot" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Kurie_plot"> <div class="vector-toc-text"> 9.2 Kurie plot </div> </a> <ul id="toc-Kurie_plot-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Helicity_(polarization)_of_neutrinos,_electrons_and_positrons_emitted_in_beta_decay" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Helicity_(polarization)_of_neutrinos,_electrons_and_positrons_emitted_in_beta_decay"> <div class="vector-toc-text"> 10 Helicity (polarization) of neutrinos, electrons and positrons emitted in beta decay </div> </a> <ul id="toc-Helicity_(polarization)_of_neutrinos,_electrons_and_positrons_emitted_in_beta_decay-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Types_of_beta_decay_transitions" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Types_of_beta_decay_transitions"> <div class="vector-toc-text"> 11 Types of beta decay transitions </div> </a> <button aria-controls="toc-Types_of_beta_decay_transitions-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> Toggle Types of beta decay transitions subsection </button> <ul id="toc-Types_of_beta_decay_transitions-sublist" class="vector-toc-list"> <li id="toc-Fermi_transitions" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Fermi_transitions"> <div class="vector-toc-text"> 11.1 Fermi transitions </div> </a> <ul id="toc-Fermi_transitions-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Gamow–Teller_transitions" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Gamow–Teller_transitions"> <div class="vector-toc-text"> 11.2 Gamow–Teller transitions </div> </a> <ul id="toc-Gamow–Teller_transitions-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Forbidden_transitions" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Forbidden_transitions"> <div class="vector-toc-text"> 11.3 Forbidden transitions </div> </a> <ul id="toc-Forbidden_transitions-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Rare_decay_modes" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Rare_decay_modes"> <div class="vector-toc-text"> 12 Rare decay modes </div> </a> <button aria-controls="toc-Rare_decay_modes-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> Toggle Rare decay modes subsection </button> <ul id="toc-Rare_decay_modes-sublist" class="vector-toc-list"> <li id="toc-Bound-state_β−_decay" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Bound-state_β−_decay"> <div class="vector-toc-text"> 12.1 Bound-state β− decay </div> </a> <ul id="toc-Bound-state_β−_decay-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Double_beta_decay" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Double_beta_decay"> <div class="vector-toc-text"> 12.2 Double beta decay </div> </a> <ul id="toc-Double_beta_decay-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> 13 See also </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> 14 References </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Bibliography" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Bibliography"> <div class="vector-toc-text"> 15 Bibliography </div> </a> <ul id="toc-Bibliography-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> 16 External links </div> </a> <ul id="toc-External_links-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="Contents" 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="Toggle the table of contents" > <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" > Toggle the table of contents </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">Beta decay</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="Go to an article in another language. Available in 65 languages" > <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-65" aria-hidden="true" > 65 languages </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Betaverval" title="Betaverval – Afrikaans" lang="af" hreflang="af" data-title="Betaverval" data-language-autonym="Afrikaans" data-language-local-name="Afrikaans" class="interlanguage-link-target">Afrikaans</a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%A7%D8%B6%D9%85%D8%AD%D9%84%D8%A7%D9%84_%D8%A8%D9%8A%D8%AA%D8%A7" title="اضمحلال بيتا – Arabic" lang="ar" hreflang="ar" data-title="اضمحلال بيتا" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target">العربية</a></li><li class="interlanguage-link interwiki-an mw-list-item"><a href="https://an.wikipedia.org/wiki/Desintegraci%C3%B3n_beta" title="Desintegración beta – Aragonese" lang="an" hreflang="an" data-title="Desintegración beta" data-language-autonym="Aragonés" data-language-local-name="Aragonese" class="interlanguage-link-target">Aragonés</a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Emisi%C3%B3n_beta" title="Emisión beta – Asturian" lang="ast" hreflang="ast" data-title="Emisión beta" data-language-autonym="Asturianu" data-language-local-name="Asturian" class="interlanguage-link-target">Asturianu</a></li><li class="interlanguage-link interwiki-azb mw-list-item"><a href="https://azb.wikipedia.org/wiki/%D8%A8%D8%AA%D8%A7_%D9%BE%D9%88%D8%B2%D9%88%D9%84%D9%88%D8%B4%D9%88" title="بتا پوزولوشو – South Azerbaijani" lang="azb" hreflang="azb" data-title="بتا پوزولوشو" data-language-autonym="تۆرکجه" data-language-local-name="South Azerbaijani" class="interlanguage-link-target">تۆرکجه</a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%AC%E0%A6%BF%E0%A6%9F%E0%A6%BE_%E0%A6%95%E0%A7%8D%E0%A6%B7%E0%A6%AF%E0%A6%BC" title="বিটা ক্ষয় – Bangla" lang="bn" hreflang="bn" data-title="বিটা ক্ষয়" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target">বাংলা</a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%91%D1%8D%D1%82%D0%B0-%D1%80%D0%B0%D1%81%D0%BF%D0%B0%D0%B4" title="Бэта-распад – Belarusian" lang="be" hreflang="be" data-title="Бэта-распад" data-language-autonym="Беларуская" data-language-local-name="Belarusian" class="interlanguage-link-target">Беларуская</a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%91%D0%B5%D1%82%D0%B0-%D1%80%D0%B0%D0%B7%D0%BF%D0%B0%D0%B4" title="Бета-разпад – Bulgarian" lang="bg" hreflang="bg" data-title="Бета-разпад" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target">Български</a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Desintegraci%C3%B3_%CE%B2" title="Desintegració β – Catalan" lang="ca" hreflang="ca" data-title="Desintegració β" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target">Català</a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Betahenfald" title="Betahenfald – Danish" lang="da" hreflang="da" data-title="Betahenfald" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target">Dansk</a></li><li class="interlanguage-link interwiki-de badge-Q70894304 mw-list-item" title=""><a href="https://de.wikipedia.org/wiki/Betazerfall" title="Betazerfall – German" lang="de" hreflang="de" data-title="Betazerfall" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target">Deutsch</a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Beetalagunemine" title="Beetalagunemine – Estonian" lang="et" hreflang="et" data-title="Beetalagunemine" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target">Eesti</a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%94%CE%B9%CE%AC%CF%83%CF%80%CE%B1%CF%83%CE%B7_%CE%B2%CE%AE%CF%84%CE%B1" title="Διάσπαση βήτα – Greek" lang="el" hreflang="el" data-title="Διάσπαση βήτα" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target">Ελληνικά</a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Desintegraci%C3%B3n_beta" title="Desintegración beta – Spanish" lang="es" hreflang="es" data-title="Desintegración beta" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target">Español</a></li><li class="interlanguage-link interwiki-eo badge-Q70894304 mw-list-item" title=""><a href="https://eo.wikipedia.org/wiki/Beta-diseri%C4%9Do" title="Beta-diseriĝo – Esperanto" lang="eo" hreflang="eo" data-title="Beta-diseriĝo" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target">Esperanto</a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Beta_desintegrazio" title="Beta desintegrazio – Basque" lang="eu" hreflang="eu" data-title="Beta desintegrazio" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target">Euskara</a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%88%D8%A7%D9%BE%D8%A7%D8%B4%DB%8C_%D8%A8%D8%AA%D8%A7" title="واپاشی بتا – Persian" lang="fa" hreflang="fa" data-title="واپاشی بتا" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target">فارسی</a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Radioactivit%C3%A9_%CE%B2" title="Radioactivité β – French" lang="fr" hreflang="fr" data-title="Radioactivité β" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target">Français</a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/B%C3%A9ite-mheath" title="Béite-mheath – Irish" lang="ga" hreflang="ga" data-title="Béite-mheath" data-language-autonym="Gaeilge" data-language-local-name="Irish" class="interlanguage-link-target">Gaeilge</a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%B2%A0%ED%83%80_%EB%B6%95%EA%B4%B4" title="베타 붕괴 – Korean" lang="ko" hreflang="ko" data-title="베타 붕괴" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target">한국어</a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%B2%D5%A5%D5%BF%D5%A1-%D5%BF%D6%80%D5%B8%D5%B0%D5%B8%D6%82%D5%B4" title="Բետա-տրոհում – Armenian" lang="hy" hreflang="hy" data-title="Բետա-տրոհում" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target">Հայերեն</a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%AC%E0%A5%80%E0%A4%9F%E0%A4%BE_%E0%A4%95%E0%A5%8D%E0%A4%B7%E0%A4%AF" title="बीटा क्षय – Hindi" lang="hi" hreflang="hi" data-title="बीटा क्षय" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target">हिन्दी</a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Beta_raspad" title="Beta raspad – Croatian" lang="hr" hreflang="hr" data-title="Beta raspad" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target">Hrvatski</a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Peluruhan_beta" title="Peluruhan beta – Indonesian" lang="id" hreflang="id" data-title="Peluruhan beta" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target">Bahasa Indonesia</a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Betasundrun" title="Betasundrun – Icelandic" lang="is" hreflang="is" data-title="Betasundrun" data-language-autonym="Íslenska" data-language-local-name="Icelandic" class="interlanguage-link-target">Íslenska</a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Decadimento_beta" title="Decadimento beta – Italian" lang="it" hreflang="it" data-title="Decadimento beta" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target">Italiano</a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%A7%D7%A8%D7%99%D7%A0%D7%AA_%D7%91%D7%98%D7%90" title="קרינת בטא – Hebrew" lang="he" hreflang="he" data-title="קרינת בטא" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target">עברית</a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%91%E1%83%94%E1%83%A2%E1%83%90-%E1%83%93%E1%83%90%E1%83%A8%E1%83%9A%E1%83%90" title="ბეტა-დაშლა – Georgian" lang="ka" hreflang="ka" data-title="ბეტა-დაშლა" data-language-autonym="ქართული" data-language-local-name="Georgian" class="interlanguage-link-target">ქართული</a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%91%D0%B5%D1%82%D0%B0-%D1%8B%D0%B4%D1%8B%D1%80%D0%B0%D1%83" title="Бета-ыдырау – Kazakh" lang="kk" hreflang="kk" data-title="Бета-ыдырау" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target">Қазақша</a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%91%D0%B5%D1%82%D0%B0-%D0%B0%D0%B6%D1%8B%D1%80%D0%BE%D0%BE" title="Бета-ажыроо – Kyrgyz" lang="ky" hreflang="ky" data-title="Бета-ажыроо" data-language-autonym="Кыргызча" data-language-local-name="Kyrgyz" class="interlanguage-link-target">Кыргызча</a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/B%C4%93ta_sabruk%C5%A1ana" title="Bēta sabrukšana – Latvian" lang="lv" hreflang="lv" data-title="Bēta sabrukšana" data-language-autonym="Latviešu" data-language-local-name="Latvian" class="interlanguage-link-target">Latviešu</a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Beta_skilimas" title="Beta skilimas – Lithuanian" lang="lt" hreflang="lt" data-title="Beta skilimas" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" class="interlanguage-link-target">Lietuvių</a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/B%C3%A9ta-boml%C3%A1s" title="Béta-bomlás – Hungarian" lang="hu" hreflang="hu" data-title="Béta-bomlás" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target">Magyar</a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%91%D0%B5%D1%82%D0%B0-%D1%80%D0%B0%D1%81%D0%BF%D0%B0%D0%B4" title="Бета-распад – Macedonian" lang="mk" hreflang="mk" data-title="Бета-распад" data-language-autonym="Македонски" data-language-local-name="Macedonian" class="interlanguage-link-target">Македонски</a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Pereputan_beta" title="Pereputan beta – Malay" lang="ms" hreflang="ms" data-title="Pereputan beta" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" class="interlanguage-link-target">Bahasa Melayu</a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/B%C3%A8taverval" title="Bètaverval – Dutch" lang="nl" hreflang="nl" data-title="Bètaverval" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target">Nederlands</a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%83%99%E3%83%BC%E3%82%BF%E5%B4%A9%E5%A3%8A" title="ベータ崩壊 – Japanese" lang="ja" hreflang="ja" data-title="ベータ崩壊" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target">日本語</a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Betahenfall" title="Betahenfall – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Betahenfall" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target">Norsk bokmål</a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Betadesintegrasjon" title="Betadesintegrasjon – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Betadesintegrasjon" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwegian Nynorsk" class="interlanguage-link-target">Norsk nynorsk</a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Beta-yemirilish" title="Beta-yemirilish – Uzbek" lang="uz" hreflang="uz" data-title="Beta-yemirilish" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" class="interlanguage-link-target">Oʻzbekcha / ўзбекча</a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%AC%E0%A9%80%E0%A8%9F%E0%A8%BE_%E0%A8%A1%E0%A8%BF%E0%A8%95%E0%A9%87" title="ਬੀਟਾ ਡਿਕੇ – Punjabi" lang="pa" hreflang="pa" data-title="ਬੀਟਾ ਡਿਕੇ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="Punjabi" class="interlanguage-link-target">ਪੰਜਾਬੀ</a></li><li class="interlanguage-link interwiki-nds mw-list-item"><a href="https://nds.wikipedia.org/wiki/Betaverfall" title="Betaverfall – Low German" lang="nds" hreflang="nds" data-title="Betaverfall" data-language-autonym="Plattdüütsch" data-language-local-name="Low German" class="interlanguage-link-target">Plattdüütsch</a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Rozpad_beta" title="Rozpad beta – Polish" lang="pl" hreflang="pl" data-title="Rozpad beta" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target">Polski</a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Emiss%C3%A3o_beta" title="Emissão beta – Portuguese" lang="pt" hreflang="pt" data-title="Emissão beta" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target">Português</a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Dezintegrare_beta" title="Dezintegrare beta – Romanian" lang="ro" hreflang="ro" data-title="Dezintegrare beta" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target">Română</a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%91%D0%B5%D1%82%D0%B0-%D1%80%D0%B0%D1%81%D0%BF%D0%B0%D0%B4" title="Бета-распад – Russian" lang="ru" hreflang="ru" data-title="Бета-распад" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target">Русский</a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/%E0%B6%B6%E0%B7%93%E0%B6%A7%E0%B7%8F_%E0%B6%9A%E0%B7%8A%E0%B7%82%E0%B6%BA_%E0%B7%80%E0%B7%93%E0%B6%B8" title="බීටා ක්ෂය වීම – Sinhala" lang="si" hreflang="si" data-title="බීටා ක්ෂය වීම" data-language-autonym="සිංහල" data-language-local-name="Sinhala" class="interlanguage-link-target">සිංහල</a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Beta_decay" title="Beta decay – Simple English" lang="en-simple" hreflang="en-simple" data-title="Beta decay" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target">Simple English</a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Beta_rozpad" title="Beta rozpad – Slovak" lang="sk" hreflang="sk" data-title="Beta rozpad" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target">Slovenčina</a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Razpad_beta" title="Razpad beta – Slovenian" lang="sl" hreflang="sl" data-title="Razpad beta" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target">Slovenščina</a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%91%D0%B5%D1%82%D0%B0_%D1%80%D0%B0%D1%81%D0%BF%D0%B0%D0%B4" title="Бета распад – Serbian" lang="sr" hreflang="sr" data-title="Бета распад" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target">Српски / srpski</a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Beta_raspad" title="Beta raspad – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Beta raspad" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croatian" class="interlanguage-link-target">Srpskohrvatski / српскохрватски</a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Beetahajoaminen" title="Beetahajoaminen – Finnish" lang="fi" hreflang="fi" data-title="Beetahajoaminen" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target">Suomi</a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Betas%C3%B6nderfall" title="Betasönderfall – Swedish" lang="sv" hreflang="sv" data-title="Betasönderfall" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target">Svenska</a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%AA%E0%AF%80%E0%AE%9F%E0%AF%8D%E0%AE%9F%E0%AE%BE_%E0%AE%9A%E0%AE%BF%E0%AE%A4%E0%AF%88%E0%AE%B5%E0%AF%81" title="பீட்டா சிதைவு – Tamil" lang="ta" hreflang="ta" data-title="பீட்டா சிதைவு" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target">தமிழ்</a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/%D0%91%D0%B5%D1%82%D0%B0-%D1%82%D0%B0%D1%80%D0%BA%D0%B0%D0%BB%D1%8B%D1%88" title="Бета-таркалыш – Tatar" lang="tt" hreflang="tt" data-title="Бета-таркалыш" data-language-autonym="Татарча / tatarça" data-language-local-name="Tatar" class="interlanguage-link-target">Татарча / tatarça</a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%81%E0%B8%B2%E0%B8%A3%E0%B8%AA%E0%B8%A5%E0%B8%B2%E0%B8%A2%E0%B9%83%E0%B8%AB%E0%B9%89%E0%B8%AD%E0%B8%99%E0%B8%B8%E0%B8%A0%E0%B8%B2%E0%B8%84%E0%B8%9A%E0%B8%B5%E0%B8%95%E0%B8%B2" title="การสลายให้อนุภาคบีตา – Thai" lang="th" hreflang="th" data-title="การสลายให้อนุภาคบีตา" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target">ไทย</a></li><li class="interlanguage-link interwiki-tg mw-list-item"><a href="https://tg.wikipedia.org/wiki/%D0%91%D0%B5%D1%82%D0%B0-%D0%BA%D0%BE%D2%B3%D0%B8%D1%88" title="Бета-коҳиш – Tajik" lang="tg" hreflang="tg" data-title="Бета-коҳиш" data-language-autonym="Тоҷикӣ" data-language-local-name="Tajik" class="interlanguage-link-target">Тоҷикӣ</a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Beta_bozunmas%C4%B1" title="Beta bozunması – Turkish" lang="tr" hreflang="tr" data-title="Beta bozunması" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target">Türkçe</a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%91%D0%B5%D1%82%D0%B0-%D1%80%D0%BE%D0%B7%D0%BF%D0%B0%D0%B4" title="Бета-розпад – Ukrainian" lang="uk" hreflang="uk" data-title="Бета-розпад" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target">Українська</a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D8%A8%DB%8C%D9%B9%D8%A7_%D8%AA%D9%86%D8%B2%D9%84" title="بیٹا تنزل – Urdu" lang="ur" hreflang="ur" data-title="بیٹا تنزل" data-language-autonym="اردو" data-language-local-name="Urdu" class="interlanguage-link-target">اردو</a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Ph%C3%A2n_r%C3%A3_beta" title="Phân rã beta – Vietnamese" lang="vi" hreflang="vi" data-title="Phân rã beta" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamese" class="interlanguage-link-target">Tiếng Việt</a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%CE%92%E8%A1%B0%E5%8F%98" title="Β衰变 – Wu" lang="wuu" hreflang="wuu" data-title="Β衰变" data-language-autonym="吴语" data-language-local-name="Wu" class="interlanguage-link-target">吴语</a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/Beta_%E8%A1%B0%E8%AE%8A" title="Beta 衰變 – Cantonese" lang="yue" hreflang="yue" data-title="Beta 衰變" data-language-autonym="粵語" data-language-local-name="Cantonese" class="interlanguage-link-target">粵語</a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%CE%92%E8%A1%B0%E5%8F%98" title="Β衰变 – Chinese" lang="zh" hreflang="zh" data-title="Β衰变" data-language-autonym="中文" data-language-local-name="Chinese" 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class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Type of radioactive decay</div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Beta-minus_Decay.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/aa/Beta-minus_Decay.svg/240px-Beta-minus_Decay.svg.png" decoding="async" width="240" height="163" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/aa/Beta-minus_Decay.svg/360px-Beta-minus_Decay.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/aa/Beta-minus_Decay.svg/480px-Beta-minus_Decay.svg.png 2x" data-file-width="250" data-file-height="170" /></a><figcaption> β−  decay in an <a href="/wiki/Atomic_nucleus" title="Atomic nucleus">atomic nucleus</a> (the accompanying antineutrino is omitted). The inset shows beta decay of a free neutron. Neither of these depictions shows the intermediate <a href="/wiki/Virtual_particle" title="Virtual particle">virtual</a> <a href="/wiki/W_boson" class="mw-redirect" title="W boson"> W− </a> boson.</figcaption></figure> <style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output .hlist .mw-empty-li{display:none}.mw-parser-output .hlist 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.sidebar{width:100%!important;clear:both;float:none!important;margin-left:0!important;margin-right:0!important}}body.skin--responsive .mw-parser-output .sidebar a>img{max-width:none!important}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-list-title,html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle{background:transparent!important}html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle a{color:var(--color-progressive)!important}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-list-title,html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle{background:transparent!important}html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle a{color:var(--color-progressive)!important}}@media print{body.ns-0 .mw-parser-output .sidebar{display:none!important}}</style><table class="sidebar sidebar-collapse nomobile nowraplinks"><tbody><tr><th class="sidebar-title"><a href="/wiki/Nuclear_physics" title="Nuclear physics">Nuclear physics</a></th></tr><tr><td class="sidebar-image"><a href="/wiki/File:NuclearReaction.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4b/NuclearReaction.svg/200px-NuclearReaction.svg.png" decoding="async" width="200" height="127" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4b/NuclearReaction.svg/300px-NuclearReaction.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4b/NuclearReaction.svg/400px-NuclearReaction.svg.png 2x" data-file-width="550" data-file-height="350" /></a></td></tr><tr><td class="sidebar-content hlist"> <ul><li><a href="/wiki/Atomic_nucleus" title="Atomic nucleus">Nucleus</a></li> <li><a href="/wiki/Nucleon" title="Nucleon">Nucleons</a> <ul><li><a href="/wiki/Proton" title="Proton">p</a></li> <li><a href="/wiki/Neutron" title="Neutron">n</a></li></ul></li> <li><a href="/wiki/Nuclear_matter" title="Nuclear matter">Nuclear matter</a></li> <li><a href="/wiki/Nuclear_force" title="Nuclear force">Nuclear force</a></li> <li><a href="/wiki/Nuclear_structure" title="Nuclear structure">Nuclear structure</a></li> <li><a href="/wiki/Nuclear_reaction" title="Nuclear reaction">Nuclear reaction</a></li></ul></td> </tr><tr><td class="sidebar-content hlist"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)"><a href="/wiki/Nuclear_model" class="mw-redirect" title="Nuclear model">Models of the nucleus</a></div><div class="sidebar-list-content mw-collapsible-content"> <ul><li><a href="/wiki/Semi-empirical_mass_formula" title="Semi-empirical mass formula">Liquid drop</a></li> <li><a href="/wiki/Nuclear_shell_model" title="Nuclear shell model">Nuclear shell model</a></li> <li><a href="/wiki/Interacting_boson_model" title="Interacting boson model">Interacting boson model</a></li> <li><a href="/wiki/Ab_initio_methods_(nuclear_physics)" title="Ab initio methods (nuclear physics)">Ab initio</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content hlist"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)"><a href="/wiki/Nuclide" title="Nuclide">Nuclides</a>' classification</div><div class="sidebar-list-content mw-collapsible-content"> <ul><li><a href="/wiki/Isotope" title="Isotope">Isotopes</a> – equal <a href="/wiki/Atomic_number" title="Atomic number">Z</a> </li></ul> <ul><li><a href="/wiki/Isobar_(nuclide)" title="Isobar (nuclide)">Isobars</a> – equal <a href="/wiki/Mass_number" title="Mass number">A</a></li></ul> <ul><li><a href="/wiki/Isotone" title="Isotone">Isotones</a> – equal <a href="/wiki/Neutron_number" title="Neutron number">N</a></li></ul> <ul><li><a href="/wiki/Isodiapher" class="mw-redirect" title="Isodiapher">Isodiaphers</a> – equal <a href="/wiki/Neutron_excess" class="mw-redirect" title="Neutron excess">N − Z</a></li></ul> <ul><li><a href="/wiki/Nuclear_isomer" title="Nuclear isomer">Isomers</a> – equal all the above</li></ul> <ul><li><a href="/wiki/Mirror_nuclei" title="Mirror nuclei">Mirror nuclei</a> – Z ↔ N</li></ul> <ul><li><a href="/wiki/Stable_isotope" class="mw-redirect" title="Stable isotope">Stable</a></li> <li><a href="/wiki/Magic_number_(physics)" title="Magic number (physics)">Magic</a></li> <li><a href="/wiki/Even_and_odd_atomic_nuclei" title="Even and odd atomic nuclei">Even/odd</a></li> <li><a href="/wiki/Halo_nucleus" title="Halo nucleus">Halo</a> <ul><li><a href="/wiki/Borromean_nucleus" title="Borromean nucleus">Borromean</a></li></ul></li></ul></div></div></td> </tr><tr><td class="sidebar-content hlist"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)">Nuclear stability</div><div class="sidebar-list-content mw-collapsible-content"> <ul><li><a href="/wiki/Nuclear_binding_energy" title="Nuclear binding energy">Binding energy</a></li> <li><a href="/wiki/Proton%E2%80%93neutron_ratio" class="mw-redirect" title="Proton–neutron ratio">p–n ratio</a></li> <li><a href="/wiki/Nuclear_drip_line" title="Nuclear drip line">Drip line</a></li> <li><a href="/wiki/Island_of_stability" title="Island of stability">Island of stability</a></li> <li><a href="/wiki/Valley_of_stability" title="Valley of stability">Valley of stability</a></li> <li><a href="/wiki/Stable_nuclide" title="Stable nuclide">Stable nuclide</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content hlist"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)"><a href="/wiki/Radioactive_decay" title="Radioactive decay">Radioactive decay</a></div><div class="sidebar-list-content mw-collapsible-content"> <ul><li><a href="/wiki/Alpha_decay" title="Alpha decay">Alpha α</a></li> <li><a class="mw-selflink selflink">Beta β</a> <ul><li><a href="/wiki/Double_beta_decay" title="Double beta decay">2β</a> <ul><li><a href="/wiki/Neutrinoless_double_beta_decay" title="Neutrinoless double beta decay">0v</a></li></ul></li> <li><a href="/wiki/Positron_emission" title="Positron emission">β+</a></li></ul></li> <li><a href="/wiki/Electron_capture" title="Electron capture">K/L capture</a></li> <li><a href="/wiki/Isomeric_transition" class="mw-redirect" title="Isomeric transition">Isomeric</a> <ul><li><a href="/wiki/Gamma_ray" title="Gamma ray">Gamma γ</a></li> <li><a href="/wiki/Internal_conversion" title="Internal conversion">Internal conversion</a></li></ul></li> <li><a href="/wiki/Spontaneous_fission" title="Spontaneous fission">Spontaneous fission</a></li> <li><a href="/wiki/Cluster_decay" title="Cluster decay">Cluster decay</a></li> <li><a href="/wiki/Neutron_emission" title="Neutron emission">Neutron emission</a></li> <li><a href="/wiki/Proton_emission" title="Proton emission">Proton emission</a></li></ul> <ul><li><a href="/wiki/Decay_energy" title="Decay energy">Decay energy</a></li> <li><a href="/wiki/Decay_chain" title="Decay chain">Decay chain</a></li> <li><a href="/wiki/Decay_product" title="Decay product">Decay product</a></li> <li><a href="/wiki/Radiogenic_nuclide" title="Radiogenic nuclide">Radiogenic nuclide</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content hlist"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)"><a href="/wiki/Nuclear_fission" title="Nuclear fission">Nuclear fission</a></div><div class="sidebar-list-content mw-collapsible-content"> <ul><li><a href="/wiki/Spontaneous_fission" title="Spontaneous fission">Spontaneous</a></li> <li><a href="/wiki/Nuclear_fission_product" title="Nuclear fission product">Products</a> <ul><li><a href="/wiki/Nucleon_pair_breaking_in_fission" title="Nucleon pair breaking in fission">pair breaking</a></li></ul></li> <li><a href="/wiki/Photofission" title="Photofission">Photofission</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content hlist"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)">Capturing processes</div><div class="sidebar-list-content mw-collapsible-content"> <ul><li><a href="/wiki/Electron_capture" title="Electron capture">electron</a> <ul><li><a href="/wiki/Double_electron_capture" title="Double electron capture">2×</a></li></ul></li> <li><a href="/wiki/Neutron_capture" title="Neutron capture">neutron</a> <ul><li><a href="/wiki/S-process" title="S-process">s</a></li> <li><a href="/wiki/R-process" title="R-process">r</a></li></ul></li> <li><a href="/wiki/Proton_capture" title="Proton capture">proton</a> <ul><li><a href="/wiki/P-process" title="P-process">p</a></li> <li><a href="/wiki/Rp-process" title="Rp-process">rp</a></li></ul></li></ul></div></div></td> </tr><tr><td class="sidebar-content hlist"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)">High-energy processes</div><div class="sidebar-list-content mw-collapsible-content"> <ul><li><a href="/wiki/Spallation" title="Spallation">Spallation</a> <ul><li><a href="/wiki/Cosmic_ray_spallation" title="Cosmic ray spallation">by cosmic ray</a></li></ul></li> <li><a href="/wiki/Photodisintegration" title="Photodisintegration">Photodisintegration</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content hlist"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)"><a href="/wiki/Nucleosynthesis" title="Nucleosynthesis">Nucleosynthesis</a> and <a href="/wiki/Nuclear_astrophysics" title="Nuclear astrophysics">nuclear astrophysics</a></div><div class="sidebar-list-content mw-collapsible-content"> <ul><li><a href="/wiki/Nuclear_fusion" title="Nuclear fusion">Nuclear fusion</a></li></ul> <ul><li>Processes: <ul><li><a href="/wiki/Stellar_nucleosynthesis" title="Stellar nucleosynthesis">Stellar</a></li> <li><a href="/wiki/Big_Bang_nucleosynthesis" title="Big Bang nucleosynthesis">Big Bang</a></li> <li><a href="/wiki/Supernova_nucleosynthesis" title="Supernova nucleosynthesis">Supernova</a></li></ul></li></ul> <ul><li>Nuclides: <ul><li><a href="/wiki/Primordial_nuclide" title="Primordial nuclide">Primordial</a></li> <li><a href="/wiki/Cosmogenic_nuclide" title="Cosmogenic nuclide">Cosmogenic</a></li> <li><a href="/wiki/Synthetic_element" title="Synthetic element">Artificial</a></li></ul></li></ul></div></div></td> </tr><tr><td class="sidebar-content hlist"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)"><a href="/wiki/High-energy_nuclear_physics" title="High-energy nuclear physics">High-energy nuclear physics</a></div><div class="sidebar-list-content mw-collapsible-content"> <ul><li><a href="/wiki/Quark%E2%80%93gluon_plasma" title="Quark–gluon plasma">Quark–gluon plasma</a></li> <li><a href="/wiki/Relativistic_Heavy_Ion_Collider" title="Relativistic Heavy Ion Collider">RHIC</a></li> <li><a href="/wiki/Large_Hadron_Collider" title="Large Hadron Collider">LHC</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content hlist"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)"><a href="/wiki/Category:Nuclear_physicists" title="Category:Nuclear physicists">Scientists</a></div><div class="sidebar-list-content mw-collapsible-content"> <ul><li><a href="/wiki/Luis_Walter_Alvarez" title="Luis Walter Alvarez">Alvarez</a></li> <li><a href="/wiki/Henri_Becquerel" title="Henri Becquerel">Becquerel</a></li> <li><a href="/wiki/Hans_Bethe" title="Hans Bethe">Bethe</a></li> <li><a href="/wiki/Aage_Bohr" title="Aage Bohr">A. Bohr</a></li> <li><a href="/wiki/Niels_Bohr" title="Niels Bohr">N. Bohr</a></li> <li><a href="/wiki/James_Chadwick" title="James Chadwick">Chadwick</a></li> <li><a href="/wiki/John_Cockcroft" title="John Cockcroft">Cockcroft</a></li> <li><a href="/wiki/Ir%C3%A8ne_Joliot-Curie" title="Irène Joliot-Curie">Ir. Curie</a></li> <li><a href="/wiki/Fr%C3%A9d%C3%A9ric_Joliot-Curie" title="Frédéric Joliot-Curie">Fr. Curie</a></li> <li><a href="/wiki/Pierre_Curie" title="Pierre Curie">Pi. Curie</a></li> <li><a href="/wiki/Marie_Curie" title="Marie Curie">Skłodowska-Curie</a></li> <li><a href="/wiki/Clinton_Davisson" title="Clinton Davisson">Davisson</a></li> <li><a href="/wiki/Enrico_Fermi" title="Enrico Fermi">Fermi</a></li> <li><a href="/wiki/Otto_Hahn" title="Otto Hahn">Hahn</a></li> <li><a href="/wiki/J._Hans_D._Jensen" title="J. Hans D. Jensen">Jensen</a></li> <li><a href="/wiki/Ernest_Lawrence" title="Ernest Lawrence">Lawrence</a></li> <li><a href="/wiki/Maria_Goeppert-Mayer" class="mw-redirect" title="Maria Goeppert-Mayer">Mayer</a></li> <li><a href="/wiki/Lise_Meitner" title="Lise Meitner">Meitner</a></li> <li><a href="/wiki/Mark_Oliphant" title="Mark Oliphant">Oliphant</a></li> <li><a href="/wiki/J._Robert_Oppenheimer" title="J. Robert Oppenheimer">Oppenheimer</a></li> <li><a href="/wiki/Alexandru_Proca" title="Alexandru Proca">Proca</a></li> <li><a href="/wiki/Edward_Mills_Purcell" title="Edward Mills Purcell">Purcell</a></li> <li><a href="/wiki/Isidor_Isaac_Rabi" title="Isidor Isaac Rabi">Rabi</a></li> <li><a href="/wiki/Ernest_Rutherford" title="Ernest Rutherford">Rutherford</a></li> <li><a href="/wiki/Frederick_Soddy" title="Frederick Soddy">Soddy</a></li> <li><a href="/wiki/Fritz_Strassmann" title="Fritz Strassmann">Strassmann</a></li> <li><a href="/wiki/W%C5%82adys%C5%82aw_%C5%9Awi%C4%85tecki_(physicist)" title="Władysław Świątecki (physicist)">Świątecki</a></li> <li><a href="/wiki/Le%C3%B3_Szil%C3%A1rd" class="mw-redirect" title="Leó Szilárd">Szilárd</a></li> <li><a href="/wiki/Edward_Teller" title="Edward Teller">Teller</a></li> <li><a href="/wiki/J._J._Thomson" title="J. J. Thomson">Thomson</a></li> <li><a href="/wiki/Ernest_Walton" title="Ernest Walton">Walton</a></li> <li><a href="/wiki/Eugene_Wigner" title="Eugene Wigner">Wigner</a></li></ul></div></div></td> </tr><tr><td class="sidebar-below hlist" style="background-color: transparent; border-color: #A2B8BF"> <ul><li><a href="/wiki/File:Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg" class="mw-file-description"><img alt="icon" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg/14px-Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg.png" decoding="async" width="14" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg/21px-Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg/28px-Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg.png 2x" data-file-width="530" data-file-height="600" /></a> <a href="/wiki/Portal:Physics" title="Portal:Physics">Physics portal</a></li> <li><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/16px-Symbol_category_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/23px-Symbol_category_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/31px-Symbol_category_class.svg.png 2x" data-file-width="180" data-file-height="185" /> <a href="/wiki/Category:Nuclear_physics" title="Category:Nuclear physics">Category</a></li></ul></td></tr><tr><td class="sidebar-navbar"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1239400231">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Nuclear_physics" title="Template:Nuclear physics"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Nuclear_physics" title="Template talk:Nuclear physics"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Nuclear_physics" title="Special:EditPage/Template:Nuclear physics"><abbr title="Edit this template">e</abbr></a></li></ul></div></td></tr></tbody></table> In <a href="/wiki/Nuclear_physics" title="Nuclear physics">nuclear physics</a>, beta decay (β-decay) is a type of <a href="/wiki/Radioactive_decay" title="Radioactive decay">radioactive decay</a> in which an <a href="/wiki/Atomic_nucleus" title="Atomic nucleus">atomic nucleus</a> emits a <a href="/wiki/Beta_particle" title="Beta particle">beta particle</a> (fast energetic <a href="/wiki/Electron" title="Electron">electron</a> or <a href="/wiki/Positron" title="Positron">positron</a>), transforming into an <a href="/wiki/Isobar_(nuclide)" title="Isobar (nuclide)">isobar</a> of that nuclide. For example, beta decay of a <a href="/wiki/Neutron" title="Neutron">neutron</a> transforms it into a <a href="/wiki/Proton" title="Proton">proton</a> by the emission of an electron accompanied by an <a href="/wiki/Antineutrino" class="mw-redirect" title="Antineutrino">antineutrino</a>; or, conversely a proton is converted into a neutron by the emission of a positron with a <a href="/wiki/Neutrino" title="Neutrino">neutrino</a> in what is called <a href="/wiki/Positron_emission" title="Positron emission">positron emission</a>. Neither the beta particle nor its associated (anti-)neutrino exist within the nucleus prior to beta decay, but are created in the decay process. By this process, unstable atoms obtain a more stable <a href="/wiki/Proton%E2%80%93neutron_ratio" class="mw-redirect" title="Proton–neutron ratio">ratio of protons to neutrons</a>. The probability of a nuclide decaying due to beta and other forms of decay is determined by its <a href="/wiki/Nuclear_binding_energy" title="Nuclear binding energy">nuclear binding energy</a>. The binding energies of all existing nuclides form what is called the nuclear band or <a href="/wiki/Valley_of_stability" title="Valley of stability">valley of stability</a>.<a href="#cite_note-konya74-1">[1]</a> For either electron or positron emission to be energetically possible, the energy release (<a href="#Energy_release">see below</a>) or <a href="/wiki/Q_value_(nuclear_science)" title="Q value (nuclear science)">Q value</a> must be positive. Beta decay is a consequence of the <a href="/wiki/Weak_interaction" title="Weak interaction">weak force</a>, which is characterized by relatively long decay times. Nucleons are composed of <a href="/wiki/Up_quark" title="Up quark">up quarks</a> and <a href="/wiki/Down_quark" title="Down quark">down quarks</a>,<a href="#cite_note-2">[2]</a> and the weak force allows a <a href="/wiki/Quark" title="Quark">quark</a> to change its <a href="/wiki/Flavour_(particle_physics)" title="Flavour (particle physics)">flavour</a> by means of a virtual <a href="/wiki/W_boson" class="mw-redirect" title="W boson">W boson</a> leading to creation of an electron/antineutrino or positron/neutrino pair. For example, a neutron, composed of two down quarks and an up quark, decays to a proton composed of a down quark and two up quarks. <a href="/wiki/Electron_capture" title="Electron capture">Electron capture</a> is sometimes included as a type of beta decay,<a href="#cite_note-3">[3]</a> because the basic nuclear process, mediated by the weak force, is the same. In electron capture, an inner atomic electron is captured by a proton in the nucleus, transforming it into a neutron, and an <a href="/wiki/Electron_neutrino" title="Electron neutrino">electron neutrino</a> is released. <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Description">Description</h2>[<a href="/w/index.php?title=Beta_decay&action=edit&section=1" title="Edit section: Description">edit</a>]</div> The two types of beta decay are known as beta minus and beta plus. In beta minus (β−) decay, a neutron is converted to a proton, and the process creates an electron and an <a href="/wiki/Electron_antineutrino" class="mw-redirect" title="Electron antineutrino">electron antineutrino</a>; while in beta plus (β+) decay, a proton is converted to a neutron and the process creates a positron and an electron neutrino. β+ decay is also known as <a href="/wiki/Positron_emission" title="Positron emission">positron emission</a>.<a href="#cite_note-4">[4]</a> Beta decay conserves a quantum number known as the <a href="/wiki/Lepton_number" title="Lepton number">lepton number</a>, or the number of electrons and their associated neutrinos (other leptons are the <a href="/wiki/Muon" title="Muon">muon</a> and <a href="/wiki/Tau_(particle)" title="Tau (particle)">tau</a> particles). These particles have lepton number +1, while their antiparticles have lepton number −1. Since a proton or neutron has lepton number zero, β+ decay (a positron, or antielectron) must be accompanied with an electron neutrino, while β− decay (an electron) must be accompanied by an electron antineutrino. An example of electron emission (β− decay) is the decay of <a href="/wiki/Carbon-14" title="Carbon-14">carbon-14</a> into <a href="/wiki/Nitrogen-14" class="mw-redirect" title="Nitrogen-14">nitrogen-14</a> with a <a href="/wiki/Half-life" title="Half-life">half-life</a> of about 5,730 years: <dl><dd>14 6C → 14 7N + e− + ν e</dd></dl> In this form of decay, the original element becomes a new chemical element in a process known as <a href="/wiki/Nuclear_transmutation" title="Nuclear transmutation">nuclear transmutation</a>. This new element has an unchanged <a href="/wiki/Mass_number" title="Mass number">mass number</a> A, but an <a href="/wiki/Atomic_number" title="Atomic number">atomic number</a> Z that is increased by one. As in all nuclear decays, the decaying element (in this case 14 6C ) is known as the parent nuclide while the resulting element (in this case 14 7N ) is known as the daughter nuclide. Another example is the decay of hydrogen-3 (<a href="/wiki/Tritium" title="Tritium">tritium</a>) into <a href="/wiki/Helium-3" title="Helium-3">helium-3</a> with a half-life of about 12.3 years: <dl><dd>3 1H → 3 2He + e− + ν e</dd></dl> An example of positron emission (β+ decay) is the decay of <a href="/wiki/Magnesium-23" class="mw-redirect" title="Magnesium-23">magnesium-23</a> into <a href="/wiki/Sodium-23" class="mw-redirect" title="Sodium-23">sodium-23</a> with a half-life of about 11.3 s: <dl><dd>23 12Mg → 23 11Na + e+ + ν e</dd></dl> β+ decay also results in nuclear transmutation, with the resulting element having an atomic number that is decreased by one. <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:RaE1.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/2b/RaE1.jpg/220px-RaE1.jpg" decoding="async" width="220" height="154" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/2b/RaE1.jpg/330px-RaE1.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/2b/RaE1.jpg/440px-RaE1.jpg 2x" data-file-width="1091" data-file-height="763" /></a><figcaption>A beta spectrum, showing a typical division of energy between electron and antineutrino</figcaption></figure> The beta spectrum, or distribution of energy values for the beta particles, is continuous. The total energy of the decay process is divided between the electron, the antineutrino, and the recoiling nuclide. In the figure to the right, an example of an electron with 0.40 MeV energy from the beta decay of 210Bi is shown. In this example, the total decay energy is 1.16 MeV, so the antineutrino has the remaining energy: 1.16 MeV − 0.40 MeV = 0.76 MeV. An electron at the far right of the curve would have the maximum possible kinetic energy, leaving the energy of the neutrino to be only its small rest mass. <div class="mw-heading mw-heading2"><h2 id="History">History</h2>[<a href="/w/index.php?title=Beta_decay&action=edit&section=2" title="Edit section: History">edit</a>]</div> <div class="mw-heading mw-heading3"><h3 id="Discovery_and_initial_characterization">Discovery and initial characterization</h3>[<a href="/w/index.php?title=Beta_decay&action=edit&section=3" title="Edit section: Discovery and initial characterization">edit</a>]</div> Radioactivity was discovered in 1896 by <a href="/wiki/Henri_Becquerel" title="Henri Becquerel">Henri Becquerel</a> in <a href="/wiki/Uranium" title="Uranium">uranium</a>, and subsequently observed by <a href="/wiki/Marie_Curie" title="Marie Curie">Marie</a> and <a href="/wiki/Pierre_Curie" title="Pierre Curie">Pierre Curie</a> in <a href="/wiki/Thorium" title="Thorium">thorium</a> and in the new elements <a href="/wiki/Polonium" title="Polonium">polonium</a> and <a href="/wiki/Radium" title="Radium">radium</a>. In 1899, <a href="/wiki/Ernest_Rutherford" title="Ernest Rutherford">Ernest Rutherford</a> separated radioactive emissions into two types: alpha and beta (now beta minus), based on penetration of objects and ability to cause ionization. Alpha rays could be stopped by thin sheets of paper or aluminium, whereas beta rays could penetrate several millimetres of aluminium. In 1900, <a href="/wiki/Paul_Villard" class="mw-redirect" title="Paul Villard">Paul Villard</a> identified a still more penetrating type of radiation, which Rutherford identified as a fundamentally new type in 1903 and termed <a href="/wiki/Gamma_ray" title="Gamma ray">gamma rays</a>. Alpha, beta, and gamma are the first three letters of the <a href="/wiki/Greek_alphabet" title="Greek alphabet">Greek alphabet</a>. In 1900, Becquerel measured the <a href="/wiki/Mass-to-charge_ratio" title="Mass-to-charge ratio">mass-to-charge ratio</a> (m/e) for beta particles by the method of <a href="/wiki/J.J._Thomson" class="mw-redirect" title="J.J. Thomson">J.J. Thomson</a> used to study cathode rays and identify the electron. He found that m/e for a beta particle is the same as for Thomson's electron, and therefore suggested that the beta particle is in fact an electron.<a href="#cite_note-Handbook-5">[5]</a> In 1901, Rutherford and <a href="/wiki/Frederick_Soddy" title="Frederick Soddy">Frederick Soddy</a> showed that alpha and beta radioactivity involves the <a href="/wiki/Nuclear_transmutation" title="Nuclear transmutation">transmutation</a> of atoms into atoms of other chemical elements. In 1913, after the products of more radioactive decays were known, Soddy and <a href="/wiki/Kazimierz_Fajans" title="Kazimierz Fajans">Kazimierz Fajans</a> independently proposed their <a href="/wiki/Radioactive_displacement_law_of_Fajans_and_Soddy" title="Radioactive displacement law of Fajans and Soddy">radioactive displacement law</a>, which states that beta (i.e., β− ) emission from one element produces another element one place to the right in the <a href="/wiki/Periodic_table" title="Periodic table">periodic table</a>, while alpha emission produces an element two places to the left. <div class="mw-heading mw-heading3"><h3 id="Neutrinos">Neutrinos</h3>[<a href="/w/index.php?title=Beta_decay&action=edit&section=4" title="Edit section: Neutrinos">edit</a>]</div> The study of beta decay provided the first physical evidence for the existence of the <a href="/wiki/Neutrino" title="Neutrino">neutrino</a>. In both alpha and gamma decay, the resulting alpha or gamma particle has a narrow energy <a href="/wiki/Frequency_distribution" class="mw-redirect" title="Frequency distribution">distribution</a>, since the particle carries the energy from the difference between the initial and final nuclear states. However, the kinetic energy distribution, or spectrum, of beta particles measured by <a href="/wiki/Lise_Meitner" title="Lise Meitner">Lise Meitner</a> and <a href="/wiki/Otto_Hahn" title="Otto Hahn">Otto Hahn</a> in 1911 and by <a href="/wiki/Jean_Danysz" class="mw-redirect" title="Jean Danysz">Jean Danysz</a> in 1913 showed multiple lines on a diffuse background. These measurements offered the first hint that beta particles have a continuous spectrum.<a href="#cite_note-Jensen-6">[6]</a> In 1914, <a href="/wiki/James_Chadwick" title="James Chadwick">James Chadwick</a> used a magnetic <a href="/wiki/Spectrometer" title="Spectrometer">spectrometer</a> with one of <a href="/wiki/Hans_Geiger" title="Hans Geiger">Hans Geiger's</a> new <a href="/wiki/Geiger_counter" title="Geiger counter">counters</a> to make more accurate measurements which showed that the spectrum was continuous.<a href="#cite_note-Jensen-6">[6]</a><a href="#cite_note-7">[7]</a> The distribution of beta particle energies was in apparent contradiction to the <a href="/wiki/Law_of_conservation_of_energy" class="mw-redirect" title="Law of conservation of energy">law of conservation of energy</a>. If beta decay were simply electron emission as assumed at the time, then the energy of the emitted electron should have a particular, well-defined value.<a href="#cite_note-Brown-8">[8]</a> For beta decay, however, the observed broad distribution of energies suggested that energy is lost in the beta decay process. This spectrum was puzzling for many years. A second problem is related to the <a href="/wiki/Conservation_of_angular_momentum" class="mw-redirect" title="Conservation of angular momentum">conservation of angular momentum</a>. Molecular band spectra showed that the <a href="/wiki/Nuclear_spin" class="mw-redirect" title="Nuclear spin">nuclear spin</a> of <a href="/wiki/Nitrogen-14" class="mw-redirect" title="Nitrogen-14">nitrogen-14</a> is 1 (i.e., equal to the <a href="/wiki/Reduced_Planck_constant" class="mw-redirect" title="Reduced Planck constant">reduced Planck constant</a>) and more generally that the spin is integral for nuclei of even <a href="/wiki/Mass_number" title="Mass number">mass number</a> and half-integral for nuclei of odd mass number. This was later explained by the <a href="/wiki/Discovery_of_the_neutron#Proton–neutron_model_of_the_nucleus" title="Discovery of the neutron">proton-neutron model of the nucleus</a>.<a href="#cite_note-Brown-8">[8]</a> Beta decay leaves the mass number unchanged, so the change of nuclear spin must be an integer. However, the electron spin is 1/2, hence angular momentum would not be conserved if beta decay were simply electron emission. From 1920 to 1927, <a href="/wiki/Charles_Drummond_Ellis" title="Charles Drummond Ellis">Charles Drummond Ellis</a> (along with Chadwick and colleagues) further established that the beta decay spectrum is continuous. In 1933, Ellis and <a href="/wiki/Nevill_Mott" class="mw-redirect" title="Nevill Mott">Nevill Mott</a> obtained strong evidence that the beta spectrum has an effective upper bound in energy. <a href="/wiki/Niels_Bohr" title="Niels Bohr">Niels Bohr</a> had suggested that the beta spectrum could be explained if <a href="/wiki/Conservation_of_energy" title="Conservation of energy">conservation of energy</a> was true only in a statistical sense, thus this <a href="/wiki/Laws_of_science" class="mw-redirect" title="Laws of science">principle</a> might be violated in any given decay.<a href="#cite_note-Brown-8">[8]</a>: 27  However, the upper bound in beta energies determined by Ellis and Mott ruled out that notion. Now, the problem of how to account for the variability of energy in known beta decay products, as well as for conservation of momentum and angular momentum in the process, became acute. In a <a href="/wiki/Electron_neutrino#Pauli's_letter" title="Electron neutrino">famous letter</a> written in 1930, <a href="/wiki/Wolfgang_Pauli" title="Wolfgang Pauli">Wolfgang Pauli</a> attempted to resolve the beta-particle energy conundrum by suggesting that, in addition to electrons and protons, atomic nuclei also contained an extremely light neutral particle, which he called the neutron. He suggested that this "neutron" was also emitted during beta decay (thus accounting for the known missing energy, momentum, and angular momentum), but it had simply not yet been observed. In 1931, <a href="/wiki/Enrico_Fermi" title="Enrico Fermi">Enrico Fermi</a> renamed Pauli's "neutron" the "neutrino" ('little neutral one' in Italian). In 1933, Fermi published his landmark <a href="/wiki/Fermi%27s_interaction" title="Fermi's interaction">theory for beta decay</a>, where he applied the principles of quantum mechanics to matter particles, supposing that they can be created and annihilated, just as the light quanta in atomic transitions. Thus, according to Fermi, neutrinos are created in the beta-decay process, rather than contained in the nucleus; the same happens to electrons. The neutrino interaction with matter was so weak that detecting it proved a severe experimental challenge. Further indirect evidence of the existence of the neutrino was obtained by observing the recoil of nuclei that emitted such a particle after absorbing an electron. Neutrinos were finally detected directly in 1956 by the American physicists <a href="/wiki/Clyde_Cowan" title="Clyde Cowan">Clyde Cowan</a> and <a href="/wiki/Frederick_Reines" title="Frederick Reines">Frederick Reines</a> in the <a href="/wiki/Cowan%E2%80%93Reines_neutrino_experiment" title="Cowan–Reines neutrino experiment">Cowan–Reines neutrino experiment</a>.<a href="#cite_note-9">[9]</a> The properties of neutrinos were (with a few minor modifications) as predicted by Pauli and Fermi. <div class="mw-heading mw-heading3"><h3 id="β+_decay_and_electron_capture"> β+  decay and electron capture</h3>[<a href="/w/index.php?title=Beta_decay&action=edit&section=5" title="Edit section: β+ decay and electron capture">edit</a>]</div> In 1934, <a href="/wiki/Fr%C3%A9d%C3%A9ric_Joliot-Curie" title="Frédéric Joliot-Curie">Frédéric</a> and <a href="/wiki/Ir%C3%A8ne_Joliot-Curie" title="Irène Joliot-Curie">Irène Joliot-Curie</a> bombarded aluminium with alpha particles to effect the nuclear reaction 4 2He  + 27 13Al  → 30 15P  + 1 0n , and observed that the product isotope 30 15P emits a positron identical to those found in cosmic rays (discovered by <a href="/wiki/Carl_David_Anderson" title="Carl David Anderson">Carl David Anderson</a> in 1932). This was the first example of β+  decay (<a href="/wiki/Positron_emission" title="Positron emission">positron emission</a>), which they termed <a href="/wiki/Artificial_radioactivity" class="mw-redirect" title="Artificial radioactivity">artificial radioactivity</a> since 30 15P is a short-lived nuclide which does not exist in nature. In recognition of their discovery, the couple were awarded the <a href="/wiki/Nobel_Prize_in_Chemistry" title="Nobel Prize in Chemistry">Nobel Prize in Chemistry</a> in 1935.<a href="#cite_note-10">[10]</a> The theory of <a href="/wiki/Electron_capture" title="Electron capture">electron capture</a> was first discussed by <a href="/wiki/Gian-Carlo_Wick" class="mw-redirect" title="Gian-Carlo Wick">Gian-Carlo Wick</a> in a 1934 paper, and then developed by <a href="/wiki/Hideki_Yukawa" title="Hideki Yukawa">Hideki Yukawa</a> and others. K-electron capture was first observed in 1937 by <a href="/wiki/Luis_Walter_Alvarez" title="Luis Walter Alvarez">Luis Alvarez</a>, in the nuclide 48V.<a href="#cite_note-k-11">[11]</a><a href="#cite_note-12">[12]</a><a href="#cite_note-13">[13]</a> Alvarez went on to study electron capture in 67Ga and other nuclides.<a href="#cite_note-k-11">[11]</a><a href="#cite_note-14">[14]</a><a href="#cite_note-15">[15]</a> <div class="mw-heading mw-heading3"><h3 id="Non-conservation_of_parity">Non-conservation of parity</h3>[<a href="/w/index.php?title=Beta_decay&action=edit&section=6" title="Edit section: Non-conservation of parity">edit</a>]</div> In 1956, <a href="/wiki/Tsung-Dao_Lee" title="Tsung-Dao Lee">Tsung-Dao Lee</a> and <a href="/wiki/Chen_Ning_Yang" class="mw-redirect" title="Chen Ning Yang">Chen Ning Yang</a> noticed that there was no evidence that <a href="/wiki/Parity_(physics)" title="Parity (physics)">parity</a> was conserved in weak interactions, and so they postulated that this symmetry may not be preserved by the weak force. They sketched the design for an experiment for testing conservation of parity in the laboratory.<a href="#cite_note-16">[16]</a> Later that year, <a href="/wiki/Chien-Shiung_Wu" title="Chien-Shiung Wu">Chien-Shiung Wu</a> and coworkers conducted the <a href="/wiki/Wu_experiment" title="Wu experiment">Wu experiment</a> showing an asymmetrical beta decay of <a href="/wiki/Cobalt-60" title="Cobalt-60">60 Co </a> at cold temperatures that proved that parity is not conserved in beta decay.<a href="#cite_note-Wu1957-17">[17]</a><a href="#cite_note-18">[18]</a> This surprising result overturned long-held assumptions about parity and the weak force. In recognition of their theoretical work, Lee and Yang were awarded the <a href="/wiki/Nobel_Prize_for_Physics" class="mw-redirect" title="Nobel Prize for Physics">Nobel Prize for Physics</a> in 1957. However Wu, who was female, was not awarded the Nobel prize.<a href="#cite_note-19">[19]</a> <div class="mw-heading mw-heading2"><h2 id="β−_decay">β− decay </h2>[<a href="/w/index.php?title=Beta_decay&action=edit&section=7" title="Edit section: β− decay">edit</a>]</div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Beta_Negative_Decay.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/89/Beta_Negative_Decay.svg/220px-Beta_Negative_Decay.svg.png" decoding="async" width="220" height="220" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/89/Beta_Negative_Decay.svg/330px-Beta_Negative_Decay.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/89/Beta_Negative_Decay.svg/440px-Beta_Negative_Decay.svg.png 2x" data-file-width="400" data-file-height="400" /></a><figcaption>The leading-order <a href="/wiki/Feynman_diagram" title="Feynman diagram">Feynman diagram</a> for β−  decay of a <a href="/wiki/Neutron" title="Neutron">neutron</a> into a <a href="/wiki/Proton" title="Proton">proton</a>, <a href="/wiki/Electron" title="Electron">electron</a>, and <a href="/wiki/Electron_antineutrino" class="mw-redirect" title="Electron antineutrino">electron antineutrino</a> via an virtual <a href="/wiki/W_boson" class="mw-redirect" title="W boson"> W− boson</a>. For higher-order diagrams see <a href="#cite_note-20">[20]</a><a href="#cite_note-21">[21]</a></figcaption></figure> In β−  decay, the <a href="/wiki/Weak_interaction" title="Weak interaction">weak interaction</a> converts an <a href="/wiki/Atomic_nucleus" title="Atomic nucleus">atomic nucleus</a> into a nucleus with <a href="/wiki/Atomic_number" title="Atomic number">atomic number</a> increased by one, while emitting an electron (<a href="/wiki/Electron" title="Electron"> e− </a>) and an electron <a href="/wiki/Neutrino#Antineutrinos" title="Neutrino">antineutrino</a> ( ν e). β−  decay generally occurs in neutron-rich nuclei.<a href="#cite_note-Loveland-22">[22]</a> The generic equation is: <dl><dd>A ZX → A Z+1X′ + e− + ν e<a href="#cite_note-konya74-1">[1]</a></dd></dl> where A and Z are the <a href="/wiki/Mass_number" title="Mass number">mass number</a> and <a href="/wiki/Atomic_number" title="Atomic number">atomic number</a> of the decaying nucleus, and X and X′ are the initial and final elements, respectively. Another example is when the <a href="/wiki/Free_neutron" class="mw-redirect" title="Free neutron">free neutron</a> (1 0n ) decays by β−  decay into a proton ( p ): <dl><dd> n → p + e− + ν e.</dd></dl> At the <a href="/wiki/Fundamental_particle" class="mw-redirect" title="Fundamental particle">fundamental</a> level (as depicted in the <a href="/wiki/Feynman_diagram" title="Feynman diagram">Feynman diagram</a> on the right), this is caused by the conversion of the negatively charged (−<style data-mw-deduplicate="TemplateStyles:r1214402035">.mw-parser-output .sfrac{white-space:nowrap}.mw-parser-output .sfrac.tion,.mw-parser-output .sfrac .tion{display:inline-block;vertical-align:-0.5em;font-size:85%;text-align:center}.mw-parser-output .sfrac .num{display:block;line-height:1em;margin:0.0em 0.1em;border-bottom:1px solid}.mw-parser-output .sfrac .den{display:block;line-height:1em;margin:0.1em 0.1em}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);clip-path:polygon(0px 0px,0px 0px,0px 0px);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}</style>⁠1/3⁠ <a href="/wiki/Elementary_charge" title="Elementary charge">e</a>) down quark to the positively charged (+<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035">⁠2/3⁠ e) up quark promoteby by a virtual <a href="/wiki/W_boson" class="mw-redirect" title="W boson"> W− boson</a>; the W− boson subsequently decays into an electron and an electron antineutrino: <dl><dd> d → u + e− + ν e.</dd></dl> <div class="mw-heading mw-heading2"><h2 id="β+_decay">β+ decay </h2>[<a href="/w/index.php?title=Beta_decay&action=edit&section=8" title="Edit section: β+ decay">edit</a>]</div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Positron_emission" title="Positron emission">Positron emission</a></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Electron_Capture_Decay.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/78/Electron_Capture_Decay.svg/220px-Electron_Capture_Decay.svg.png" decoding="async" width="220" height="220" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/78/Electron_Capture_Decay.svg/330px-Electron_Capture_Decay.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/78/Electron_Capture_Decay.svg/440px-Electron_Capture_Decay.svg.png 2x" data-file-width="310" data-file-height="310" /></a><figcaption>The leading-order <a href="/wiki/Feynman_diagram" title="Feynman diagram">Feynman diagram</a> for β+  decay of a <a href="/wiki/Proton" title="Proton">proton</a> into a <a href="/wiki/Neutron" title="Neutron">neutron</a>, <a href="/wiki/Positron" title="Positron">positron</a>, and <a href="/wiki/Electron_neutrino" title="Electron neutrino">electron neutrino</a> via an intermediate virtual <a href="/wiki/W_boson" class="mw-redirect" title="W boson"> W+ boson</a></figcaption></figure> In β+  decay, or positron emission, the weak interaction converts an atomic nucleus into a nucleus with atomic number decreased by one, while emitting a positron ( e+ ) and an <a href="/wiki/Electron_neutrino" title="Electron neutrino">electron neutrino</a> ( ν e). β+  decay generally occurs in proton-rich nuclei. The generic equation is: <dl><dd>A ZX → A Z−1X′ + e+ + ν e<a href="#cite_note-konya74-1">[1]</a></dd></dl> This may be considered as the decay of a proton inside the nucleus to a neutron: <dl><dd>p → n + e+ + ν e<a href="#cite_note-konya74-1">[1]</a></dd></dl> However, β+  decay cannot occur in an isolated proton because it requires energy, due to the <a href="/wiki/Mass" title="Mass">mass</a> of the neutron being greater than the mass of the proton. β+  decay can only happen inside nuclei when the daughter nucleus has a greater <a href="/wiki/Nuclear_binding_energy" title="Nuclear binding energy">binding energy</a> (and therefore a lower total energy) than the mother nucleus. The difference between these energies goes into the reaction of converting a proton into a neutron, a positron, and a neutrino and into the kinetic energy of these particles. This process is opposite to negative beta decay, in that the weak interaction converts a proton into a neutron by converting an up quark into a down quark resulting in the emission of a W+ or the absorption of a W− . When a W+ boson is emitted, it decays into a <a href="/wiki/Positron" title="Positron">positron</a> and an <a href="/wiki/Electron_neutrino" title="Electron neutrino">electron neutrino</a>: <dl><dd> u → d + e+ + ν e.</dd></dl> <div class="mw-heading mw-heading2"><h2 id="Electron_capture_(K-capture/L-capture)">Electron capture (K-capture/L-capture)</h2>[<a href="/w/index.php?title=Beta_decay&action=edit&section=9" title="Edit section: Electron capture (K-capture/L-capture)">edit</a>]</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Electron_capture" title="Electron capture">Electron capture</a></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Electron-capture.svg" class="mw-file-description"><img alt="Leading-order EC Feynman diagrams" src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5c/Electron-capture.svg/309px-Electron-capture.svg.png" decoding="async" width="309" height="180" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5c/Electron-capture.svg/464px-Electron-capture.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5c/Electron-capture.svg/618px-Electron-capture.svg.png 2x" data-file-width="494" data-file-height="287" /></a><figcaption>The leading-order <a href="/wiki/Feynman_diagram" title="Feynman diagram">Feynman diagrams</a> for <a href="/wiki/Electron_capture" title="Electron capture">electron capture</a> decay. An <a href="/wiki/Electron" title="Electron">electron</a> interacts with an <a href="/wiki/Up_quark" title="Up quark">up quark</a> in the nucleus via a <a href="/wiki/W_and_Z_bosons" title="W and Z bosons">W boson</a> to create a <a href="/wiki/Down_quark" title="Down quark">down quark</a> and <a href="/wiki/Electron_neutrino" title="Electron neutrino">electron neutrino</a>. Two diagrams comprise the leading (second) order, though as a <a href="/wiki/Virtual_particle" title="Virtual particle">virtual particle</a>, the type (and charge) of the W-boson is indistinguishable.</figcaption></figure> In all cases where β+  decay (positron emission) of a nucleus is allowed energetically, so too is <a href="/wiki/Electron_capture" title="Electron capture">electron capture</a> allowed. This is a process during which a nucleus captures one of its atomic electrons, resulting in the emission of a neutrino: <dl><dd>A ZX + e− → A Z−1X′ + ν e</dd></dl> An example of electron capture is one of the decay modes of <a href="/wiki/Krypton-81" class="mw-redirect" title="Krypton-81">krypton-81</a> into <a href="/wiki/Bromine-81" class="mw-redirect" title="Bromine-81">bromine-81</a>: <dl><dd>81 36Kr + e− → 81 35Br + ν e</dd></dl> All emitted neutrinos are of the same energy. In proton-rich nuclei where the energy difference between the initial and final states is less than 2mec2, β+  decay is not energetically possible, and electron capture is the sole decay mode.<a href="#cite_note-Zuber-23">[23]</a> If the captured electron comes from the innermost shell of the atom, the <a href="/wiki/Electron_shell" title="Electron shell">K-shell</a>, which has the highest probability to interact with the nucleus, the process is called K-capture.<a href="#cite_note-Jevremovic2009-24">[24]</a> If it comes from the L-shell, the process is called L-capture, etc. Electron capture is a competing (simultaneous) decay process for all nuclei that can undergo β+ decay. The converse, however, is not true: electron capture is the only type of decay that is allowed in proton-rich nuclides that do not have sufficient energy to emit a positron and neutrino.<a href="#cite_note-Zuber-23">[23]</a> <div class="mw-heading mw-heading2"><h2 id="Nuclear_transmutation">Nuclear transmutation</h2>[<a href="/w/index.php?title=Beta_decay&action=edit&section=10" title="Edit section: Nuclear transmutation">edit</a>]</div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Table_isotopes_en.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c4/Table_isotopes_en.svg/250px-Table_isotopes_en.svg.png" decoding="async" width="250" height="358" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c4/Table_isotopes_en.svg/375px-Table_isotopes_en.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c4/Table_isotopes_en.svg/500px-Table_isotopes_en.svg.png 2x" data-file-width="580" data-file-height="830" /></a><figcaption>Graph of isotopes by type of nuclear decay. Orange and blue nuclides are unstable, with the black squares between these regions representing stable nuclides. The unbroken line passing below many of the nuclides represents the theoretical position on the graph of nuclides for which proton number is the same as neutron number. The graph shows that elements with more than 20 protons must have more neutrons than protons, in order to be stable.</figcaption></figure> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Nuclear_drip_line" title="Nuclear drip line">Nuclear drip line</a></div> If the proton and neutron are part of an <a href="/wiki/Atomic_nucleus" title="Atomic nucleus">atomic nucleus</a>, the above described decay processes <a href="/wiki/Nuclear_transmutation" title="Nuclear transmutation">transmute</a> one chemical element into another. For example: <dl><dd><table border="0"> <tbody><tr style="height:2em;"> <td><a href="/wiki/Caesium-137" title="Caesium-137">137 55Cs </a> </td> <td> </td> <td> </td> <td>→ </td> <td><a href="/wiki/Barium-137" class="mw-redirect" title="Barium-137">137 56Ba </a> </td> <td>+ </td> <td><a href="/wiki/Electron" title="Electron"> e− </a> </td> <td>+ </td> <td><a href="/wiki/Electron_antineutrino" class="mw-redirect" title="Electron antineutrino"> ν e</a> </td> <td>(beta minus decay) </td></tr> <tr style="height:2em;"> <td><a href="/wiki/Sodium-22" class="mw-redirect" title="Sodium-22">22 11Na </a> </td> <td> </td> <td> </td> <td>→ </td> <td><a href="/wiki/Neon-22" class="mw-redirect" title="Neon-22">22 10Ne </a> </td> <td>+ </td> <td><a href="/wiki/Positron" title="Positron"> e+ </a> </td> <td>+ </td> <td><a href="/wiki/Electron_neutrino" title="Electron neutrino"> ν e</a> </td> <td>(beta plus decay) </td></tr> <tr style="height:2em;"> <td><a href="/wiki/Sodium-22" class="mw-redirect" title="Sodium-22">22 11Na </a> </td> <td>+ </td> <td><a href="/wiki/Electron" title="Electron"> e− </a> </td> <td>→ </td> <td><a href="/wiki/Neon-22" class="mw-redirect" title="Neon-22">22 10Ne </a> </td> <td>+ </td> <td><a href="/wiki/Electron_neutrino" title="Electron neutrino"> ν e</a> </td> <td> </td> <td> </td> <td>(electron capture) </td></tr></tbody></table></dd></dl> Beta decay does not change the number (A) of <a href="/wiki/Nucleon" title="Nucleon">nucleons</a> in the nucleus, but changes only its <a href="/wiki/Electric_charge" title="Electric charge">charge</a> Z. Thus the set of all <a href="/wiki/Nuclide" title="Nuclide">nuclides</a> with the same A can be introduced; these <a href="/wiki/Isobar_(nuclide)" title="Isobar (nuclide)">isobaric nuclides</a> may turn into each other via beta decay. For a given A there is one that is most stable. It is said to be beta stable, because it presents a local minimum of the <a href="/wiki/Mass_excess" title="Mass excess">mass excess</a>: if such a nucleus has (A, Z) numbers, the neighbour nuclei (A, Z−1) and (A, Z+1) have higher mass excess and can beta decay into (A, Z), but not vice versa. For all odd mass numbers A, there is only one known beta-stable isobar. For even A, there are up to three different beta-stable isobars experimentally known; for example, 124 50Sn , 124 52Te , and 124 54Xe are all beta-stable. There are about 350 known <a href="/wiki/Beta-decay_stable_isobars" title="Beta-decay stable isobars">beta-decay stable nuclides</a>.<a href="#cite_note-nndc_Inte-25">[25]</a> <div class="mw-heading mw-heading3"><h3 id="Competition_of_beta_decay_types">Competition of beta decay types</h3>[<a href="/w/index.php?title=Beta_decay&action=edit&section=11" title="Edit section: Competition of beta decay types">edit</a>]</div> Usually unstable nuclides are clearly either "neutron rich" or "proton rich", with the former undergoing beta decay and the latter undergoing electron capture (or more rarely, due to the higher energy requirements, positron decay). However, in a few cases of odd-proton, odd-neutron radionuclides, it may be energetically favorable for the radionuclide to decay to an even-proton, even-neutron isobar either by undergoing beta-positive or beta-negative decay. An often-cited example is the single isotope <a href="/wiki/Copper-64" title="Copper-64">64 29Cu </a> (29 protons, 35 neutrons), which illustrates three types of beta decay in competition. Copper-64 has a half-life of about 12.7 hours. This isotope has one unpaired proton and one unpaired neutron, so either the proton or the neutron can decay. This particular nuclide (though not all nuclides in this situation) is almost equally likely to decay through proton decay by <a href="/wiki/Positron_emission" title="Positron emission">positron emission</a> (18%) or <a href="/wiki/Electron_capture" title="Electron capture">electron capture</a> (43%) to 64 28Ni , as it is through neutron decay by electron emission (39%) to 64 30Zn .<a href="#cite_note-26">[26]</a> <div class="mw-heading mw-heading3"><h3 id="Stability_of_naturally_occurring_nuclides">Stability of naturally occurring nuclides</h3>[<a href="/w/index.php?title=Beta_decay&action=edit&section=12" title="Edit section: Stability of naturally occurring nuclides">edit</a>]</div> Most naturally occurring nuclides on earth are beta stable. Nuclides that are not beta stable have <a href="/wiki/Half-life" title="Half-life">half-lives</a> ranging from under a second to periods of time significantly greater than the <a href="/wiki/Age_of_the_universe" title="Age of the universe">age of the universe</a>. One common example of a long-lived isotope is the odd-proton odd-neutron nuclide <a href="/wiki/Potassium-40" title="Potassium-40">40 19K </a>, which undergoes all three types of beta decay ( β− , β+ and electron capture) with a half-life of 1.277×109 years.<a href="#cite_note-27">[27]</a> <div class="mw-heading mw-heading2"><h2 id="Conservation_rules_for_beta_decay">Conservation rules for beta decay</h2>[<a href="/w/index.php?title=Beta_decay&action=edit&section=13" title="Edit section: Conservation rules for beta decay">edit</a>]</div> <div class="mw-heading mw-heading3"><h3 id="Baryon_number_is_conserved">Baryon number is conserved</h3>[<a href="/w/index.php?title=Beta_decay&action=edit&section=14" title="Edit section: Baryon number is conserved">edit</a>]</div> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B={\frac {n_{q}-n_{\bar {q}}}{3}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>B</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>q</mi> </mrow> </msub> <mo>−</mo> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>q</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> </msub> </mrow> <mn>3</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B={\frac {n_{q}-n_{\bar {q}}}{3}}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f7aeadf34de60d91e2ffc875cb48f33dba1c3b34" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:13.58ex; height:5.509ex;" alt="{\displaystyle B={\frac {n_{q}-n_{\bar {q}}}{3}}}"> where <ul><li><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n_{q}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>q</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n_{q}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ac20020d472c5f064427f1bd3f02679d8ff84fab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.383ex; height:2.343ex;" alt="{\displaystyle n_{q}}"> is the number of constituent quarks, and</li> <li><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n_{\overline {q}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>q</mi> <mo accent="false">¯</mo> </mover> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n_{\overline {q}}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a2e093aa7e3e6de879ceab7c485fd7c49c4e74d8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.492ex; height:2.343ex;" alt="{\displaystyle n_{\overline {q}}}"> is the number of constituent antiquarks.</li></ul> Beta decay just changes <a href="/wiki/Neutron" title="Neutron">neutron</a> to <a href="/wiki/Proton" title="Proton">proton</a> or, in the case of positive beta decay (<a href="/wiki/Electron_capture" title="Electron capture">electron capture</a>) <a href="/wiki/Proton" title="Proton">proton</a> to <a href="/wiki/Neutron" title="Neutron">neutron</a> so the number of individual <a href="/wiki/Quarks" class="mw-redirect" title="Quarks">quarks</a> doesn't change. It is only the baryon flavor that changes, here labelled as the <a href="/wiki/Isospin" title="Isospin">isospin</a>. Up and down <a href="/wiki/Quarks" class="mw-redirect" title="Quarks">quarks</a> have total isospin <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle I={\frac {1}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mi>I</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle I={\frac {1}{2}}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8fe5a027bff7af3e6fa7ffad42e5d7e312ea1ecf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:5.928ex; height:3.509ex;" alt="{\textstyle I={\frac {1}{2}}}"> and isospin projections <math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I_{\text{z}}={\begin{cases}{\frac {1}{2}}&{\text{up quark}}\\-{\frac {1}{2}}&{\text{down quark}}\end{cases}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>z</mtext> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>{</mo> <mtable columnalign="left left" rowspacing=".2em" columnspacing="1em" displaystyle="false"> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </mtd> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mtext>up quark</mtext> </mrow> </mtd> </mtr> <mtr> <mtd> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </mtd> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mtext>down quark</mtext> </mrow> </mtd> </mtr> </mtable> <mo fence="true" stretchy="true" symmetric="true"></mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I_{\text{z}}={\begin{cases}{\frac {1}{2}}&{\text{up quark}}\\-{\frac {1}{2}}&{\text{down quark}}\end{cases}}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/836098adb02f23cd77dac64cb04d1f0f69cc89d5" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:25.325ex; height:7.509ex;" alt="{\displaystyle I_{\text{z}}={\begin{cases}{\frac {1}{2}}&{\text{up quark}}\\-{\frac {1}{2}}&{\text{down quark}}\end{cases}}}"> All other quarks have I = 0. In general <math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I_{\text{z}}={\frac {1}{2}}(n_{\text{u}}-n_{\text{d}})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>z</mtext> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mo stretchy="false">(</mo> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>u</mtext> </mrow> </msub> <mo>−</mo> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>d</mtext> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I_{\text{z}}={\frac {1}{2}}(n_{\text{u}}-n_{\text{d}})}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/800c54a9867a589145b4b3dfec7e30ff2e1f5d1c" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:16.814ex; height:5.176ex;" alt="{\displaystyle I_{\text{z}}={\frac {1}{2}}(n_{\text{u}}-n_{\text{d}})}"> <div class="mw-heading mw-heading3"><h3 id="Lepton_number_is_conserved">Lepton number is conserved</h3>[<a href="/w/index.php?title=Beta_decay&action=edit&section=15" title="Edit section: Lepton number is conserved">edit</a>]</div> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle L\equiv n_{\ell }-n_{\bar {\ell }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>L</mi> <mo>≡</mo> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>ℓ</mi> </mrow> </msub> <mo>−</mo> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>ℓ</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L\equiv n_{\ell }-n_{\bar {\ell }}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f91996e20c4147ce122142578b0ccbdfcc806682" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:12.541ex; height:2.843ex;" alt="{\displaystyle L\equiv n_{\ell }-n_{\bar {\ell }}}"> so all leptons have assigned a value of +1, antileptons −1, and non-leptonic particles 0. <math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{matrix}&{\text{n}}&\rightarrow &{\text{p}}&+&{\text{e}}^{-}&+&{\bar {\nu }}_{\text{e}}\\L:&0&=&0&+&1&-&1\end{matrix}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd /> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mtext>n</mtext> </mrow> </mtd> <mtd> <mo stretchy="false">→</mo> </mtd> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mtext>p</mtext> </mrow> </mtd> <mtd> <mo>+</mo> </mtd> <mtd> <msup> <mrow class="MJX-TeXAtom-ORD"> <mtext>e</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> </mrow> </msup> </mtd> <mtd> <mo>+</mo> </mtd> <mtd> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>ν</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>e</mtext> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <mi>L</mi> <mo>:</mo> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mo>=</mo> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mo>+</mo> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mo>−</mo> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{matrix}&{\text{n}}&\rightarrow &{\text{p}}&+&{\text{e}}^{-}&+&{\bar {\nu }}_{\text{e}}\\L:&0&=&0&+&1&-&1\end{matrix}}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0f2bb43ea7e6513e017509ebdbceea4fdfa8145d" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:33.231ex; height:6.176ex;" alt="{\displaystyle {\begin{matrix}&{\text{n}}&\rightarrow &{\text{p}}&+&{\text{e}}^{-}&+&{\bar {\nu }}_{\text{e}}\\L:&0&=&0&+&1&-&1\end{matrix}}}"> <div class="mw-heading mw-heading3"><h3 id="Angular_momentum">Angular momentum</h3>[<a href="/w/index.php?title=Beta_decay&action=edit&section=16" title="Edit section: Angular momentum">edit</a>]</div> For allowed decays, the net orbital angular momentum is zero, hence only spin quantum numbers are considered. The electron and antineutrino are <a href="/wiki/Fermions" class="mw-redirect" title="Fermions">fermions</a>, spin-1/2 objects, therefore they may couple to total <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S=1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <mo>=</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S=1}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d5e2b58c1aaaf2718fb801e97bf21d1f72726372" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.76ex; height:2.176ex;" alt="{\displaystyle S=1}"> (parallel) or <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S=0}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4ae0fc3192b864f55a46749d8a64e7cf7783d04c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.76ex; height:2.176ex;" alt="{\displaystyle S=0}"> (anti-parallel). For forbidden decays, orbital angular momentum must also be taken into consideration. <div class="mw-heading mw-heading2"><h2 id="Energy_release">Energy release</h2>[<a href="/w/index.php?title=Beta_decay&action=edit&section=17" title="Edit section: Energy release">edit</a>]</div> The <a href="/wiki/Q_value_(nuclear_science)" title="Q value (nuclear science)">Q value</a> is defined as the total energy released in a given nuclear decay. In beta decay, Q is therefore also the sum of the kinetic energies of the emitted beta particle, neutrino, and recoiling nucleus. (Because of the large mass of the nucleus compared to that of the beta particle and neutrino, the kinetic energy of the recoiling nucleus can generally be neglected.) Beta particles can therefore be emitted with any <a href="/wiki/Kinetic_energy" title="Kinetic energy">kinetic energy</a> ranging from 0 to Q.<a href="#cite_note-konya74-1">[1]</a> A typical Q is around 1 <a href="/wiki/MeV" class="mw-redirect" title="MeV">MeV</a>, but can range from a few <a href="/wiki/KeV" class="mw-redirect" title="KeV">keV</a> to a few tens of MeV. Since the <a href="/wiki/Mass%E2%80%93energy_equivalence" title="Mass–energy equivalence">rest mass</a> of the electron is 511 keV, the most energetic beta particles are <a href="/wiki/Ultrarelativistic_limit" title="Ultrarelativistic limit">ultrarelativistic</a>, with speeds very close to the <a href="/wiki/Speed_of_light" title="Speed of light">speed of light</a>. In the case of 187Re, the maximum speed of the beta particle is only 9.8% of the speed of light. The following table gives some examples: <table class="wikitable zebra"> <caption>Examples of beta decay energies </caption> <tbody><tr> <th>Isotope</th> <th>Energy (<a href="/wiki/Electronvolt" title="Electronvolt">keV</a>)</th> <th>Decay mode</th> <th>Comments </th></tr> <tr> <td>free <a href="/wiki/Neutron" title="Neutron">Neutron</a></td> <td>0782.33</td> <td style="text-align:center;">β−</td> <td> </td></tr> <tr> <td>003H (Tritium)</td> <td>0018.59</td> <td align="center">β−</td> <td>Second lowest known β− energy, being used in the <a href="/wiki/KATRIN" title="KATRIN">KATRIN</a> experiment. </td></tr> <tr> <td>011C</td> <td>0960.4 1982.4</td> <td style="text-align:center;">β+ ε+</td> <td> </td></tr> <tr> <td><a href="/wiki/Carbon-14" title="Carbon-14">014C</a></td> <td>0156.475</td> <td style="text-align:center;">β−</td> <td> </td></tr> <tr> <td>020F</td> <td>5390.86</td> <td style="text-align:center;">β−</td> <td> </td></tr> <tr> <td>037K</td> <td>5125.48 6147.48</td> <td style="text-align:center;">β+ ε+</td> <td> </td></tr> <tr> <td>163Ho</td> <td>0002.555</td> <td style="text-align:center;">ε+</td> <td> </td></tr> <tr> <td>187Re</td> <td>0002.467</td> <td style="text-align:center;">β−</td> <td>Lowest known β− energy, being used in the <a href="/w/index.php?title=Microcalorimeter_Arrays_for_a_Rhenium_Experiment&action=edit&redlink=1" class="new" title="Microcalorimeter Arrays for a Rhenium Experiment (page does not exist)">Microcalorimeter Arrays for a Rhenium Experiment</a> experiment </td></tr> <tr> <td>210Bi</td> <td>1162.2</td> <td style="text-align:center;">β−</td> <td> </td></tr></tbody></table> <div class="mw-heading mw-heading3"><h3 id="β−_decay_2">β− decay</h3>[<a href="/w/index.php?title=Beta_decay&action=edit&section=18" title="Edit section: β− decay">edit</a>]</div> Consider the generic equation for beta decay <dl><dd>A ZX → A Z+1X′ + e− + ν e.</dd></dl> The Q value for this decay is <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Q=\left[m_{N}\left({\ce {^{\mathit {A}}_{\mathit {Z}}X}}\right)-m_{N}\left({\ce {^{\mathit {A}}_{{\mathit {Z}}+1}X'}}\right)-m_{e}-m_{{\overline {\nu }}_{e}}\right]c^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Q</mi> <mo>=</mo> <mrow> <mo>[</mo> <mrow> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>N</mi> </mrow> </msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mmultiscripts> <mtext>X</mtext> <none /> <none /> <mprescripts /> <mrow class="MJX-TeXAtom-ORD"> <mtext class="MJX-tex-mathit" mathvariant="italic">Z</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext class="MJX-tex-mathit" mathvariant="italic">A</mtext> </mrow> </mmultiscripts> </mrow> <mo>)</mo> </mrow> <mo>−</mo> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>N</mi> </mrow> </msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <msup> <mmultiscripts> <mtext>X</mtext> <none /> <none /> <mprescripts /> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext class="MJX-tex-mathit" mathvariant="italic">Z</mtext> </mrow> </mrow> <mo>+</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext class="MJX-tex-mathit" mathvariant="italic">A</mtext> </mrow> </mmultiscripts> <mo>′</mo> </msup> </mrow> <mo>)</mo> </mrow> <mo>−</mo> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> </mrow> </msub> <mo>−</mo> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>ν</mi> <mo accent="false">¯</mo> </mover> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> </mrow> </msub> </mrow> </msub> </mrow> <mo>]</mo> </mrow> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Q=\left[m_{N}\left({\ce {^{\mathit {A}}_{\mathit {Z}}X}}\right)-m_{N}\left({\ce {^{\mathit {A}}_{{\mathit {Z}}+1}X'}}\right)-m_{e}-m_{{\overline {\nu }}_{e}}\right]c^{2}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c5e1eec434e575480cf49bcab3a7f465e7ebc685" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:47.193ex; height:4.843ex;" alt="{\displaystyle Q=\left[m_{N}\left({\ce {^{\mathit {A}}_{\mathit {Z}}X}}\right)-m_{N}\left({\ce {^{\mathit {A}}_{{\mathit {Z}}+1}X'}}\right)-m_{e}-m_{{\overline {\nu }}_{e}}\right]c^{2}}">,</dd></dl> where <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m_{N}\left({\ce {^{\mathit {A}}_{\mathit {Z}}X}}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>N</mi> </mrow> </msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mmultiscripts> <mtext>X</mtext> <none /> <none /> <mprescripts /> <mrow class="MJX-TeXAtom-ORD"> <mtext class="MJX-tex-mathit" mathvariant="italic">Z</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext class="MJX-tex-mathit" mathvariant="italic">A</mtext> </mrow> </mmultiscripts> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m_{N}\left({\ce {^{\mathit {A}}_{\mathit {Z}}X}}\right)}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dd1e641de4bedd79cd25a61ceb6bd830a5013427" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:9.387ex; height:3.343ex;" alt="{\displaystyle m_{N}\left({\ce {^{\mathit {A}}_{\mathit {Z}}X}}\right)}"> is the mass of the nucleus of the A ZX atom, <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><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/101c68942dbc208f055ae7a3b5dc24e2363facaf" 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}}"> is the mass of the electron, and <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m_{{\overline {\nu }}_{e}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>ν</mi> <mo accent="false">¯</mo> </mover> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> </mrow> </msub> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m_{{\overline {\nu }}_{e}}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/99ce711b2a2f1f723796e233c8dd8ddb663d3d86" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.062ex; height:2.343ex;" alt="{\displaystyle m_{{\overline {\nu }}_{e}}}"> is the mass of the electron antineutrino. In other words, the total energy released is the mass energy of the initial nucleus, minus the mass energy of the final nucleus, electron, and antineutrino. The mass of the nucleus mN is related to the standard <a href="/wiki/Atomic_mass" title="Atomic mass">atomic mass</a> m by <math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m\left({\ce {^{\mathit {A}}_{\mathit {Z}}X}}\right)c^{2}=m_{N}\left({\ce {^{\mathit {A}}_{\mathit {Z}}X}}\right)c^{2}+Zm_{e}c^{2}-\sum _{i=1}^{Z}B_{i}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mmultiscripts> <mtext>X</mtext> <none /> <none /> <mprescripts /> <mrow class="MJX-TeXAtom-ORD"> <mtext class="MJX-tex-mathit" mathvariant="italic">Z</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext class="MJX-tex-mathit" mathvariant="italic">A</mtext> </mrow> </mmultiscripts> </mrow> <mo>)</mo> </mrow> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>N</mi> </mrow> </msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mmultiscripts> <mtext>X</mtext> <none /> <none /> <mprescripts /> <mrow class="MJX-TeXAtom-ORD"> <mtext class="MJX-tex-mathit" mathvariant="italic">Z</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext class="MJX-tex-mathit" mathvariant="italic">A</mtext> </mrow> </mmultiscripts> </mrow> <mo>)</mo> </mrow> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mi>Z</mi> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> </mrow> </msub> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>Z</mi> </mrow> </munderover> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m\left({\ce {^{\mathit {A}}_{\mathit {Z}}X}}\right)c^{2}=m_{N}\left({\ce {^{\mathit {A}}_{\mathit {Z}}X}}\right)c^{2}+Zm_{e}c^{2}-\sum _{i=1}^{Z}B_{i}.}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6a71eab2b5b094cec34d28be0be8ef7e90afd8c8" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:44.491ex; height:7.343ex;" alt="{\displaystyle m\left({\ce {^{\mathit {A}}_{\mathit {Z}}X}}\right)c^{2}=m_{N}\left({\ce {^{\mathit {A}}_{\mathit {Z}}X}}\right)c^{2}+Zm_{e}c^{2}-\sum _{i=1}^{Z}B_{i}.}"> That is, the total atomic mass is the mass of the nucleus, plus the mass of the electrons, minus the sum of all electron binding energies Bi for the atom. This equation is rearranged to find <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m_{N}\left({\ce {^{\mathit {A}}_{\mathit {Z}}X}}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>N</mi> </mrow> </msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mmultiscripts> <mtext>X</mtext> <none /> <none /> <mprescripts /> <mrow class="MJX-TeXAtom-ORD"> <mtext class="MJX-tex-mathit" mathvariant="italic">Z</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext class="MJX-tex-mathit" mathvariant="italic">A</mtext> </mrow> </mmultiscripts> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m_{N}\left({\ce {^{\mathit {A}}_{\mathit {Z}}X}}\right)}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dd1e641de4bedd79cd25a61ceb6bd830a5013427" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:9.387ex; height:3.343ex;" alt="{\displaystyle m_{N}\left({\ce {^{\mathit {A}}_{\mathit {Z}}X}}\right)}">, and <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m_{N}\left({\ce {^{\mathit {A}}_{{\mathit {Z}}+1}X'}}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>N</mi> </mrow> </msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <msup> <mmultiscripts> <mtext>X</mtext> <none /> <none /> <mprescripts /> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext class="MJX-tex-mathit" mathvariant="italic">Z</mtext> </mrow> </mrow> <mo>+</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext class="MJX-tex-mathit" mathvariant="italic">A</mtext> </mrow> </mmultiscripts> <mo>′</mo> </msup> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m_{N}\left({\ce {^{\mathit {A}}_{{\mathit {Z}}+1}X'}}\right)}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c79dbfbc70fe747eac439a656212b56c44dcea04" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:12.605ex; height:4.843ex;" alt="{\displaystyle m_{N}\left({\ce {^{\mathit {A}}_{{\mathit {Z}}+1}X'}}\right)}"> is found similarly. Substituting these nuclear masses into the Q-value equation, while neglecting the nearly-zero antineutrino mass and the difference in electron binding energies, which is very small for high-Z atoms, we have <math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Q=\left[m\left({\ce {^{\mathit {A}}_{\mathit {Z}}X}}\right)-m\left({\ce {^{\mathit {A}}_{{\mathit {Z}}+1}X'}}\right)\right]c^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Q</mi> <mo>=</mo> <mrow> <mo>[</mo> <mrow> <mi>m</mi> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mmultiscripts> <mtext>X</mtext> <none /> <none /> <mprescripts /> <mrow class="MJX-TeXAtom-ORD"> <mtext class="MJX-tex-mathit" mathvariant="italic">Z</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext class="MJX-tex-mathit" mathvariant="italic">A</mtext> </mrow> </mmultiscripts> </mrow> <mo>)</mo> </mrow> <mo>−</mo> <mi>m</mi> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <msup> <mmultiscripts> <mtext>X</mtext> <none /> <none /> <mprescripts /> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext class="MJX-tex-mathit" mathvariant="italic">Z</mtext> </mrow> </mrow> <mo>+</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext class="MJX-tex-mathit" mathvariant="italic">A</mtext> </mrow> </mmultiscripts> <mo>′</mo> </msup> </mrow> <mo>)</mo> </mrow> </mrow> <mo>]</mo> </mrow> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Q=\left[m\left({\ce {^{\mathit {A}}_{\mathit {Z}}X}}\right)-m\left({\ce {^{\mathit {A}}_{{\mathit {Z}}+1}X'}}\right)\right]c^{2}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/821caea8313714b516ee3aeb19c7ae54c61a4c20" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:31.029ex; height:4.843ex;" alt="{\displaystyle Q=\left[m\left({\ce {^{\mathit {A}}_{\mathit {Z}}X}}\right)-m\left({\ce {^{\mathit {A}}_{{\mathit {Z}}+1}X'}}\right)\right]c^{2}}"> This energy is carried away as kinetic energy by the electron and antineutrino. Because the reaction will proceed only when the Q value is positive, β− decay can occur when the mass of atom A ZX is greater than the mass of atom A Z+1X′ .<a href="#cite_note-Krane1987-28">[28]</a> <div class="mw-heading mw-heading3"><h3 id="β+_decay_2">β+ decay</h3>[<a href="/w/index.php?title=Beta_decay&action=edit&section=19" title="Edit section: β+ decay">edit</a>]</div> The equations for β+ decay are similar, with the generic equation <dl><dd>A ZX → A Z−1X′ + e+ + ν e</dd></dl> giving <math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Q=\left[m_{N}\left({\ce {^{\mathit {A}}_{\mathit {Z}}X}}\right)-m_{N}\left({\ce {^{\mathit {A}}_{{\mathit {Z}}-1}X'}}\right)-m_{e}-m_{\nu _{e}}\right]c^{2}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Q</mi> <mo>=</mo> <mrow> <mo>[</mo> <mrow> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>N</mi> </mrow> </msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mmultiscripts> <mtext>X</mtext> <none /> <none /> <mprescripts /> <mrow class="MJX-TeXAtom-ORD"> <mtext class="MJX-tex-mathit" mathvariant="italic">Z</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext class="MJX-tex-mathit" mathvariant="italic">A</mtext> </mrow> </mmultiscripts> </mrow> <mo>)</mo> </mrow> <mo>−</mo> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>N</mi> </mrow> </msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <msup> <mmultiscripts> <mtext>X</mtext> <none /> <none /> <mprescripts /> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext class="MJX-tex-mathit" mathvariant="italic">Z</mtext> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> </mrow> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext class="MJX-tex-mathit" mathvariant="italic">A</mtext> </mrow> </mmultiscripts> <mo>′</mo> </msup> </mrow> <mo>)</mo> </mrow> <mo>−</mo> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> </mrow> </msub> <mo>−</mo> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>ν</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> </mrow> </msub> </mrow> </msub> </mrow> <mo>]</mo> </mrow> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Q=\left[m_{N}\left({\ce {^{\mathit {A}}_{\mathit {Z}}X}}\right)-m_{N}\left({\ce {^{\mathit {A}}_{{\mathit {Z}}-1}X'}}\right)-m_{e}-m_{\nu _{e}}\right]c^{2}.}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0b2aecfbd59ef3a2d936653889874f1850c1c75e" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:47.649ex; height:4.843ex;" alt="{\displaystyle Q=\left[m_{N}\left({\ce {^{\mathit {A}}_{\mathit {Z}}X}}\right)-m_{N}\left({\ce {^{\mathit {A}}_{{\mathit {Z}}-1}X'}}\right)-m_{e}-m_{\nu _{e}}\right]c^{2}.}"> However, in this equation, the electron masses do not cancel, and we are left with <math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Q=\left[m\left({\ce {^{\mathit {A}}_{\mathit {Z}}X}}\right)-m\left({\ce {^{\mathit {A}}_{{\mathit {Z}}-1}X'}}\right)-2m_{e}\right]c^{2}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Q</mi> <mo>=</mo> <mrow> <mo>[</mo> <mrow> <mi>m</mi> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mmultiscripts> <mtext>X</mtext> <none /> <none /> <mprescripts /> <mrow class="MJX-TeXAtom-ORD"> <mtext class="MJX-tex-mathit" mathvariant="italic">Z</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext class="MJX-tex-mathit" mathvariant="italic">A</mtext> </mrow> </mmultiscripts> </mrow> <mo>)</mo> </mrow> <mo>−</mo> <mi>m</mi> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <msup> <mmultiscripts> <mtext>X</mtext> <none /> <none /> <mprescripts /> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext class="MJX-tex-mathit" mathvariant="italic">Z</mtext> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> </mrow> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext class="MJX-tex-mathit" mathvariant="italic">A</mtext> </mrow> </mmultiscripts> <mo>′</mo> </msup> </mrow> <mo>)</mo> </mrow> <mo>−</mo> <mn>2</mn> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> </mrow> </msub> </mrow> <mo>]</mo> </mrow> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Q=\left[m\left({\ce {^{\mathit {A}}_{\mathit {Z}}X}}\right)-m\left({\ce {^{\mathit {A}}_{{\mathit {Z}}-1}X'}}\right)-2m_{e}\right]c^{2}.}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d34016918031f38bd87c6585486db7bcb4bc0638" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:38.717ex; height:4.843ex;" alt="{\displaystyle Q=\left[m\left({\ce {^{\mathit {A}}_{\mathit {Z}}X}}\right)-m\left({\ce {^{\mathit {A}}_{{\mathit {Z}}-1}X'}}\right)-2m_{e}\right]c^{2}.}"> Because the reaction will proceed only when the Q value is positive, β+ decay can occur when the mass of atom A ZX exceeds that of A Z-1X′ by at least twice the mass of the electron.<a href="#cite_note-Krane1987-28">[28]</a> <div class="mw-heading mw-heading3"><h3 id="Electron_capture">Electron capture</h3>[<a href="/w/index.php?title=Beta_decay&action=edit&section=20" title="Edit section: Electron capture">edit</a>]</div> The analogous calculation for electron capture must take into account the binding energy of the electrons. This is because the atom will be left in an excited state after capturing the electron, and the binding energy of the captured innermost electron is significant. Using the generic equation for electron capture <dl><dd>A ZX + e− → A Z−1X′ + ν e</dd></dl> we have <math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Q=\left[m_{N}\left({\ce {^{\mathit {A}}_{\mathit {Z}}X}}\right)+m_{e}-m_{N}\left({\ce {^{\mathit {A}}_{{\mathit {Z}}-1}X'}}\right)-m_{\nu _{e}}\right]c^{2},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Q</mi> <mo>=</mo> <mrow> <mo>[</mo> <mrow> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>N</mi> </mrow> </msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mmultiscripts> <mtext>X</mtext> <none /> <none /> <mprescripts /> <mrow class="MJX-TeXAtom-ORD"> <mtext class="MJX-tex-mathit" mathvariant="italic">Z</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext class="MJX-tex-mathit" mathvariant="italic">A</mtext> </mrow> </mmultiscripts> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> </mrow> </msub> <mo>−</mo> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>N</mi> </mrow> </msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <msup> <mmultiscripts> <mtext>X</mtext> <none /> <none /> <mprescripts /> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext class="MJX-tex-mathit" mathvariant="italic">Z</mtext> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> </mrow> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext class="MJX-tex-mathit" mathvariant="italic">A</mtext> </mrow> </mmultiscripts> <mo>′</mo> </msup> </mrow> <mo>)</mo> </mrow> <mo>−</mo> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>ν</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> </mrow> </msub> </mrow> </msub> </mrow> <mo>]</mo> </mrow> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Q=\left[m_{N}\left({\ce {^{\mathit {A}}_{\mathit {Z}}X}}\right)+m_{e}-m_{N}\left({\ce {^{\mathit {A}}_{{\mathit {Z}}-1}X'}}\right)-m_{\nu _{e}}\right]c^{2},}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3f3a0073da219b288e4f08d1e83b74a6bcb850cc" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:47.649ex; height:4.843ex;" alt="{\displaystyle Q=\left[m_{N}\left({\ce {^{\mathit {A}}_{\mathit {Z}}X}}\right)+m_{e}-m_{N}\left({\ce {^{\mathit {A}}_{{\mathit {Z}}-1}X'}}\right)-m_{\nu _{e}}\right]c^{2},}"> which simplifies to <math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Q=\left[m\left({\ce {^{\mathit {A}}_{\mathit {Z}}X}}\right)-m\left({\ce {^{\mathit {A}}_{{\mathit {Z}}-1}X'}}\right)\right]c^{2}-B_{n},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Q</mi> <mo>=</mo> <mrow> <mo>[</mo> <mrow> <mi>m</mi> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mmultiscripts> <mtext>X</mtext> <none /> <none /> <mprescripts /> <mrow class="MJX-TeXAtom-ORD"> <mtext class="MJX-tex-mathit" mathvariant="italic">Z</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext class="MJX-tex-mathit" mathvariant="italic">A</mtext> </mrow> </mmultiscripts> </mrow> <mo>)</mo> </mrow> <mo>−</mo> <mi>m</mi> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <msup> <mmultiscripts> <mtext>X</mtext> <none /> <none /> <mprescripts /> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext class="MJX-tex-mathit" mathvariant="italic">Z</mtext> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> </mrow> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext class="MJX-tex-mathit" mathvariant="italic">A</mtext> </mrow> </mmultiscripts> <mo>′</mo> </msup> </mrow> <mo>)</mo> </mrow> </mrow> <mo>]</mo> </mrow> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Q=\left[m\left({\ce {^{\mathit {A}}_{\mathit {Z}}X}}\right)-m\left({\ce {^{\mathit {A}}_{{\mathit {Z}}-1}X'}}\right)\right]c^{2}-B_{n},}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/256ab0a779c0e70d9bf7858dbe54e986a938c88b" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:37.499ex; height:4.843ex;" alt="{\displaystyle Q=\left[m\left({\ce {^{\mathit {A}}_{\mathit {Z}}X}}\right)-m\left({\ce {^{\mathit {A}}_{{\mathit {Z}}-1}X'}}\right)\right]c^{2}-B_{n},}"> where Bn is the binding energy of the captured electron. Because the binding energy of the electron is much less than the mass of the electron, nuclei that can undergo β+ decay can always also undergo electron capture, but the reverse is not true.<a href="#cite_note-Krane1987-28">[28]</a> <div class="mw-heading mw-heading2"><h2 id="Beta_emission_spectrum">Beta emission spectrum</h2>[<a href="/w/index.php?title=Beta_decay&action=edit&section=21" title="Edit section: Beta emission spectrum">edit</a>]</div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Beta_spectrum_of_RaE.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e6/Beta_spectrum_of_RaE.jpg/220px-Beta_spectrum_of_RaE.jpg" decoding="async" width="220" height="154" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e6/Beta_spectrum_of_RaE.jpg/330px-Beta_spectrum_of_RaE.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e6/Beta_spectrum_of_RaE.jpg/440px-Beta_spectrum_of_RaE.jpg 2x" data-file-width="1091" data-file-height="763" /></a><figcaption>Beta spectrum of 210Bi. Emax = Q = 1.16 MeV is the maximum energy</figcaption></figure> Beta decay can be considered as a <a href="/wiki/Perturbation_theory_(quantum_mechanics)" title="Perturbation theory (quantum mechanics)">perturbation</a> as described in quantum mechanics, and thus <a href="/wiki/Fermi%27s_Golden_Rule" class="mw-redirect" title="Fermi's Golden Rule">Fermi's Golden Rule</a> can be applied. This leads to an expression for the kinetic energy spectrum N(T) of emitted betas as follows:<a href="#cite_note-29">[29]</a> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle N(T)=C_{L}(T)F(Z,T)pE(Q-T)^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>N</mi> <mo stretchy="false">(</mo> <mi>T</mi> <mo stretchy="false">)</mo> <mo>=</mo> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>T</mi> <mo stretchy="false">)</mo> <mi>F</mi> <mo stretchy="false">(</mo> <mi>Z</mi> <mo>,</mo> <mi>T</mi> <mo stretchy="false">)</mo> <mi>p</mi> <mi>E</mi> <mo stretchy="false">(</mo> <mi>Q</mi> <mo>−</mo> <mi>T</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N(T)=C_{L}(T)F(Z,T)pE(Q-T)^{2}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/40ce3b31c6de856e29d17e9121c725fe28818bcd" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:35.091ex; height:3.176ex;" alt="{\displaystyle N(T)=C_{L}(T)F(Z,T)pE(Q-T)^{2}}"> where T is the kinetic energy, CL is a shape function that depends on the forbiddenness of the decay (it is constant for allowed decays), F(Z, T) is the Fermi Function (see below) with Z the charge of the final-state nucleus, E = T + mc2 is the total energy, <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p={\sqrt {(E/c)^{2}-(mc)^{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mo stretchy="false">(</mo> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <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> <mi>c</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p={\sqrt {(E/c)^{2}-(mc)^{2}}}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5ec1c0b4e1656711ca92eaa4499c0531fd8fe4b5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.671ex; margin-left: -0.089ex; width:22.241ex; height:4.843ex;" alt="{\displaystyle p={\sqrt {(E/c)^{2}-(mc)^{2}}}}"> is the momentum, and Q is the <a href="/wiki/Q_value_(nuclear_science)" title="Q value (nuclear science)">Q value</a> of the decay. The kinetic energy of the emitted neutrino is given approximately by Q minus the kinetic energy of the beta. As an example, the beta decay spectrum of 210Bi (originally called RaE) is shown to the right. <div class="mw-heading mw-heading3"><h3 id="Fermi_function">Fermi function</h3>[<a href="/w/index.php?title=Beta_decay&action=edit&section=22" title="Edit section: Fermi function">edit</a>]</div> The Fermi function that appears in the beta spectrum formula accounts for the Coulomb attraction / repulsion between the emitted beta and the final state nucleus. Approximating the associated wavefunctions to be spherically symmetric, the Fermi function can be analytically calculated to be:<a href="#cite_note-30">[30]</a> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F(Z,T)={\frac {2(1+S)}{\Gamma (1+2S)^{2}}}(2p\rho )^{2S-2}e^{\pi \eta }|\Gamma (S+i\eta )|^{2},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> <mo stretchy="false">(</mo> <mi>Z</mi> <mo>,</mo> <mi>T</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>2</mn> <mo stretchy="false">(</mo> <mn>1</mn> <mo>+</mo> <mi>S</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <mi mathvariant="normal">Γ</mi> <mo stretchy="false">(</mo> <mn>1</mn> <mo>+</mo> <mn>2</mn> <mi>S</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo stretchy="false">(</mo> <mn>2</mn> <mi>p</mi> <mi>ρ</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <mi>S</mi> <mo>−</mo> <mn>2</mn> </mrow> </msup> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>π</mi> <mi>η</mi> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi mathvariant="normal">Γ</mi> <mo stretchy="false">(</mo> <mi>S</mi> <mo>+</mo> <mi>i</mi> <mi>η</mi> <mo stretchy="false">)</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F(Z,T)={\frac {2(1+S)}{\Gamma (1+2S)^{2}}}(2p\rho )^{2S-2}e^{\pi \eta }|\Gamma (S+i\eta )|^{2},}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/70539be64d3e5bf7f72df881b63b3985d71aec93" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:48.027ex; height:6.509ex;" alt="{\displaystyle F(Z,T)={\frac {2(1+S)}{\Gamma (1+2S)^{2}}}(2p\rho )^{2S-2}e^{\pi \eta }|\Gamma (S+i\eta )|^{2},}"> where p is the final momentum, Γ the <a href="/wiki/Gamma_function" title="Gamma function">Gamma function</a>, and (if α is the <a href="/wiki/Fine-structure_constant" title="Fine-structure constant">fine-structure constant</a> and rN the radius of the final state nucleus) <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S={\sqrt {1-\alpha ^{2}Z^{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>1</mn> <mo>−</mo> <msup> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>Z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S={\sqrt {1-\alpha ^{2}Z^{2}}}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/62e120ef54706c322426b20b8e271c80a32997c9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:16.229ex; height:3.509ex;" alt="{\displaystyle S={\sqrt {1-\alpha ^{2}Z^{2}}}}">, <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \eta =\pm Ze^{2}E/(\hbar cp)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>η</mi> <mo>=</mo> <mo>±</mo> <mi>Z</mi> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mo stretchy="false">(</mo> <mi class="MJX-variant">ℏ</mi> <mi>c</mi> <mi>p</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \eta =\pm Ze^{2}E/(\hbar cp)}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/616c507613c660e071138df91f772b52ce6771bb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:18.124ex; height:3.176ex;" alt="{\displaystyle \eta =\pm Ze^{2}E/(\hbar cp)}"> (+ for electrons, − for positrons), and <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rho =r_{N}/\hbar }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ρ</mi> <mo>=</mo> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>N</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi class="MJX-variant">ℏ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho =r_{N}/\hbar }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/638687aa38d16109000acca1f6b6c92b99a772d5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.509ex; height:2.843ex;" alt="{\displaystyle \rho =r_{N}/\hbar }">. For non-relativistic betas (Q ≪ mec2), this expression can be approximated by:<a href="#cite_note-31">[31]</a> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F(Z,T)\approx {\frac {2\pi \eta }{1-e^{-2\pi \eta }}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> <mo stretchy="false">(</mo> <mi>Z</mi> <mo>,</mo> <mi>T</mi> <mo stretchy="false">)</mo> <mo>≈</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>2</mn> <mi>π</mi> <mi>η</mi> </mrow> <mrow> <mn>1</mn> <mo>−</mo> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>2</mn> <mi>π</mi> <mi>η</mi> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F(Z,T)\approx {\frac {2\pi \eta }{1-e^{-2\pi \eta }}}.}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/202ef10938240d5211686463dbda7c6d1a86b3fe" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:21.67ex; height:5.843ex;" alt="{\displaystyle F(Z,T)\approx {\frac {2\pi \eta }{1-e^{-2\pi \eta }}}.}"> Other approximations can be found in the literature.<a href="#cite_note-32">[32]</a><a href="#cite_note-33">[33]</a> <div class="mw-heading mw-heading3"><h3 id="Kurie_plot">Kurie plot</h3>[<a href="/w/index.php?title=Beta_decay&action=edit&section=23" title="Edit section: Kurie plot">edit</a>]</div> A Kurie plot (also known as a Fermi–Kurie plot) is a graph used in studying beta decay developed by <a href="/wiki/Franz_N._D._Kurie" title="Franz N. D. Kurie">Franz N. D. Kurie</a>, in which the square root of the number of beta particles whose momenta (or energy) lie within a certain narrow range, divided by the Fermi function, is plotted against beta-particle energy.<a href="#cite_note-34">[34]</a><a href="#cite_note-35">[35]</a> It is a straight line for allowed transitions and some forbidden transitions, in accord with the Fermi beta-decay theory. The energy-axis (x-axis) intercept of a Kurie plot corresponds to the maximum energy imparted to the electron/positron (the decay's Q value). With a Kurie plot one can find the limit on the effective mass of a neutrino.<a href="#cite_note-36">[36]</a> <div class="mw-heading mw-heading2"><h2 id="Helicity_(polarization)_of_neutrinos,_electrons_and_positrons_emitted_in_beta_decay">Helicity (polarization) of neutrinos, electrons and positrons emitted in beta decay</h2>[<a href="/w/index.php?title=Beta_decay&action=edit&section=24" title="Edit section: Helicity (polarization) of neutrinos, electrons and positrons emitted in beta decay">edit</a>]</div> After the discovery of parity non-conservation (see <a class="mw-selflink-fragment" href="#Non-conservation_of_parity">History</a>), it was found that, in beta decay, electrons are emitted mostly with negative <a href="/wiki/Chirality_(physics)" title="Chirality (physics)">helicity</a>, i.e., they move, naively speaking, like left-handed screws driven into a material (they have negative longitudinal <a href="/wiki/Spin_polarization" title="Spin polarization">polarization</a>).<a href="#cite_note-37">[37]</a> Conversely, positrons have mostly positive helicity, i.e., they move like right-handed screws. Neutrinos (emitted in positron decay) have negative helicity, while antineutrinos (emitted in electron decay) have positive helicity.<a href="#cite_note-38">[38]</a> The higher the energy of the particles, the higher their polarization. <div class="mw-heading mw-heading2"><h2 id="Types_of_beta_decay_transitions">Types of beta decay transitions</h2>[<a href="/w/index.php?title=Beta_decay&action=edit&section=25" title="Edit section: Types of beta decay transitions">edit</a>]</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Beta_decay_transition" title="Beta decay transition">Beta decay transition</a></div> Beta decays can be classified according to the angular momentum (<a href="/wiki/Angular_momentum_operator" title="Angular momentum operator">L value</a>) and total spin (<a href="/wiki/Spin_(physics)" title="Spin (physics)">S value</a>) of the emitted radiation. Since total angular momentum must be conserved, including orbital and spin angular momentum, beta decay occurs by a variety of quantum state transitions to various nuclear angular momentum or spin states, known as "Fermi" or "Gamow–Teller" transitions. When beta decay particles carry no angular momentum (L = 0), the decay is referred to as "allowed", otherwise it is "forbidden". Other decay modes, which are rare, are known as bound state decay and double beta decay. <div class="mw-heading mw-heading3"><h3 id="Fermi_transitions">Fermi transitions</h3>[<a href="/w/index.php?title=Beta_decay&action=edit&section=26" title="Edit section: Fermi transitions">edit</a>]</div> A Fermi transition is a beta decay in which the spins of the emitted electron (positron) and anti-neutrino (neutrino) couple to total spin <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S=0}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4ae0fc3192b864f55a46749d8a64e7cf7783d04c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.76ex; height:2.176ex;" alt="{\displaystyle S=0}">, leading to an angular momentum change <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta J=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>J</mi> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta J=0}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4e75f16531aead77f8f6cb649637b30188f0b570" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.668ex; height:2.176ex;" alt="{\displaystyle \Delta J=0}"> between the initial and final states of the nucleus (assuming an allowed transition). In the non-relativistic limit, the nuclear part of the operator for a Fermi transition is given by <math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {O}}_{F}=G_{V}\sum _{a}{\hat {\tau }}_{a\pm }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">O</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>F</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>G</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>V</mi> </mrow> </msub> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </munder> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>τ</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> <mo>±</mo> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {O}}_{F}=G_{V}\sum _{a}{\hat {\tau }}_{a\pm }}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/854ef73c0e432ab34e03424427b3ded48d2f0fea" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:17.612ex; height:5.509ex;" alt="{\displaystyle {\mathcal {O}}_{F}=G_{V}\sum _{a}{\hat {\tau }}_{a\pm }}"> with <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle G_{V}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>G</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>V</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle G_{V}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2eb9098627fa58a96db71271676284e5bb794a7f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.323ex; height:2.509ex;" alt="{\displaystyle G_{V}}"> the weak vector coupling constant, <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \tau _{\pm }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>τ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>±</mo> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tau _{\pm }}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d4295e2d9371a9d80a339535fb7ad4b548ed49a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.527ex; height:2.009ex;" alt="{\displaystyle \tau _{\pm }}"> the <a href="/wiki/Isospin" title="Isospin">isospin</a> <a href="/wiki/Ladder_operator" title="Ladder operator">raising and lowering operators</a>, and <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ffd2487510aa438433a2579450ab2b3d557e5edc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.23ex; height:1.676ex;" alt="{\displaystyle a}"> running over all protons and neutrons in the nucleus. <div class="mw-heading mw-heading3"><h3 id="Gamow–Teller_transitions">Gamow–Teller transitions</h3>[<a href="/w/index.php?title=Beta_decay&action=edit&section=27" title="Edit section: Gamow–Teller transitions">edit</a>]</div> A Gamow–Teller transition is a beta decay in which the spins of the emitted electron (positron) and anti-neutrino (neutrino) couple to total spin <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S=1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <mo>=</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S=1}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d5e2b58c1aaaf2718fb801e97bf21d1f72726372" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.76ex; height:2.176ex;" alt="{\displaystyle S=1}">, leading to an angular momentum change <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta J=0,\pm 1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>J</mi> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mo>±</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta J=0,\pm 1}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a866d60b59d314187a95d3ef3666667deaac7cfb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:11.673ex; height:2.509ex;" alt="{\displaystyle \Delta J=0,\pm 1}"> between the initial and final states of the nucleus (assuming an allowed transition). In this case, the nuclear part of the operator is given by <math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {O}}_{GT}=G_{A}\sum _{a}{\hat {\sigma }}_{a}{\hat {\tau }}_{a\pm }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">O</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>G</mi> <mi>T</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>G</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </munder> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>σ</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msub> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>τ</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> <mo>±</mo> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {O}}_{GT}=G_{A}\sum _{a}{\hat {\sigma }}_{a}{\hat {\tau }}_{a\pm }}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f00fcae926d10df70de6548c187e386649af530b" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:21.23ex; height:5.509ex;" alt="{\displaystyle {\mathcal {O}}_{GT}=G_{A}\sum _{a}{\hat {\sigma }}_{a}{\hat {\tau }}_{a\pm }}"> with <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle G_{A}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>G</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle G_{A}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d48fb2edbe56d334f9634e421c3e5db1a405d1eb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.292ex; height:2.509ex;" alt="{\displaystyle G_{A}}"> the weak axial-vector coupling constant, and <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sigma }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>σ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sigma }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/59f59b7c3e6fdb1d0365a494b81fb9a696138c36" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle \sigma }"> the <a href="/wiki/Pauli_matrices" title="Pauli matrices">spin Pauli matrices</a>, which can produce a spin-flip in the decaying nucleon. <div class="mw-heading mw-heading3"><h3 id="Forbidden_transitions">Forbidden transitions</h3>[<a href="/w/index.php?title=Beta_decay&action=edit&section=28" title="Edit section: Forbidden transitions">edit</a>]</div> When L > 0, the decay is referred to as "<a href="/wiki/Forbidden_transition" class="mw-redirect" title="Forbidden transition">forbidden</a>". Nuclear <a href="/wiki/Selection_rule" title="Selection rule">selection rules</a> require high L values to be accompanied by changes in <a href="/wiki/Nuclear_spin" class="mw-redirect" title="Nuclear spin">nuclear spin</a> (J) and <a href="/wiki/Parity_(physics)" title="Parity (physics)">parity</a> (π). The selection rules for the Lth forbidden transitions are: <math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta J=L-1,L,L+1;\Delta \pi =(-1)^{L},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>J</mi> <mo>=</mo> <mi>L</mi> <mo>−</mo> <mn>1</mn> <mo>,</mo> <mi>L</mi> <mo>,</mo> <mi>L</mi> <mo>+</mo> <mn>1</mn> <mo>;</mo> <mi mathvariant="normal">Δ</mi> <mi>π</mi> <mo>=</mo> <mo stretchy="false">(</mo> <mo>−</mo> <mn>1</mn> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> </mrow> </msup> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta J=L-1,L,L+1;\Delta \pi =(-1)^{L},}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/079c6ef49f11faa38b1a2630e6563f4ecb0a942e" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:35.506ex; height:3.176ex;" alt="{\displaystyle \Delta J=L-1,L,L+1;\Delta \pi =(-1)^{L},}"> where Δπ = 1 or −1 corresponds to no parity change or parity change, respectively. The special case of a transition between isobaric analogue states, where the structure of the final state is very similar to the structure of the initial state, is referred to as "superallowed" for beta decay, and proceeds very quickly. The following table lists the Δ<var style="padding-right: 1px;">J</var> and Δ<var style="padding-right: 1px;">π</var> values for the first few values of L: <table class="wikitable"> <tbody><tr> <th>Forbiddenness</th> <th>Δ<var style="padding-right: 1px;">J</var></th> <th>Δ<var style="padding-right: 1px;">π</var> </th></tr> <tr> <td>Superallowed</td> <td>0</td> <td style="background:#FFC7C7;color:black;vertical-align:middle;text-align:center;" class="table-no">No </td></tr> <tr> <td>Allowed</td> <td>0, 1</td> <td style="background:#FFC7C7;color:black;vertical-align:middle;text-align:center;" class="table-no">No </td></tr> <tr> <td>First forbidden</td> <td>0, 1, 2</td> <td style="background:#9EFF9E;color:black;vertical-align:middle;text-align:center;" class="table-yes">Yes </td></tr> <tr> <td>Second forbidden</td> <td>1, 2, 3</td> <td style="background:#FFC7C7;color:black;vertical-align:middle;text-align:center;" class="table-no">No </td></tr> <tr> <td>Third forbidden</td> <td>2, 3, 4</td> <td style="background:#9EFF9E;color:black;vertical-align:middle;text-align:center;" class="table-yes">Yes </td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="Rare_decay_modes">Rare decay modes</h2>[<a href="/w/index.php?title=Beta_decay&action=edit&section=29" title="Edit section: Rare decay modes">edit</a>]</div> <div class="mw-heading mw-heading3"><h3 id="Bound-state_β−_decay">Bound-state β− decay</h3>[<a href="/w/index.php?title=Beta_decay&action=edit&section=30" title="Edit section: Bound-state β− decay">edit</a>]</div> A very small minority of free neutron decays (about four per million) are so-called "two-body decays", in which the proton, electron and antineutrino are produced, but the electron fails to gain the 13.6 eV energy necessary to escape the proton, and therefore simply remains bound to it, as a neutral <a href="/wiki/Hydrogen_atom" title="Hydrogen atom">hydrogen atom</a>.<a href="#cite_note-39">[39]</a> In this type of beta decay, in essence all of the neutron <a href="/wiki/Decay_energy" title="Decay energy">decay energy</a> is carried off by the antineutrino. For fully ionized atoms (bare nuclei), it is possible in likewise manner for electrons to fail to escape the atom, and to be emitted from the nucleus into low-lying atomic bound states (orbitals). This cannot occur for neutral atoms with low-lying bound states which are already filled by electrons. Bound-state β decays were predicted by <a href="/wiki/Raymond_Daudel" title="Raymond Daudel">Daudel</a>, Jean, and Lecoin in 1947,<a href="#cite_note-40">[40]</a> and the phenomenon in fully ionized atoms was first observed for <a href="/wiki/Isotopes_of_dysprosium" title="Isotopes of dysprosium">163Dy66+</a> in 1992 by Jung et al. of the <a href="/wiki/GSI_Helmholtz_Centre_for_Heavy_Ion_Research" title="GSI Helmholtz Centre for Heavy Ion Research">Darmstadt Heavy-Ion Research Center</a>. Although neutral 163 Dy is a stable isotope, the fully ionized 163Dy66+ undergoes β decay into the K and L shells with a half-life of 47 days.<a href="#cite_note-41">[41]</a> The resulting nucleus – <a href="/wiki/Isotopes_of_holmium" title="Isotopes of holmium">163 Ho</a> – is stable only in the fully ionized state and will decay via <a href="/wiki/Electron_capture" title="Electron capture">electron capture</a> into 163 Dy in the neutral state. The half life for neutral <a href="/wiki/Isotopes_of_holmium" title="Isotopes of holmium">163 Ho</a> is 4750 years. Another possibility is that a fully ionized atom undergoes greatly accelerated β decay, as observed for 187Re by Bosch et al., also at Darmstadt. Neutral 187Re does undergo β decay with a half-life of 41.6×109 years,<a href="#cite_note-42">[42]</a> but for fully ionized 187Re75+ this is shortened to only 32.9 years.<a href="#cite_note-43">[43]</a> For comparison, the variation of decay rates of other nuclear processes due to chemical environment is <a href="/wiki/Radioactive_decay#Changing_rates" title="Radioactive decay">less than 1%</a>. <div class="mw-heading mw-heading3"><h3 id="Double_beta_decay">Double beta decay</h3>[<a href="/w/index.php?title=Beta_decay&action=edit&section=31" title="Edit section: Double beta decay">edit</a>]</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Double_beta_decay" title="Double beta decay">Double beta decay</a></div> Some nuclei can undergo double beta decay (ββ decay) where the charge of the nucleus changes by two units. Double beta decay is difficult to study, as the process has an extremely long half-life. In nuclei for which both β decay and ββ decay are possible, the rarer ββ decay process is effectively impossible to observe. However, in nuclei where β decay is forbidden but ββ decay is allowed, the process can be seen and a half-life measured.<a href="#cite_note-Bilenky-44">[44]</a> Thus, ββ decay is usually studied only for beta stable nuclei. Like single beta decay, double beta decay does not change A; thus, at least one of the nuclides with some given A has to be stable with regard to both single and double beta decay. "Ordinary" double beta decay results in the emission of two electrons and two antineutrinos. If neutrinos are <a href="/wiki/Majorana_particle" class="mw-redirect" title="Majorana particle">Majorana particles</a> (i.e., they are their own antiparticles), then a decay known as <a href="/wiki/Neutrinoless_double_beta_decay" title="Neutrinoless double beta decay">neutrinoless double beta decay</a> will occur. Most neutrino physicists believe that neutrinoless double beta decay has never been observed.<a href="#cite_note-Bilenky-44">[44]</a> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2>[<a href="/w/index.php?title=Beta_decay&action=edit&section=32" title="Edit section: See also">edit</a>]</div> <ul><li><a href="/wiki/Common_beta_emitters" title="Common beta emitters">Common beta emitters</a></li> <li><a href="/wiki/Neutrino" title="Neutrino">Neutrino</a></li> <li><a href="/wiki/Betavoltaics" class="mw-redirect" title="Betavoltaics">Betavoltaics</a></li> <li><a href="/wiki/Particle_radiation" title="Particle radiation">Particle radiation</a></li> <li><a href="/wiki/Radionuclide" title="Radionuclide">Radionuclide</a></li> <li><a href="/wiki/Tritium_illumination" class="mw-redirect" title="Tritium illumination">Tritium illumination</a>, a form of <a href="/wiki/Fluorescent_lighting" class="mw-redirect" title="Fluorescent lighting">fluorescent lighting</a> powered by beta decay</li> <li><a href="/wiki/Pandemonium_effect" title="Pandemonium effect">Pandemonium effect</a></li> <li><a href="/wiki/Total_absorption_spectroscopy" title="Total absorption spectroscopy">Total absorption spectroscopy</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2>[<a href="/w/index.php?title=Beta_decay&action=edit&section=33" title="Edit section: References">edit</a>]</div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist reflist-columns references-column-width" style="column-width: 30em;"> <ol class="references"> <li id="cite_note-konya74-1">^ <a href="#cite_ref-konya74_1-0">a</a> <a href="#cite_ref-konya74_1-1">b</a> <a href="#cite_ref-konya74_1-2">c</a> <a href="#cite_ref-konya74_1-3">d</a> <a href="#cite_ref-konya74_1-4">e</a> <style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFKonyaNagy2012" class="citation book cs1">Konya, J.; Nagy, N. 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"Neutrinoless double beta-decay". <a href="/w/index.php?title=Physics_of_Particles_and_Nuclei&action=edit&redlink=1" class="new" title="Physics of Particles and Nuclei (page does not exist)">Physics of Particles and Nuclei</a>. 41 (5): 690–715. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<a rel="nofollow" class="external text" href="https://arxiv.org/abs/1001.1946">1001.1946</a>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2010PPN....41..690B">2010PPN....41..690B</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1134%2FS1063779610050035">10.1134/S1063779610050035</a>. <a href="/wiki/Hdl_(identifier)" class="mw-redirect" title="Hdl (identifier)">hdl</a>:<a rel="nofollow" class="external text" href="https://hdl.handle.net/10486%2F663891">10486/663891</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:55217197">55217197</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physics+of+Particles+and+Nuclei&rft.atitle=Neutrinoless+double+beta-decay&rft.volume=41&rft.issue=5&rft.pages=690-715&rft.date=2010&rft_id=info%3Ahdl%2F10486%2F663891&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A55217197%23id-name%3DS2CID&rft_id=info%3Abibcode%2F2010PPN....41..690B&rft_id=info%3Aarxiv%2F1001.1946&rft_id=info%3Adoi%2F10.1134%2FS1063779610050035&rft.aulast=Bilenky&rft.aufirst=S.+M.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABeta+decay" class="Z3988"> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="Bibliography">Bibliography</h2>[<a href="/w/index.php?title=Beta_decay&action=edit&section=34" title="Edit section: Bibliography">edit</a>]</div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFTomonaga1997" class="citation book cs1"><a href="/wiki/Sin-Itiro_Tomonaga" class="mw-redirect" title="Sin-Itiro Tomonaga">Tomonaga, S.-I.</a> (1997). The Story of Spin. <a href="/wiki/University_of_Chicago_Press" title="University of Chicago Press">University of Chicago Press</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Story+of+Spin&rft.pub=University+of+Chicago+Press&rft.date=1997&rft.aulast=Tomonaga&rft.aufirst=S.-I.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABeta+decay" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFTuli2011" class="citation book cs1">Tuli, J. K. (2011). <a rel="nofollow" class="external text" href="http://www.nndc.bnl.gov/wallet/wall35.pdf">Nuclear Wallet Cards</a> (PDF) (8th ed.). <a href="/wiki/Brookhaven_National_Laboratory" title="Brookhaven National Laboratory">Brookhaven National Laboratory</a>. <a rel="nofollow" class="external text" href="https://ghostarchive.org/archive/20221009/http://www.nndc.bnl.gov/wallet/wall35.pdf">Archived</a> (PDF) from the original on 2022-10-09.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Nuclear+Wallet+Cards&rft.edition=8th&rft.pub=Brookhaven+National+Laboratory&rft.date=2011&rft.aulast=Tuli&rft.aufirst=J.+K.&rft_id=http%3A%2F%2Fwww.nndc.bnl.gov%2Fwallet%2Fwall35.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABeta+decay" class="Z3988"></li></ul> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2>[<a href="/w/index.php?title=Beta_decay&action=edit&section=35" title="Edit section: External links">edit</a>]</div> <ul><li><a href="/wiki/File:Ndslivechart.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/b/b0/Ndslivechart.png" decoding="async" width="45" height="31" class="mw-file-element" data-file-width="45" data-file-height="31" /></a> <a rel="nofollow" class="external text" href="http://www-nds.iaea.org/livechart">The Live Chart of Nuclides - IAEA </a> with filter on decay type</li> <li>Beta decay simulation <a rel="nofollow" class="external autonumber" href="https://phet.colorado.edu/en/simulation/legacy/beta-decay">[1]</a></li></ul> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1236075235">.mw-parser-output .navbox{box-sizing:border-box;border:1px solid #a2a9b1;width:100%;clear:both;font-size:88%;text-align:center;padding:1px;margin:1em auto 0}.mw-parser-output .navbox .navbox{margin-top:0}.mw-parser-output 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