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class="vector-toc-numb">2</span> <span>The role of neutrons</span> </div> </a> <ul id="toc-The_role_of_neutrons-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Neutrons,_protons,_and_binding_energy" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Neutrons,_protons,_and_binding_energy"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Neutrons, protons, and binding energy</span> </div> </a> <ul id="toc-Neutrons,_protons,_and_binding_energy-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Proton_and_neutron_drip_lines" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Proton_and_neutron_drip_lines"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Proton and neutron drip lines</span> </div> </a> <ul id="toc-Proton_and_neutron_drip_lines-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Island_of_stability" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Island_of_stability"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Island of stability</span> </div> </a> <ul id="toc-Island_of_stability-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Discussion" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Discussion"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Discussion</span> </div> </a> <ul id="toc-Discussion-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li 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class="sidebar-image"><span typeof="mw:File"><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></span></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"><i>Z</i></a><br /></li></ul> <ul><li><a href="/wiki/Isobar_(nuclide)" title="Isobar (nuclide)">Isobars</a> – equal <a href="/wiki/Mass_number" title="Mass number"><i>A</i></a></li></ul> <ul><li><a href="/wiki/Isotone" title="Isotone">Isotones</a> – equal <a href="/wiki/Neutron_number" title="Neutron number"><i>N</i></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"><i>N</i> − <i>Z</i></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> – <i>Z</i> ↔ <i>N</i></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 class="mw-selflink selflink">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 href="/wiki/Beta_decay" title="Beta decay">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<sup>+</sup></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<br /> <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><small>Processes:</small> <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><span class="nowrap"><span class="nowrap"><span class="noviewer" typeof="mw:File"><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></span> </span><a href="/wiki/Portal:Physics" title="Portal:Physics">Physics portal</a></span></li> <li><span class="nowrap"><span class="noviewer" typeof="mw:File"><span title="Category"><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" /></span></span> <a href="/wiki/Category:Nuclear_physics" title="Category:Nuclear physics">Category</a></span></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> <p>In <a href="/wiki/Nuclear_physics" title="Nuclear physics">nuclear physics</a>, the <b>valley of stability</b> (also called the <b>belt of stability</b>, <b>nuclear valley</b>, <b>energy valley</b>, or <b>beta stability valley</b>) is a characterization of the stability of <a href="/wiki/Nuclide" title="Nuclide">nuclides</a> to <a href="/wiki/Radioactivity" class="mw-redirect" title="Radioactivity">radioactivity</a> based on their binding energy.<sup id="cite_ref-Mackintosh_1-0" class="reference"><a href="#cite_note-Mackintosh-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> Nuclides are composed of <a href="/wiki/Proton" title="Proton">protons</a> and <a href="/wiki/Neutron" title="Neutron">neutrons</a>. The shape of the valley refers to the profile of binding energy as a function of the numbers of neutrons and protons, with the lowest part of the valley corresponding to the region of most <a href="/wiki/Stable_nuclide" title="Stable nuclide">stable nuclei</a>.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> The line of stable nuclides down the center of the valley of stability is known as the <a href="/wiki/Beta-decay_stable_isobars" title="Beta-decay stable isobars">line of beta stability</a>. The sides of the valley correspond to increasing instability to <a href="/wiki/Beta_decay" title="Beta decay">beta decay</a> (β<sup>−</sup> or β<sup>+</sup>). The decay of a nuclide becomes more energetically favorable the further it is from the line of beta stability. The boundaries of the valley correspond to the <a href="/wiki/Nuclear_drip_line" title="Nuclear drip line">nuclear drip lines</a>, where nuclides become so unstable they emit <a href="/wiki/Proton_emission" title="Proton emission">single protons</a> or <a href="/wiki/Neutron_emission" title="Neutron emission">single neutrons</a>. Regions of instability within the valley at high <a href="/wiki/Atomic_number" title="Atomic number">atomic number</a> also include radioactive decay by <a href="/wiki/Alpha_decay" title="Alpha decay">alpha radiation</a> or <a href="/wiki/Spontaneous_fission" title="Spontaneous fission">spontaneous fission</a>. The shape of the valley is roughly an elongated <a href="/wiki/Paraboloid" title="Paraboloid">paraboloid</a> corresponding to the nuclide <a href="/wiki/Binding_energy" title="Binding energy">binding energies</a> as a function of neutron and atomic numbers.<sup id="cite_ref-Mackintosh_1-1" class="reference"><a href="#cite_note-Mackintosh-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p><p>The nuclides within the valley of stability encompass the entire <a href="/wiki/Table_of_nuclides" title="Table of nuclides">table of nuclides</a>. The chart of those nuclides is also known as a Segrè chart, after the physicist <a href="/wiki/Emilio_Segr%C3%A8" title="Emilio Segrè">Emilio Segrè</a>.<sup id="cite_ref-Byrne_3-0" class="reference"><a href="#cite_note-Byrne-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> The Segrè chart may be considered a map of the nuclear valley. The region of proton and neutron combinations outside of the valley of stability is referred to as the sea of instability.<sup id="cite_ref-LLNL_4-0" class="reference"><a href="#cite_note-LLNL-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Seaborg1_5-0" class="reference"><a href="#cite_note-Seaborg1-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p><p>Scientists have long searched for long-lived heavy isotopes outside of the valley of stability,<sup id="cite_ref-longlived_6-0" class="reference"><a href="#cite_note-longlived-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-rare-isotope_7-0" class="reference"><a href="#cite_note-rare-isotope-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Boutin_8-0" class="reference"><a href="#cite_note-Boutin-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> hypothesized by <a href="/wiki/Glenn_T._Seaborg" title="Glenn T. Seaborg">Glenn T. Seaborg</a> in the late 1960s.<sup id="cite_ref-Seaborg2_9-0" class="reference"><a href="#cite_note-Seaborg2-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-OS-NYT_10-0" class="reference"><a href="#cite_note-OS-NYT-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> These relatively stable nuclides are expected to have particular configurations of "<a href="/wiki/Magic_number_(physics)" title="Magic number (physics)">magic</a>" atomic and <a href="/wiki/Neutron_number" title="Neutron number">neutron numbers</a>, and form a so-called <a href="/wiki/Island_of_stability" title="Island of stability">island of stability</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Description">Description</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Valley_of_stability&action=edit&section=1" title="Edit section: Description"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>All atomic nuclei are composed of protons and neutrons bound together by the <a href="/wiki/Nuclear_force" title="Nuclear force">nuclear force</a>. There are 286 <a href="/wiki/Primordial_isotope" class="mw-redirect" title="Primordial isotope">primordial</a> nuclides that occur naturally on earth, each corresponding to a unique number of protons, called the <a href="/wiki/Atomic_number" title="Atomic number">atomic number</a>, <i>Z</i>, and a unique number of neutrons, called the <a href="/wiki/Neutron_number" title="Neutron number">neutron number</a>, <i>N</i>. The <a href="/wiki/Mass_number" title="Mass number">mass number</a>, <i>A</i>, of a nuclide is the sum of atomic and neutron numbers, <i>A</i> = <i>Z</i> + <i>N</i>. Not all nuclides are stable, however. According to Byrne,<sup id="cite_ref-Byrne_3-1" class="reference"><a href="#cite_note-Byrne-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> stable nuclides are defined as those having a <a href="/wiki/Half-life" title="Half-life">half-life</a> greater than 10<sup>18</sup> years, and there are many combinations of protons and neutrons that form nuclides that are unstable. A common example of an unstable nuclide is <a href="/wiki/Carbon-14" title="Carbon-14">carbon-14</a> that decays by <a href="/wiki/Beta_decay" title="Beta decay">beta decay</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: </p> <dl><dd><span style="white-space:nowrap;"><span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1.0em;font-size:80%;text-align:right"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">14</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">6</sub></span></span>C<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:0.8em;line-height:1.0em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sub></span></span></span> → <span style="white-space:nowrap;"><span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1.0em;font-size:80%;text-align:right"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">14</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">7</sub></span></span>N<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:0.8em;line-height:1.0em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sub></span></span></span> + <span style="white-space:nowrap;"><span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:0.8em;line-height:1.0em;font-size:80%;text-align:right"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sub></span></span>e<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:0.8em;line-height:1.0em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">−</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sub></span></span></span> + <span style="white-space:nowrap;"><span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:0.8em;line-height:1.0em;font-size:80%;text-align:right"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sub></span></span><span style="text-decoration:overline;">ν</span><span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1.0em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">e</sub></span></span></span></dd></dl> <p>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> and a beta particle and an electron <a href="/wiki/Antineutrino" class="mw-redirect" title="Antineutrino">antineutrino</a> are emitted. An essential property of this and all nuclide decays is that the total energy of the <a href="/wiki/Decay_product" title="Decay product">decay product</a> is less than that of the original nuclide. The difference between the initial and final nuclide binding energies is carried away by the kinetic energies of the decay products, often the beta particle and its associated neutrino.<sup id="cite_ref-Byrne_3-2" class="reference"><a href="#cite_note-Byrne-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p><p>The concept of the <b>valley of stability</b> is a way of organizing all of the nuclides according to <a href="/wiki/Binding_energy" title="Binding energy">binding energy</a> as a function of neutron and proton numbers.<sup id="cite_ref-Mackintosh_1-2" class="reference"><a href="#cite_note-Mackintosh-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> Most stable nuclides have roughly equal numbers of protons and neutrons, so the line for which <i>Z</i> = <i>N</i> forms a rough initial line defining stable nuclides. The greater the number of protons, the more neutrons are required to stabilize a nuclide; nuclides with larger values for <i>Z</i> require an even larger number of neutrons, <i>N</i> > <i>Z</i>, to be stable. The valley of stability is formed by the negative of binding energy, the binding energy being the energy required to break apart the nuclide into its proton and neutron components. The stable nuclides have high binding energy, and these nuclides lie along the bottom of the valley of stability. Nuclides with weaker binding energy have combinations of <i>N</i> and <i>Z</i> that lie off of the line of stability and further up the sides of the valley of stability. Unstable nuclides can be formed in <a href="/wiki/Nuclear_reactors" class="mw-redirect" title="Nuclear reactors">nuclear reactors</a> or <a href="/wiki/Supernovas" class="mw-redirect" title="Supernovas">supernovas</a>, for example. Such nuclides often decay in sequences of <a href="/wiki/Nuclear_reaction" title="Nuclear reaction">reactions</a> called <a href="/wiki/Decay_chain" title="Decay chain">decay chains</a> that take the resulting nuclides sequentially down the slopes of the valley of stability. The sequence of decays take nuclides toward greater binding energies, and the nuclides terminating the chain are stable.<sup id="cite_ref-Mackintosh_1-3" class="reference"><a href="#cite_note-Mackintosh-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> The valley of stability provides both a conceptual approach for how to organize the myriad stable and unstable nuclides into a coherent picture and an intuitive way to understand how and why sequences of radioactive decay occur.<sup id="cite_ref-Mackintosh_1-4" class="reference"><a href="#cite_note-Mackintosh-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p> <ul class="gallery mw-gallery-packed"> <li class="gallerybox" style="width: 288px"> <div class="thumb" style="width: 286px;"><span typeof="mw:File"><a href="/wiki/File:BindingNuDat2.png" class="mw-file-description" title="Chart of nuclides (isotopes) by binding energy, depicting the valley of stability. The diagonal line corresponds to equal numbers of neutrons and protons. Dark blue squares represent nuclides with the greatest binding energy, hence they correspond to the most stable nuclides. The binding energy is greatest along the floor of the valley of stability."><img alt="Chart of nuclides (isotopes) by binding energy, depicting the valley of stability. The diagonal line corresponds to equal numbers of neutrons and protons. Dark blue squares represent nuclides with the greatest binding energy, hence they correspond to the most stable nuclides. The binding energy is greatest along the floor of the valley of stability." src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3b/BindingNuDat2.png/429px-BindingNuDat2.png" decoding="async" width="286" height="200" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3b/BindingNuDat2.png/643px-BindingNuDat2.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3b/BindingNuDat2.png/857px-BindingNuDat2.png 2x" data-file-width="1000" data-file-height="700" /></a></span></div> <div class="gallerytext">Chart of nuclides (isotopes) by binding energy, depicting the valley of stability. The diagonal line corresponds to equal numbers of neutrons and protons. Dark blue squares represent nuclides with the greatest binding energy, hence they correspond to the most stable nuclides. The binding energy is greatest along the floor of the valley of stability.</div> </li> <li class="gallerybox" style="width: 288px"> <div class="thumb" style="width: 286px;"><span typeof="mw:File"><a href="/wiki/File:HalflifeNuDat2.png" class="mw-file-description" title="Chart of nuclides by half life. Black squares represent nuclides with the longest half lives hence they correspond to the most stable nuclides. The most stable, long-lived nuclides lie along the floor of the valley of stability. Nuclides with more than 20 protons must have more neutrons than protons to be stable."><img alt="Chart of nuclides by half life. Black squares represent nuclides with the longest half lives hence they correspond to the most stable nuclides. The most stable, long-lived nuclides lie along the floor of the valley of stability. Nuclides with more than 20 protons must have more neutrons than protons to be stable." src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c0/HalflifeNuDat2.png/429px-HalflifeNuDat2.png" decoding="async" width="286" height="200" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c0/HalflifeNuDat2.png/643px-HalflifeNuDat2.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c0/HalflifeNuDat2.png/857px-HalflifeNuDat2.png 2x" data-file-width="1000" data-file-height="700" /></a></span></div> <div class="gallerytext">Chart of nuclides by half life. Black squares represent nuclides with the longest half lives hence they correspond to the most stable nuclides. The most stable, long-lived nuclides lie along the floor of the valley of stability. Nuclides with more than 20 protons must have more neutrons than protons to be stable.</div> </li> <li class="gallerybox" style="width: 288px"> <div class="thumb" style="width: 286px;"><span typeof="mw:File"><a href="/wiki/File:DecayModeNuDat2.png" class="mw-file-description" title="Chart of nuclides by type of decay. Black squares are stable nuclides. Nuclides with excessive neutrons or protons are unstable to β− (light blue) or β+ (green) decay, respectively. At high atomic number, alpha emission (orange) or spontaneous fission (dark blue) become common decay modes."><img alt="Chart of nuclides by type of decay. Black squares are stable nuclides. Nuclides with excessive neutrons or protons are unstable to β− (light blue) or β+ (green) decay, respectively. At high atomic number, alpha emission (orange) or spontaneous fission (dark blue) become common decay modes." src="//upload.wikimedia.org/wikipedia/commons/thumb/0/02/DecayModeNuDat2.png/429px-DecayModeNuDat2.png" decoding="async" width="286" height="200" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/02/DecayModeNuDat2.png/643px-DecayModeNuDat2.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/02/DecayModeNuDat2.png/857px-DecayModeNuDat2.png 2x" data-file-width="1000" data-file-height="700" /></a></span></div> <div class="gallerytext">Chart of nuclides by type of decay. Black squares are stable nuclides. Nuclides with excessive neutrons or protons are unstable to β<sup>−</sup> (light blue) or β<sup>+</sup> (green) decay, respectively. At high atomic number, alpha emission (orange) or spontaneous fission (dark blue) become common decay modes.</div> </li> </ul> <div class="mw-heading mw-heading2"><h2 id="The_role_of_neutrons">The role of neutrons</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Valley_of_stability&action=edit&section=2" title="Edit section: The role of neutrons"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The protons and neutrons that comprise an atomic nucleus behave almost identically within the nucleus. The approximate symmetry of <a href="/wiki/Isospin" title="Isospin">isospin</a> treats these particles as identical, but in a different quantum state. This symmetry is only approximate, however, and the <a href="/wiki/Nuclear_force" title="Nuclear force">nuclear force</a> that binds nucleons together is a complicated function depending on nucleon type, spin state, electric charge, momentum, etc. and with contributions from non-<a href="/wiki/Central_forces" class="mw-redirect" title="Central forces">central forces</a>. The nuclear force is not a fundamental force of nature, but a consequence of the residual effects of the <a href="/wiki/Strong_force" class="mw-redirect" title="Strong force">strong force</a> that surround the nucleons. One consequence of these complications is that although <a href="/wiki/Deuterium" title="Deuterium">deuterium</a>, a bound state of a proton (p) and a neutron (n) is stable, exotic nuclides such as <a href="/wiki/Diproton" class="mw-redirect" title="Diproton">diproton</a> or <a href="/wiki/Neutronium" title="Neutronium">dineutron</a> are unbound.<sup id="cite_ref-Schirber_11-0" class="reference"><a href="#cite_note-Schirber-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> The nuclear force is not sufficiently strong to form either p-p or n-n bound states, or equivalently, the nuclear force does not form a <a href="/wiki/Potential_well" title="Potential well">potential well</a> deep enough to bind these identical nucleons.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (October 2019)">citation needed</span></a></i>]</sup> </p><p>Stable nuclides require approximately equal numbers of protons and neutrons. The stable nuclide <a href="/wiki/Carbon-12" title="Carbon-12">carbon-12</a> (<sup>12</sup>C) is composed of six neutrons and six protons, for example. Protons have a positive charge, hence within a nuclide with many protons there are large repulsive forces between protons arising from the <a href="/wiki/Coulomb%27s_law" title="Coulomb's law">Coulomb force</a>. By acting to separate protons from one another, the neutrons within a nuclide play an essential role in stabilizing nuclides. With increasing atomic number, even greater numbers of neutrons are required to obtain stability. The heaviest stable element, <a href="/wiki/Isotopes_of_lead" title="Isotopes of lead">lead</a> (Pb), has many more neutrons than protons. The stable nuclide <sup>206</sup>Pb has <i>Z</i> = 82 and <i>N</i> = 124, for example. For this reason, the valley of stability does not follow the line <i>Z</i> = <i>N</i> for A larger than 40 (<i>Z</i> = 20 is the element <a href="/wiki/Isotopes_of_calcium" title="Isotopes of calcium">calcium</a>).<sup id="cite_ref-Byrne_3-3" class="reference"><a href="#cite_note-Byrne-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> Neutron number increases along the line of beta stability at a faster rate than atomic number. </p><p>The line of beta stability follows a particular curve of <a href="/wiki/Neutron%E2%80%93proton_ratio" title="Neutron–proton ratio">neutron–proton ratio</a>, corresponding to the most stable nuclides. On one side of the valley of stability, this ratio is small, corresponding to an excess of protons over neutrons in the nuclides. These nuclides tend to be unstable to β<sup>+</sup> decay or electron capture, since such decay converts a proton to a neutron. The decay serves to move the nuclides toward a more stable neutron-proton ratio. On the other side of the valley of stability, this ratio is large, corresponding to an excess of neutrons over protons in the nuclides. These nuclides tend to be unstable to β<sup>−</sup> decay, since such decay converts neutrons to protons. On this side of the valley of stability, β<sup>−</sup> decay also serves to move nuclides toward a more stable neutron-proton ratio. </p> <div class="mw-heading mw-heading2"><h2 id="Neutrons,_protons,_and_binding_energy"><span id="Neutrons.2C_protons.2C_and_binding_energy"></span>Neutrons, protons, and binding energy</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Valley_of_stability&action=edit&section=3" title="Edit section: Neutrons, protons, and binding energy"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></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">See also: <a href="/wiki/Semi-empirical_mass_formula" title="Semi-empirical mass formula">Semi-empirical mass formula</a></div> <p>The mass of an atomic nucleus is given by </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m=Zm_{p}+Nm_{n}-{\frac {E_{B}}{c^{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> <mo>=</mo> <mi>Z</mi> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> <mo>+</mo> <mi>N</mi> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m=Zm_{p}+Nm_{n}-{\frac {E_{B}}{c^{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5afc5a86e1914a4175a41b0e737846744590ec82" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:24.953ex; height:5.509ex;" alt="{\displaystyle m=Zm_{p}+Nm_{n}-{\frac {E_{B}}{c^{2}}}}"></span></dd></dl> <p>where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m_{p}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m_{p}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d7d93b292637f64f747f3fe0ea4bad9f2bd65637" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.1ex; height:2.343ex;" alt="{\displaystyle m_{p}}"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m_{n}}"> <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> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m_{n}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ae8181c5cf15da902bbaa5c2291aeb8167fe78ae" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.259ex; height:2.009ex;" alt="{\displaystyle m_{n}}"></span> are the rest mass of a proton and a neutron, respectively, and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{B}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{B}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2b71d40b28612bb3f7578929558cccef2bb5798d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.195ex; height:2.509ex;" alt="{\displaystyle E_{B}}"></span> is the total <a href="/wiki/Binding_energy" title="Binding energy">binding energy</a> of the nucleus. The <a href="/wiki/Mass%E2%80%93energy_equivalence" title="Mass–energy equivalence">mass–energy equivalence</a> is used here. The binding energy is subtracted from the sum of the proton and neutron masses because the mass of the nucleus is <i>less</i> than that sum. This property, called the <a href="/wiki/Mass_defect" class="mw-redirect" title="Mass defect">mass defect</a>, is necessary for a stable nucleus; within a nucleus, the nuclides are trapped by a <a href="/wiki/Potential_well" title="Potential well">potential well</a>. A semi-empirical mass formula states that the binding energy will take the form </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{B}=a_{V}A-a_{S}A^{2/3}-a_{C}{\frac {Z^{2}}{A^{1/3}}}-a_{A}{\frac {(A-2Z)^{2}}{A}}\pm \delta (A,Z)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>V</mi> </mrow> </msub> <mi>A</mi> <mo>−</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>S</mi> </mrow> </msub> <msup> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>3</mn> </mrow> </msup> <mo>−</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>Z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>3</mn> </mrow> </msup> </mfrac> </mrow> <mo>−</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo stretchy="false">(</mo> <mi>A</mi> <mo>−</mo> <mn>2</mn> <mi>Z</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mi>A</mi> </mfrac> </mrow> <mo>±</mo> <mi>δ</mi> <mo stretchy="false">(</mo> <mi>A</mi> <mo>,</mo> <mi>Z</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{B}=a_{V}A-a_{S}A^{2/3}-a_{C}{\frac {Z^{2}}{A^{1/3}}}-a_{A}{\frac {(A-2Z)^{2}}{A}}\pm \delta (A,Z)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6aef4eefb3d3928b95aea62a4bfb12b529331bd0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:58.212ex; height:6.176ex;" alt="{\displaystyle E_{B}=a_{V}A-a_{S}A^{2/3}-a_{C}{\frac {Z^{2}}{A^{1/3}}}-a_{A}{\frac {(A-2Z)^{2}}{A}}\pm \delta (A,Z)}"></span><sup id="cite_ref-OSUFormula_12-0" class="reference"><a href="#cite_note-OSUFormula-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup></dd></dl> <p>The difference between the mass of a nucleus and the sum of the masses of the neutrons and protons that comprise it is known as the <a href="/wiki/Mass_defect" class="mw-redirect" title="Mass defect">mass defect</a>. E<sub>B</sub> is often divided by the mass number to obtain binding energy per nucleon for comparisons of binding energies between nuclides. Each of the terms in this formula has a theoretical basis. The coefficients <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a_{V}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>V</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a_{V}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ad98daca4fcd22c3603e5644c79848a82fdeaace" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.726ex; height:2.009ex;" alt="{\displaystyle a_{V}}"></span>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a_{S}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>S</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a_{S}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1533c9504259f50f11a4219785e42068ecf11610" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.522ex; height:2.009ex;" alt="{\displaystyle a_{S}}"></span>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a_{C}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a_{C}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4e2caa2bf7f599288ca8d79628ab6fc0f265cde5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.711ex; height:2.009ex;" alt="{\displaystyle a_{C}}"></span>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a_{A}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a_{A}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/187a574b62266ad7c236172391d575b150e69bc9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.695ex; height:2.009ex;" alt="{\displaystyle a_{A}}"></span> and a coefficient that appears in the formula for <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \delta (A,Z)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>δ</mi> <mo stretchy="false">(</mo> <mi>A</mi> <mo>,</mo> <mi>Z</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \delta (A,Z)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/785e97563abbcee669ac235b9fee016717e92e6a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.315ex; height:2.843ex;" alt="{\displaystyle \delta (A,Z)}"></span> are determined empirically. </p><p>The binding energy expression gives a quantitative estimate for the neutron-proton ratio. The energy is a quadratic expression in <span class="texhtml mvar" style="font-style:italic;">Z</span> that is minimized when the neutron-proton ratio is <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle N/Z\approx 1+{\frac {a_{C}}{2a_{A}}}A^{2/3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>Z</mi> <mo>≈</mo> <mn>1</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> <mrow> <mn>2</mn> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> </mrow> </mfrac> </mrow> <msup> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>3</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N/Z\approx 1+{\frac {a_{C}}{2a_{A}}}A^{2/3}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e0ada7166c3f07e49c8b73a7a65e11c2b7dc6335" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:21.142ex; height:5.009ex;" alt="{\displaystyle N/Z\approx 1+{\frac {a_{C}}{2a_{A}}}A^{2/3}}"></span>. This equation for the neutron-proton ratio shows that in stable nuclides the number of neutrons is greater than the number of protons by a factor that scales as <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A^{2/3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>3</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A^{2/3}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9babd2501f6e47397bc85717e3c55be784407bbe" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.441ex; height:2.843ex;" alt="{\displaystyle A^{2/3}}"></span>. </p> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Binding_energy_curve_-_common_isotopes2.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/28/Binding_energy_curve_-_common_isotopes2.jpg/330px-Binding_energy_curve_-_common_isotopes2.jpg" decoding="async" width="330" height="221" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/28/Binding_energy_curve_-_common_isotopes2.jpg/495px-Binding_energy_curve_-_common_isotopes2.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/28/Binding_energy_curve_-_common_isotopes2.jpg/660px-Binding_energy_curve_-_common_isotopes2.jpg 2x" data-file-width="680" data-file-height="455" /></a><figcaption>The negative of binding energy per nucleon for the stable nuclides located along the bottom of the valley of stability. <a href="/wiki/Iron-56" title="Iron-56">Iron-56</a> is about the most stable nuclide, and it is about the lowest point within the valley of stability.</figcaption></figure> <p>The figure at right shows the average binding energy per nucleon as a function of atomic mass number along the line of beta stability, that is, along the bottom of the valley of stability. For very small atomic mass number (H, He, Li), binding energy per nucleon is small, and this energy increases rapidly with atomic mass number. <a href="/wiki/Nickel-62" title="Nickel-62">Nickel-62</a> (28 protons, 34 neutrons) has the highest mean binding energy of all nuclides, while <a href="/wiki/Iron-58" class="mw-redirect" title="Iron-58">iron-58</a> (26 protons, 32 neutrons) and <a href="/wiki/Iron-56" title="Iron-56">iron-56</a> (26 protons, 30 neutrons) are a close second and third.<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> These nuclides lie at the very bottom of the valley of stability. From this bottom, the average binding energy per nucleon slowly decreases with increasing atomic mass number. The heavy nuclide <a href="/wiki/Uranium-238" title="Uranium-238"><sup>238</sup>U</a> is not stable, but is slow to decay with a half-life of 4.5 billion years.<sup id="cite_ref-Mackintosh_1-5" class="reference"><a href="#cite_note-Mackintosh-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> It has relatively small binding energy per nucleon. </p><p>For β<sup>−</sup> decay, nuclear reactions have the generic form </p> <dl><dd><span style="white-space:nowrap;"><span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1.0em;font-size:80%;text-align:right"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"><span class="texhtml mvar" style="font-style:italic;">A</span></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"><span class="texhtml mvar" style="font-style:italic;">Z</span></sub></span></span>X<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:0.8em;line-height:1.0em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sub></span></span></span> → <span style="white-space:nowrap;"><span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1.0em;font-size:80%;text-align:right"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"><span class="texhtml mvar" style="font-style:italic;">A</span></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"><span class="texhtml"><i>Z</i>+1</span></sub></span></span>X′<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:0.8em;line-height:1.0em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sub></span></span></span> + <span style="white-space:nowrap;"><span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:0.8em;line-height:1.0em;font-size:80%;text-align:right"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sub></span></span>e<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:0.8em;line-height:1.0em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">−</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sub></span></span></span> + <span style="white-space:nowrap;"><span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:0.8em;line-height:1.0em;font-size:80%;text-align:right"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sub></span></span><span style="text-decoration:overline;">ν</span><span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1.0em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">e</sub></span></span></span><sup id="cite_ref-konya74_14-0" class="reference"><a href="#cite_note-konya74-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup></dd></dl> <p>where <span class="texhtml mvar" style="font-style:italic;">A</span> and <span class="texhtml mvar" style="font-style:italic;">Z</span> 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 nuclides, respectively. For β<sup>+</sup> decay, the generic form is </p> <dl><dd><span style="white-space:nowrap;"><span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1.0em;font-size:80%;text-align:right"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"><span class="texhtml mvar" style="font-style:italic;">A</span></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"><span class="texhtml mvar" style="font-style:italic;">Z</span></sub></span></span>X<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:0.8em;line-height:1.0em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sub></span></span></span> → <span style="white-space:nowrap;"><span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1.0em;font-size:80%;text-align:right"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"><span class="texhtml mvar" style="font-style:italic;">A</span></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"><span class="texhtml"><i>Z</i>−1</span></sub></span></span>X′<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:0.8em;line-height:1.0em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sub></span></span></span> + <span style="white-space:nowrap;"><span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:0.8em;line-height:1.0em;font-size:80%;text-align:right"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sub></span></span>e<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:0.8em;line-height:1.0em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">+</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sub></span></span></span> + <span style="white-space:nowrap;"><span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:0.8em;line-height:1.0em;font-size:80%;text-align:right"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sub></span></span>ν<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1.0em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">e</sub></span></span></span><sup id="cite_ref-konya74_14-1" class="reference"><a href="#cite_note-konya74-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup></dd></dl> <p>These reactions correspond to the decay of a neutron to a proton, or the decay of a proton to a neutron, within the nucleus, respectively. These reactions begin on one side or the other of the valley of stability, and the directions of the reactions are to move the initial nuclides down the valley walls towards a region of greater stability, that is, toward greater binding energy. </p> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Valley_of_Stability_Parabola_2.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Valley_of_Stability_Parabola_2.jpg/330px-Valley_of_Stability_Parabola_2.jpg" decoding="async" width="330" height="218" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Valley_of_Stability_Parabola_2.jpg/495px-Valley_of_Stability_Parabola_2.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Valley_of_Stability_Parabola_2.jpg/660px-Valley_of_Stability_Parabola_2.jpg 2x" data-file-width="766" data-file-height="506" /></a><figcaption>The negative of binding energy per nucleon for nuclides with atomic mass number 125 plotted as a function of atomic number. The profile of binding energy across the valley of stability is roughly a parabola. <a href="/wiki/Isotopes_of_tellurium" title="Isotopes of tellurium">Tellurium</a>-125 (<sub>52</sub>Te) is stable, while <a href="/wiki/Isotopes_of_antimony" title="Isotopes of antimony">antimony</a>-125 (<sub>51</sub>Sb) is unstable to β− decay.</figcaption></figure> <p>The figure at right shows the average binding energy per nucleon across the valley of stability for nuclides with mass number <i>A</i> = 125.<sup id="cite_ref-Krane_15-0" class="reference"><a href="#cite_note-Krane-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> At the bottom of this curve is <a href="/wiki/Isotopes_of_tellurium" title="Isotopes of tellurium">tellurium</a> (<sub>52</sub>Te), which is stable. Nuclides to the left of <sub>52</sub>Te are unstable with an excess of neutrons, while those on the right are unstable with an excess of protons. A nuclide on the left therefore undergoes β<sup>−</sup> decay, which converts a neutron to a proton, hence shifts the nuclide to the right and toward greater stability. A nuclide on the right similarly undergoes β<sup>+</sup> decay, which shifts the nuclide to the left and toward greater stability. </p><p>Heavy nuclides are susceptible to α decay, and these nuclear reactions have the generic form, </p> <dl><dd><span style="white-space:nowrap;"><span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1.0em;font-size:80%;text-align:right"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"><span class="texhtml mvar" style="font-style:italic;">A</span></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"><span class="texhtml mvar" style="font-style:italic;">Z</span></sub></span></span>X<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:0.8em;line-height:1.0em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sub></span></span></span> → <span style="white-space:nowrap;"><span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1.0em;font-size:80%;text-align:right"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"><span class="texhtml"><i>A</i>-4</span></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"><span class="texhtml"><i>Z</i>-2</span></sub></span></span>X′<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:0.8em;line-height:1.0em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sub></span></span></span> + <span style="white-space:nowrap;"><span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1.0em;font-size:80%;text-align:right"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">4</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sub></span></span>He<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:0.8em;line-height:1.0em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sub></span></span></span></dd></dl> <p>As in β decay, the decay product X′ has greater binding energy and it is closer to the middle of the valley of stability. The <a href="/wiki/Alpha_particle" title="Alpha particle">α particle</a> carries away two neutrons and two protons, leaving a lighter nuclide. Since heavy nuclides have many more neutrons than protons, α decay increases a nuclide's neutron-proton ratio. </p> <div class="mw-heading mw-heading2"><h2 id="Proton_and_neutron_drip_lines">Proton and neutron drip lines</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Valley_of_stability&action=edit&section=4" title="Edit section: Proton and neutron drip lines"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main articles: <a href="/wiki/Nuclear_drip_line" title="Nuclear drip line">Nuclear drip line</a>, <a href="/wiki/Proton_emission" title="Proton emission">proton emission</a>, and <a href="/wiki/Neutron_emission" title="Neutron emission">neutron emission</a></div> <p>The boundaries of the valley of stability, that is, the upper limits of the valley walls, are the neutron drip line on the neutron-rich side, and the proton drip line on the proton-rich side. The nucleon drip lines are at the extremes of the neutron-proton ratio. At neutron–proton ratios beyond the drip lines, no nuclei can exist. The location of the neutron drip line is not well known for most of the Segrè chart, whereas the proton and alpha drip lines have been measured for a wide range of elements. Drip lines are defined for protons, neutrons, and alpha particles, and these all play important roles in nuclear physics. </p><p>The difference in binding energy between neighboring nuclides increases as the sides of the valley of stability are ascended, and correspondingly the nuclide half-lives decrease, as indicated in the figure above. If one were to add nucleons one at a time to a given nuclide, the process will eventually lead to a newly formed nuclide that is so unstable that it promptly decays by emitting a proton (or neutron). Colloquially speaking, the nucleon has 'leaked' or 'dripped' out of the nucleus, hence giving rise to the term "drip line". </p><p>Proton emission is not seen in naturally occurring nuclides. Proton emitters can be produced via <a href="/wiki/Nuclear_reaction" title="Nuclear reaction">nuclear reactions</a>, usually utilizing <a href="/wiki/Linear_particle_accelerator" title="Linear particle accelerator">linear particle accelerators</a> (linac). Although prompt (i.e. not beta-delayed) proton emission was observed from an isomer in <a href="/wiki/Cobalt-53" class="mw-redirect" title="Cobalt-53">cobalt-53</a> as early as 1969, no other proton-emitting states were found until 1981, when the proton radioactive ground states of <a href="/wiki/Lutetium-151" class="mw-redirect" title="Lutetium-151">lutetium-151</a> and <a href="/wiki/Thulium-147" class="mw-redirect" title="Thulium-147">thulium-147</a> were observed at experiments at the <a href="/wiki/Gesellschaft_f%C3%BCr_Schwerionenforschung" class="mw-redirect" title="Gesellschaft für Schwerionenforschung">GSI</a> in West Germany.<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> Research in the field flourished after this breakthrough, and to date more than 25 nuclides have been found to exhibit proton emission. The study of proton emission has aided the understanding of nuclear deformation, masses and structure, and it is an example of <a href="/wiki/Quantum_tunneling" class="mw-redirect" title="Quantum tunneling">quantum tunneling</a>. </p><p>Two examples of nuclides that emit neutrons are <a href="/wiki/Beryllium-13" class="mw-redirect" title="Beryllium-13">beryllium-13</a> (mean life <span class="nowrap"><span data-sort-value="6979270000000000000♠"></span>2.7<span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>−21</sup> <a href="/wiki/Second" title="Second">s</a></span>) and <a href="/wiki/Helium-5" class="mw-redirect" title="Helium-5">helium-5</a> (<span class="nowrap"><span data-sort-value="6978700000000000000♠"></span>7<span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>−22</sup> s</span>). Since only a neutron is lost in this process, the atom does not gain or lose any protons, and so it does not become an atom of a different element. Instead, the atom will become a new <a href="/wiki/Isotope" title="Isotope">isotope</a> of the original element, such as <a href="/wiki/Beryllium-13" class="mw-redirect" title="Beryllium-13">beryllium-13</a> becoming <a href="/wiki/Beryllium-12" class="mw-redirect" title="Beryllium-12">beryllium-12</a> after emitting one of its neutrons.<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> </p><p>In <a href="/wiki/Nuclear_engineering" title="Nuclear engineering">nuclear engineering</a>, a <a href="/wiki/Prompt_neutron" title="Prompt neutron">prompt neutron</a> is a <a href="/wiki/Neutron" title="Neutron">neutron</a> immediately emitted by a <a href="/wiki/Nuclear_fission" title="Nuclear fission">nuclear fission</a> event. Prompt neutrons emerge from the fission of an unstable <a href="/wiki/Fissionable" class="mw-redirect" title="Fissionable">fissionable</a> or <a href="/wiki/Fissile" class="mw-redirect" title="Fissile">fissile</a> heavy nucleus almost instantaneously. <a href="/wiki/Delayed_neutron" title="Delayed neutron">Delayed neutron decay</a> can occur within the same context, emitted after <a href="/wiki/Beta_decay" title="Beta decay">beta decay</a> of one of the <a href="/wiki/Fission_product" class="mw-redirect" title="Fission product">fission products</a>. Delayed neutron decay can occur at times from a few milliseconds to a few minutes.<sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> The U.S. <a href="/wiki/Nuclear_Regulatory_Commission" title="Nuclear Regulatory Commission">Nuclear Regulatory Commission</a> defines a prompt neutron as a neutron emerging from fission within 10<sup>−14</sup> seconds.<sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Island_of_stability">Island of stability</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Valley_of_stability&action=edit&section=5" title="Edit section: Island of stability"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></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/Island_of_stability" title="Island of stability">Island of stability</a></div> <p>The island of stability is a region outside the valley of stability where it is predicted that a set of heavy <a href="/wiki/Isotopes" class="mw-redirect" title="Isotopes">isotopes</a> with near <a href="/wiki/Magic_number_(physics)" title="Magic number (physics)">magic numbers</a> of protons and neutrons will locally reverse the trend of decreasing stability in <a href="/wiki/Transuranium_element" title="Transuranium element">elements heavier than uranium</a>. The hypothesis for the island of stability is based upon the <a href="/wiki/Nuclear_shell_model" title="Nuclear shell model">nuclear shell model</a>, which implies that the <a href="/wiki/Atomic_nucleus" title="Atomic nucleus">atomic nucleus</a> is built up in "shells" in a manner similar to the structure of the much larger electron shells in atoms. In both cases, shells are just groups of quantum <a href="/wiki/Energy_level" title="Energy level">energy levels</a> that are relatively close to each other. Energy levels from quantum states in two different shells will be separated by a relatively large energy gap. So when the number of <a href="/wiki/Neutron" title="Neutron">neutrons</a> and <a href="/wiki/Proton" title="Proton">protons</a> completely fills the <a href="/wiki/Energy_level" title="Energy level">energy levels</a> of a given shell in the nucleus, the <a href="/wiki/Binding_energy" title="Binding energy">binding energy</a> per nucleon will reach a local maximum and thus that particular configuration will have a longer lifetime than nearby isotopes that do not possess filled shells.<sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> </p><p>A filled shell would have "<a href="/wiki/Magic_number_(physics)" title="Magic number (physics)">magic numbers</a>" of neutrons and protons. One possible magic number of neutrons for spherical nuclei is 184, and some possible matching proton numbers are 114, 120 and 126. These configurations imply that the most stable spherical isotopes would be <a href="/wiki/Flerovium" title="Flerovium">flerovium</a>-298, <a href="/wiki/Unbinilium" title="Unbinilium">unbinilium</a>-304 and <a href="/wiki/Unbihexium" title="Unbihexium">unbihexium</a>-310. Of particular note is <sup>298</sup>Fl, which would be "<a href="/wiki/Double_magic" class="mw-redirect" title="Double magic">doubly magic</a>" (both its <a href="/wiki/Proton_number" class="mw-redirect" title="Proton number">proton number</a> of 114 and <a href="/wiki/Neutron_number" title="Neutron number">neutron number</a> of 184 are thought to be magic). This doubly magic configuration is the most likely to have a very long half-life. The next lighter doubly magic spherical nucleus is <a href="/wiki/Lead" title="Lead">lead</a>-208, the heaviest known stable nucleus and most stable heavy metal. </p> <div class="mw-heading mw-heading2"><h2 id="Discussion">Discussion</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Valley_of_stability&action=edit&section=6" title="Edit section: Discussion"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The valley of stability can be helpful in interpreting and understanding properties of nuclear decay processes such as <a href="/wiki/Decay_chains" class="mw-redirect" title="Decay chains">decay chains</a> and <a href="/wiki/Nuclear_fission" title="Nuclear fission">nuclear fission</a>. </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Valley_of_Stability_U-238_Series.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/2d/Valley_of_Stability_U-238_Series.png/480px-Valley_of_Stability_U-238_Series.png" decoding="async" width="480" height="309" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/2d/Valley_of_Stability_U-238_Series.png/720px-Valley_of_Stability_U-238_Series.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/2d/Valley_of_Stability_U-238_Series.png/960px-Valley_of_Stability_U-238_Series.png 2x" data-file-width="3060" data-file-height="1972" /></a><figcaption>The uranium-238 series is a series of α (N and Z less 2) and β− decays (N less 1, Z plus 1) to nuclides that are successively deeper into the valley of stability. The series terminates at lead-206, a stable nuclide at the bottom of the valley of stability.</figcaption></figure> <p>Radioactive decay often proceeds via a sequence of steps known as a decay chain. For example, <a href="/wiki/Uranium-238" title="Uranium-238"><sup>238</sup>U</a> decays to <sup>234</sup>Th which decays to <sup>234m</sup>Pa and so on, eventually reaching <a href="/wiki/Lead-206" class="mw-redirect" title="Lead-206"><sup>206</sup>Pb</a>: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{array}{l}{}\\{\ce {^{238}_{92}U->[\alpha ][4.5\times 10^{9}\ {\ce {y}}]{^{234}_{90}Th}->[\beta ^{-}][24\ {\ce {d}}]{^{234\!m}_{91}Pa}}}{\ce {->[\beta ^{-}][1\ {\ce {min}}]}}{\ce {^{234}_{92}U->[\alpha ][2.4\times 10^{5}\ {\ce {y}}]{^{230}_{90}Th}->[\alpha ][7.7\times 10^{4}\ {\ce {y}}]}}\\{\ce {^{226}_{88}Ra->[\alpha ][1600\ y]{^{222}_{86}Rn}->[\alpha ][3.8\ {\ce {d}}]{^{218}_{84}Po}->[\alpha ][3\ {\ce {min}}]{^{214}_{82}Pb}->[\beta ^{-}][27\ {\ce {min}}]{^{214}_{83}Bi}->[\beta ^{-}][20\ {\ce {min}}]}}\\{\ce {^{214}_{84}Po->[\alpha ][164\ \mu {\ce {s}}]{^{210}_{82}Pb}->[\beta ^{-}][22\ {\ce {y}}]{^{210}_{83}Bi}->[\beta ^{-}][5\ {\ce {d}}]{^{210}_{84}Po}->[\alpha ][138\ {\ce {d}}]{^{206}_{82}Pb}}}\\{}\end{array}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="left" rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mmultiscripts> <mtext>U</mtext> <none /> <none /> <mprescripts /> <mn>92</mn> <mn>238</mn> </mmultiscripts> <mrow class="MJX-TeXAtom-REL"> <munderover> <mo>→</mo> <mpadded width="+0.611em" lspace="0.278em" voffset="-.24em"> <mn>4.5</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>9</mn> </mrow> </msup> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mtext>y</mtext> </mrow> </mpadded> <mpadded width="+0.611em" lspace="0.278em" voffset=".15em"> <mi>α</mi> </mpadded> </munderover> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mmultiscripts> <mtext>Th</mtext> <none /> <none /> <mprescripts /> <mn>90</mn> <mn>234</mn> </mmultiscripts> </mrow> <mrow class="MJX-TeXAtom-REL"> <munderover> <mo>→</mo> <mpadded width="+0.611em" lspace="0.278em" voffset="-.24em"> <mn>24</mn> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mtext>d</mtext> </mrow> </mpadded> <mpadded width="+0.611em" lspace="0.278em" voffset=".15em"> <msup> <mi>β</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> </mrow> </msup> </mpadded> </munderover> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mmultiscripts> <mtext>Pa</mtext> <none /> <none /> <mprescripts /> <mn>91</mn> <mrow> <mn>234</mn> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> <mtext>m</mtext> </mrow> </mmultiscripts> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-REL"> <munderover> <mo>→</mo> <mpadded width="+0.611em" lspace="0.278em" voffset="-.24em"> <mn>1</mn> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mtext>min</mtext> </mrow> </mpadded> <mpadded width="+0.611em" lspace="0.278em" voffset=".15em"> <msup> <mi>β</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> </mrow> </msup> </mpadded> </munderover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mmultiscripts> <mtext>U</mtext> <none /> <none /> <mprescripts /> <mn>92</mn> <mn>234</mn> </mmultiscripts> <mrow class="MJX-TeXAtom-REL"> <munderover> <mo>→</mo> <mpadded width="+0.611em" lspace="0.278em" voffset="-.24em"> <mn>2.4</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </msup> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mtext>y</mtext> </mrow> </mpadded> <mpadded width="+0.611em" lspace="0.278em" voffset=".15em"> <mi>α</mi> </mpadded> </munderover> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mmultiscripts> <mtext>Th</mtext> <none /> <none /> <mprescripts /> <mn>90</mn> <mn>230</mn> </mmultiscripts> </mrow> <mrow class="MJX-TeXAtom-REL"> <munderover> <mo>→</mo> <mpadded width="+0.611em" lspace="0.278em" voffset="-.24em"> <mn>7.7</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mtext>y</mtext> </mrow> </mpadded> <mpadded width="+0.611em" lspace="0.278em" voffset=".15em"> <mi>α</mi> </mpadded> </munderover> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mmultiscripts> <mtext>Ra</mtext> <none /> <none /> <mprescripts /> <mn>88</mn> <mn>226</mn> </mmultiscripts> <mrow class="MJX-TeXAtom-REL"> <munderover> <mo>→</mo> <mpadded width="+0.611em" lspace="0.278em" voffset="-.24em"> <mn>1600</mn> <mtext> </mtext> <mi>y</mi> </mpadded> <mpadded width="+0.611em" lspace="0.278em" voffset=".15em"> <mi>α</mi> </mpadded> </munderover> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mmultiscripts> <mtext>Rn</mtext> <none /> <none /> <mprescripts /> <mn>86</mn> <mn>222</mn> </mmultiscripts> </mrow> <mrow class="MJX-TeXAtom-REL"> <munderover> <mo>→</mo> <mpadded width="+0.611em" lspace="0.278em" voffset="-.24em"> <mn>3.8</mn> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mtext>d</mtext> </mrow> </mpadded> <mpadded width="+0.611em" lspace="0.278em" voffset=".15em"> <mi>α</mi> </mpadded> </munderover> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mmultiscripts> <mtext>Po</mtext> <none /> <none /> <mprescripts /> <mn>84</mn> <mn>218</mn> </mmultiscripts> </mrow> <mrow class="MJX-TeXAtom-REL"> <munderover> <mo>→</mo> <mpadded width="+0.611em" lspace="0.278em" voffset="-.24em"> <mn>3</mn> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mtext>min</mtext> </mrow> </mpadded> <mpadded width="+0.611em" lspace="0.278em" voffset=".15em"> <mi>α</mi> </mpadded> </munderover> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mmultiscripts> <mtext>Pb</mtext> <none /> <none /> <mprescripts /> <mn>82</mn> <mn>214</mn> </mmultiscripts> </mrow> <mrow class="MJX-TeXAtom-REL"> <munderover> <mo>→</mo> <mpadded width="+0.611em" lspace="0.278em" voffset="-.24em"> <mn>27</mn> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mtext>min</mtext> </mrow> </mpadded> <mpadded width="+0.611em" lspace="0.278em" voffset=".15em"> <msup> <mi>β</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> </mrow> </msup> </mpadded> </munderover> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mmultiscripts> <mtext>Bi</mtext> <none /> <none /> <mprescripts /> <mn>83</mn> <mn>214</mn> </mmultiscripts> </mrow> <mrow class="MJX-TeXAtom-REL"> <munderover> <mo>→</mo> <mpadded width="+0.611em" lspace="0.278em" voffset="-.24em"> <mn>20</mn> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mtext>min</mtext> </mrow> </mpadded> <mpadded width="+0.611em" lspace="0.278em" voffset=".15em"> <msup> <mi>β</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> </mrow> </msup> </mpadded> </munderover> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mmultiscripts> <mtext>Po</mtext> <none /> <none /> <mprescripts /> <mn>84</mn> <mn>214</mn> </mmultiscripts> <mrow class="MJX-TeXAtom-REL"> <munderover> <mo>→</mo> <mpadded width="+0.611em" lspace="0.278em" voffset="-.24em"> <mn>164</mn> <mtext> </mtext> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>s</mtext> </mrow> </mpadded> <mpadded width="+0.611em" lspace="0.278em" voffset=".15em"> <mi>α</mi> </mpadded> </munderover> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mmultiscripts> <mtext>Pb</mtext> <none /> <none /> <mprescripts /> <mn>82</mn> <mn>210</mn> </mmultiscripts> </mrow> <mrow class="MJX-TeXAtom-REL"> <munderover> <mo>→</mo> <mpadded width="+0.611em" lspace="0.278em" voffset="-.24em"> <mn>22</mn> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mtext>y</mtext> </mrow> </mpadded> <mpadded width="+0.611em" lspace="0.278em" voffset=".15em"> <msup> <mi>β</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> </mrow> </msup> </mpadded> </munderover> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mmultiscripts> <mtext>Bi</mtext> <none /> <none /> <mprescripts /> <mn>83</mn> <mn>210</mn> </mmultiscripts> </mrow> <mrow class="MJX-TeXAtom-REL"> <munderover> <mo>→</mo> <mpadded width="+0.611em" lspace="0.278em" voffset="-.24em"> <mn>5</mn> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mtext>d</mtext> </mrow> </mpadded> <mpadded width="+0.611em" lspace="0.278em" voffset=".15em"> <msup> <mi>β</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> </mrow> </msup> </mpadded> </munderover> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mmultiscripts> <mtext>Po</mtext> <none /> <none /> <mprescripts /> <mn>84</mn> <mn>210</mn> </mmultiscripts> </mrow> <mrow class="MJX-TeXAtom-REL"> <munderover> <mo>→</mo> <mpadded width="+0.611em" lspace="0.278em" voffset="-.24em"> <mn>138</mn> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mtext>d</mtext> </mrow> </mpadded> <mpadded width="+0.611em" lspace="0.278em" voffset=".15em"> <mi>α</mi> </mpadded> </munderover> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mmultiscripts> <mtext>Pb</mtext> <none /> <none /> <mprescripts /> <mn>82</mn> <mn>206</mn> </mmultiscripts> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> </mrow> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{array}{l}{}\\{\ce {^{238}_{92}U->[\alpha ][4.5\times 10^{9}\ {\ce {y}}]{^{234}_{90}Th}->[\beta ^{-}][24\ {\ce {d}}]{^{234\!m}_{91}Pa}}}{\ce {->[\beta ^{-}][1\ {\ce {min}}]}}{\ce {^{234}_{92}U->[\alpha ][2.4\times 10^{5}\ {\ce {y}}]{^{230}_{90}Th}->[\alpha ][7.7\times 10^{4}\ {\ce {y}}]}}\\{\ce {^{226}_{88}Ra->[\alpha ][1600\ y]{^{222}_{86}Rn}->[\alpha ][3.8\ {\ce {d}}]{^{218}_{84}Po}->[\alpha ][3\ {\ce {min}}]{^{214}_{82}Pb}->[\beta ^{-}][27\ {\ce {min}}]{^{214}_{83}Bi}->[\beta ^{-}][20\ {\ce {min}}]}}\\{\ce {^{214}_{84}Po->[\alpha ][164\ \mu {\ce {s}}]{^{210}_{82}Pb}->[\beta ^{-}][22\ {\ce {y}}]{^{210}_{83}Bi}->[\beta ^{-}][5\ {\ce {d}}]{^{210}_{84}Po}->[\alpha ][138\ {\ce {d}}]{^{206}_{82}Pb}}}\\{}\end{array}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ba2b0c735b768ae8bdff71e9622addbc3a6ab68f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -12.338ex; width:67.821ex; height:25.843ex;" alt="{\displaystyle {\begin{array}{l}{}\\{\ce {^{238}_{92}U->[\alpha ][4.5\times 10^{9}\ {\ce {y}}]{^{234}_{90}Th}->[\beta ^{-}][24\ {\ce {d}}]{^{234\!m}_{91}Pa}}}{\ce {->[\beta ^{-}][1\ {\ce {min}}]}}{\ce {^{234}_{92}U->[\alpha ][2.4\times 10^{5}\ {\ce {y}}]{^{230}_{90}Th}->[\alpha ][7.7\times 10^{4}\ {\ce {y}}]}}\\{\ce {^{226}_{88}Ra->[\alpha ][1600\ y]{^{222}_{86}Rn}->[\alpha ][3.8\ {\ce {d}}]{^{218}_{84}Po}->[\alpha ][3\ {\ce {min}}]{^{214}_{82}Pb}->[\beta ^{-}][27\ {\ce {min}}]{^{214}_{83}Bi}->[\beta ^{-}][20\ {\ce {min}}]}}\\{\ce {^{214}_{84}Po->[\alpha ][164\ \mu {\ce {s}}]{^{210}_{82}Pb}->[\beta ^{-}][22\ {\ce {y}}]{^{210}_{83}Bi}->[\beta ^{-}][5\ {\ce {d}}]{^{210}_{84}Po}->[\alpha ][138\ {\ce {d}}]{^{206}_{82}Pb}}}\\{}\end{array}}}"></span></dd></dl> <p>With each step of this sequence of reactions, energy is released and the <a href="/wiki/Decay_product" title="Decay product">decay products</a> move further down the valley of stability towards the line of beta stability. <sup>206</sup>Pb is stable and lies on the line of beta stability. </p> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Nuclear_fission.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/15/Nuclear_fission.svg/180px-Nuclear_fission.svg.png" decoding="async" width="180" height="281" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/15/Nuclear_fission.svg/270px-Nuclear_fission.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/15/Nuclear_fission.svg/360px-Nuclear_fission.svg.png 2x" data-file-width="309" data-file-height="482" /></a><figcaption>Nuclear fission seen with a uranium-235 nucleus</figcaption></figure> <p>The <a href="/wiki/Nuclear_fission" title="Nuclear fission">fission</a> processes that occur within <a href="/wiki/Nuclear_reactors" class="mw-redirect" title="Nuclear reactors">nuclear reactors</a> are accompanied by the release of neutrons that sustain the <a href="/wiki/Chain_reaction" title="Chain reaction">chain reaction</a>. Fission occurs when a heavy nuclide such as <a href="/wiki/Uranium-235" title="Uranium-235">uranium-235</a> absorbs a neutron and breaks into nuclides of lighter elements such as <a href="/wiki/Barium" title="Barium">barium</a> or <a href="/wiki/Krypton" title="Krypton">krypton</a>, usually with the release of additional neutrons. Like all nuclides with a high atomic number, these uranium nuclei require many neutrons to bolster their stability, so they have a large neutron-proton ratio (<i>N</i>/<i>Z</i>). The nuclei resulting from a fission (<a href="/wiki/Nuclear_fission_product" title="Nuclear fission product">fission products</a>) inherit a similar <i>N</i>/<i>Z</i>, but have atomic numbers that are approximately half that of uranium.<sup id="cite_ref-Mackintosh_1-6" class="reference"><a href="#cite_note-Mackintosh-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> Isotopes with the atomic number of the fission products and an <i>N</i>/<i>Z</i> near that of uranium or other fissionable nuclei have too many neutrons to be stable; this neutron excess is why multiple free neutrons but no free protons are usually emitted in the fission process, and it is also why many fission product nuclei undergo a long chain of β<sup>−</sup> decays, each of which converts a nucleus <i>N</i>/<i>Z</i> to (<i>N</i> − 1)/(<i>Z</i> + 1), where <i>N</i> and <i>Z</i> are, respectively, the numbers of neutrons and protons contained in the nucleus. </p><p>When fission reactions are sustained at a given rate, such as in a liquid-cooled or solid fuel nuclear reactor, the nuclear fuel in the system produces many <a href="/wiki/Neutrino" title="Neutrino">antineutrinos</a> for each fission that has occurred. These antineutrinos come from the decay of fission products that, as their nuclei progress down a β<sup>−</sup> decay chain toward the valley of stability, emit an antineutrino along with each β<sup>−</sup> particle. In 1956, <a href="/wiki/Frederick_Reines" title="Frederick Reines">Reines</a> and <a href="/wiki/Clyde_Cowan" title="Clyde Cowan">Cowan</a> exploited the (anticipated) intense flux of antineutrinos from a nuclear reactor in the design of <a href="/wiki/Cowan%E2%80%93Reines_neutrino_experiment" title="Cowan–Reines neutrino experiment">an experiment</a> to detect and confirm the existence of these elusive particles.<sup id="cite_ref-Nobel_lecture_21-0" class="reference"><a href="#cite_note-Nobel_lecture-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Valley_of_stability&action=edit&section=7" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1184024115">.mw-parser-output .div-col{margin-top:0.3em;column-width:30em}.mw-parser-output .div-col-small{font-size:90%}.mw-parser-output .div-col-rules{column-rule:1px solid #aaa}.mw-parser-output .div-col dl,.mw-parser-output .div-col ol,.mw-parser-output .div-col ul{margin-top:0}.mw-parser-output .div-col li,.mw-parser-output .div-col dd{page-break-inside:avoid;break-inside:avoid-column}</style><div class="div-col"> <ul><li><a href="/wiki/Alpha_decay" title="Alpha decay">Alpha decay</a></li> <li><a href="/wiki/Gamma_decay" class="mw-redirect" title="Gamma decay">Gamma 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> <li><a href="/wiki/Cluster_decay" title="Cluster decay">Cluster decay</a></li> <li><a href="/wiki/Stable_nuclide" title="Stable nuclide">Stable nuclide</a></li> <li><a href="/wiki/Nuclear_shell_model" title="Nuclear shell model">Nuclear shell model</a></li> <li><a href="/wiki/Nuclear_drip_line" title="Nuclear drip line">Nuclear drip line</a></li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Valley_of_stability&action=edit&section=8" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></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-Mackintosh-1"><span class="mw-cite-backlink">^ <a href="#cite_ref-Mackintosh_1-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Mackintosh_1-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-Mackintosh_1-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-Mackintosh_1-3"><sup><i><b>d</b></i></sup></a> <a href="#cite_ref-Mackintosh_1-4"><sup><i><b>e</b></i></sup></a> <a href="#cite_ref-Mackintosh_1-5"><sup><i><b>f</b></i></sup></a> <a href="#cite_ref-Mackintosh_1-6"><sup><i><b>g</b></i></sup></a></span> <span class="reference-text"><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="CITEREFMackintoshAi-KhaliliJonsonPena2001" class="citation book cs1">Mackintosh, R.; Ai-Khalili, J.; Jonson, B.; Pena, T. (2001). <a rel="nofollow" class="external text" href="https://archive.org/details/nucleustripintoh0000unse"><i>Nucleus: A trip into the heart of matter</i></a>. Baltimore, Maryland: The Johns Hopkins University Press. pp. Chapter 6. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-801_8-6860-2" title="Special:BookSources/0-801 8-6860-2"><bdi>0-801 8-6860-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Nucleus%3A+A+trip+into+the+heart+of+matter&rft.place=Baltimore%2C+Maryland&rft.pages=Chapter+6&rft.pub=The+Johns+Hopkins+University+Press&rft.date=2001&rft.isbn=0-8018-6860-2&rft.aulast=Mackintosh&rft.aufirst=R.&rft.au=Ai-Khalili%2C+J.&rft.au=Jonson%2C+B.&rft.au=Pena%2C+T.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fnucleustripintoh0000unse&rfr_id=info%3Asid%2Fen.wikipedia.org%3AValley+of+stability" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation cs2"><a rel="nofollow" class="external text" href="https://www.youtube.com/watch?v=UTOp_2ZVZmM"><i>The valley of stability</i></a>, 20 June 2013<span class="reference-accessdate">, retrieved <span class="nowrap">2023-12-01</span></span></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+valley+of+stability&rft.date=2013-06-20&rft_id=https%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3DUTOp_2ZVZmM&rfr_id=info%3Asid%2Fen.wikipedia.org%3AValley+of+stability" class="Z3988"></span></span> </li> <li id="cite_note-Byrne-3"><span class="mw-cite-backlink">^ <a href="#cite_ref-Byrne_3-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Byrne_3-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-Byrne_3-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-Byrne_3-3"><sup><i><b>d</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFByrne2011" class="citation book cs1">Byrne, J. (2011). <i>Neutrons, Nuclei and Matter: An Exploration of the Physics of Slow Neutrons</i>. 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Retrieved <span class="nowrap">February 20,</span> 2015</span>. <q>Nobel Prize lecture</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=The+Neutrino%3A+From+Poltergeist+to+Particle&rft.pub=Nobel+Foundation&rft.date=1995-12-08&rft.aulast=Reines&rft.aufirst=Frederick&rft_id=http%3A%2F%2Fnobelprize.org%2Fnobel_prizes%2Fphysics%2Flaureates%2F1995%2Freines-lecture.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AValley+of+stability" class="Z3988"></span></span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Valley_of_stability&action=edit&section=9" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><span class="mw-default-size" typeof="mw:File"><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></span> <a rel="nofollow" class="external text" href="https://www-nds.iaea.org/livechart">The Live Chart of Nuclides - IAEA</a> with filter on decay type</li> <li><a rel="nofollow" class="external text" href="https://www.youtube.com/watch?v=UTOp_2ZVZmM&t=192">The Valley of Stability (video)</a> – a virtual "flight" through 3D representation of the nuclide chart, by <a href="/wiki/French_Alternative_Energies_and_Atomic_Energy_Commission" title="French Alternative Energies and Atomic Energy Commission">CEA</a> (France)</li> <li><a rel="nofollow" class="external text" href="http://www.nupecc.org/pans/Data/CHAPT_6.PDF">The nuclear landscape: The variety and abundance of nuclei</a> – Chapter 6 of the book <i>Nucleus: A trip into the heart of matter</i> by Mackintosh, Ai-Khalili, Jonson, and Pena describes the valley of stability and its implications (Baltimore, Maryland:The Johns Hopkins University Press), 2001. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-801%2B8-6860-2" title="Special:BookSources/0-801+8-6860-2">0-801 8-6860-2</a></li></ul>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://en.wikipedia.org/w/index.php?title=Valley_of_stability&oldid=1250271884">https://en.wikipedia.org/w/index.php?title=Valley_of_stability&oldid=1250271884</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Help:Category" title="Help:Category">Categories</a>: <ul><li><a href="/wiki/Category:Nuclear_physics" title="Category:Nuclear physics">Nuclear physics</a></li><li><a href="/wiki/Category:Radioactivity" title="Category:Radioactivity">Radioactivity</a></li><li><a href="/wiki/Category:Isotopes" title="Category:Isotopes">Isotopes</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Hidden categories: <ul><li><a href="/wiki/Category:Articles_with_short_description" title="Category:Articles with short description">Articles with short description</a></li><li><a href="/wiki/Category:Short_description_is_different_from_Wikidata" title="Category:Short description is different from Wikidata">Short description is different from Wikidata</a></li><li><a href="/wiki/Category:All_articles_with_unsourced_statements" title="Category:All articles with unsourced statements">All articles with unsourced statements</a></li><li><a href="/wiki/Category:Articles_with_unsourced_statements_from_October_2019" title="Category:Articles with unsourced statements from October 2019">Articles with unsourced statements from October 2019</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> This page was last edited on 9 October 2024, at 12:40<span class="anonymous-show"> (UTC)</span>.</li> <li id="footer-info-copyright">Text is available under the <a href="/wiki/Wikipedia:Text_of_the_Creative_Commons_Attribution-ShareAlike_4.0_International_License" title="Wikipedia:Text of the Creative Commons Attribution-ShareAlike 4.0 International License">Creative Commons Attribution-ShareAlike 4.0 License</a>; additional terms may apply. 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