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Radioactive decay

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</style><div role="note" class="hatnote navigation-not-searchable">"Radioactive" and "Radioactivity" redirect here. For other uses, see <a href="Radioactive_(disambiguation)" class="mw-disambig" title="Radioactive (disambiguation)">Radioactive (disambiguation)</a> and <a href="Radioactivity_(disambiguation)" class="mw-disambig" title="Radioactivity (disambiguation)">Radioactivity (disambiguation)</a>.</div>

<div role="note" class="hatnote navigation-not-searchable">For particle decay in a more general context, see <a href="Particle_decay" title="Particle decay">Particle decay</a>. For more information on hazards of various kinds of radiation from decay, see <a href="Ionizing_radiation" title="Ionizing radiation">Ionizing radiation</a>.</div>

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</style><table class="sidebar sidebar-collapse nomobile nowraplinks"><tbody><tr><th class="sidebar-title"><a href="Nuclear_physics" title="Nuclear physics">Nuclear physics</a></th></tr><tr><td class="sidebar-image"></td></tr><tr><td class="sidebar-content hlist">

<ul><li><a href="Atomic_nucleus" title="Atomic nucleus">Nucleus</a></li>

<li><a href="Nucleon" title="Nucleon">Nucleons</a>

<li><a href="Nuclear_matter" title="Nuclear matter">Nuclear matter</a></li>

<li><a href="Nuclear_force" title="Nuclear force">Nuclear force</a></li>

<li><a href="Nuclear_structure" title="Nuclear structure">Nuclear structure</a></li>

<li><a href="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="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="Semi-empirical_mass_formula" title="Semi-empirical mass formula">Liquid drop</a></li>

<li><a href="Nuclear_shell_model" title="Nuclear shell model">Nuclear shell model</a></li>

<li><a href="Interacting_boson_model" title="Interacting boson model">Interacting boson model</a></li>

<li><a href="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="Nuclide" title="Nuclide">Nuclides</a>' classification</div><div class="sidebar-list-content mw-collapsible-content">

<ul><li><a href="Isotope" title="Isotope">Isotopes</a> – equal <a href="Atomic_number" title="Atomic number">Z</a> </li></ul>

<ul><li><a href="Isobar_(nuclide)" title="Isobar (nuclide)">Isobars</a> – equal <a href="Mass_number" title="Mass number">A</a></li></ul>

<ul><li><a href="Isotone" title="Isotone">Isotones</a> – equal <a href="Neutron_number" title="Neutron number">N</a></li></ul>

<ul><li><a href="Isodiapher" class="mw-redirect" title="Isodiapher">Isodiaphers</a> – equal <a href="Neutron_excess" class="mw-redirect" title="Neutron excess">N − Z</a></li></ul>

<ul><li><a href="Nuclear_isomer" title="Nuclear isomer">Isomers</a> – equal all the above</li></ul>

<ul><li><a href="Mirror_nuclei" title="Mirror nuclei">Mirror nuclei</a> – Z ↔ N</li></ul>

<ul><li><a href="Stable_isotope" class="mw-redirect" title="Stable isotope">Stable</a></li>

<li><a href="Magic_number_(physics)" title="Magic number (physics)">Magic</a></li>

<ul><li><a href="Borromean_nucleus" title="Borromean nucleus">Borromean</a></li></ul></li></ul></div></div></td>

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<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="Nuclear_binding_energy" title="Nuclear binding energy">Binding energy</a></li>

<li><a href="Proton%E2%80%93neutron_ratio" class="mw-redirect" title="Proton–neutron ratio">p–n ratio</a></li>

<li><a href="Island_of_stability" title="Island of stability">Island of stability</a></li>

<li><a href="Valley_of_stability" title="Valley of stability">Valley of stability</a></li>

<li><a href="Stable_nuclide" title="Stable nuclide">Stable nuclide</a></li></ul></div></div></td>

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<ul><li><a href="Alpha_decay" title="Alpha decay">Alpha α</a></li>

<li><a href="Electron_capture" title="Electron capture">K/L capture</a></li>

<li><a href="Isomeric_transition" class="mw-redirect" title="Isomeric transition">Isomeric</a>

<ul><li><a href="Gamma_ray" title="Gamma ray">Gamma γ</a></li>

<li><a href="Internal_conversion" title="Internal conversion">Internal conversion</a></li></ul></li>

<li><a href="Spontaneous_fission" title="Spontaneous fission">Spontaneous fission</a></li>

<li><a href="Cluster_decay" title="Cluster decay">Cluster decay</a></li>

<li><a href="Neutron_emission" title="Neutron emission">Neutron emission</a></li>

<li><a href="Proton_emission" title="Proton emission">Proton emission</a></li></ul>

<ul><li><a href="Decay_energy" title="Decay energy">Decay energy</a></li>

<li><a href="Decay_chain" title="Decay chain">Decay chain</a></li>

<li><a href="Decay_product" title="Decay product">Decay product</a></li>

<li><a href="Radiogenic_nuclide" title="Radiogenic nuclide">Radiogenic nuclide</a></li></ul></div></div></td>

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<div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)"><a href="Nuclear_fission" title="Nuclear fission">Nuclear fission</a></div><div class="sidebar-list-content mw-collapsible-content">

<ul><li><a href="Spontaneous_fission" title="Spontaneous fission">Spontaneous</a></li>

<li><a href="Nuclear_fission_product" title="Nuclear fission product">Products</a>

<ul><li><a href="Nucleon_pair_breaking_in_fission" title="Nucleon pair breaking in fission">pair breaking</a></li></ul></li>

<li><a href="Photofission" title="Photofission">Photofission</a></li></ul></div></div></td>

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<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="Electron_capture" title="Electron capture">electron</a>

<li><a href="Neutron_capture" title="Neutron capture">neutron</a>

<li><a href="Proton_capture" title="Proton capture">proton</a>

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<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="Spallation" title="Spallation">Spallation</a>

<ul><li><a href="Cosmic_ray_spallation" title="Cosmic ray spallation">by cosmic ray</a></li></ul></li>

<li><a href="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="Nucleosynthesis" title="Nucleosynthesis">Nucleosynthesis</a> and <a href="Nuclear_astrophysics" title="Nuclear astrophysics">nuclear astrophysics</a></div><div class="sidebar-list-content mw-collapsible-content">

<ul><li><a href="Nuclear_fusion" title="Nuclear fusion">Nuclear fusion</a></li></ul>

<ul><li>Processes:

<ul><li><a href="Stellar_nucleosynthesis" title="Stellar nucleosynthesis">Stellar</a></li>

<li><a href="Supernova_nucleosynthesis" title="Supernova nucleosynthesis">Supernova</a></li></ul></li></ul>

<ul><li>Nuclides:

<ul><li><a href="Primordial_nuclide" title="Primordial nuclide">Primordial</a></li>

<li><a href="Cosmogenic_nuclide" title="Cosmogenic nuclide">Cosmogenic</a></li>

<li><a href="Synthetic_element" title="Synthetic element">Artificial</a></li></ul></li></ul></div></div></td>

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<div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)"><a href="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="Quark%E2%80%93gluon_plasma" title="Quark–gluon plasma">Quark–gluon plasma</a></li>

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<div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)">Scientists</div><div class="sidebar-list-content mw-collapsible-content">

<ul><li><a href="Luis_Walter_Alvarez" title="Luis Walter Alvarez">Alvarez</a></li>

<li><a href="Henri_Becquerel" title="Henri Becquerel">Becquerel</a></li>

<li><a href="Hans_Bethe" title="Hans Bethe">Bethe</a></li>

<li><a href="James_Chadwick" title="James Chadwick">Chadwick</a></li>

<li><a href="John_Cockcroft" title="John Cockcroft">Cockcroft</a></li>

<li><a href="Ir%C3%A8ne_Joliot-Curie" title="Irène Joliot-Curie">Ir. Curie</a></li>

<li><a href="Fr%C3%A9d%C3%A9ric_Joliot-Curie" title="Frédéric Joliot-Curie">Fr. Curie</a></li>

<li><a href="Pierre_Curie" title="Pierre Curie">Pi. Curie</a></li>

<li><a href="Marie_Curie" title="Marie Curie">Skłodowska-Curie</a></li>

<li><a href="Clinton_Davisson" title="Clinton Davisson">Davisson</a></li>

<li><a href="Enrico_Fermi" title="Enrico Fermi">Fermi</a></li>

<li><a href="J._Hans_D._Jensen" title="J. Hans D. Jensen">Jensen</a></li>

<li><a href="Ernest_Lawrence" title="Ernest Lawrence">Lawrence</a></li>

<li><a href="Maria_Goeppert-Mayer" class="mw-redirect" title="Maria Goeppert-Mayer">Mayer</a></li>

<li><a href="Lise_Meitner" title="Lise Meitner">Meitner</a></li>

<li><a href="Mark_Oliphant" title="Mark Oliphant">Oliphant</a></li>

<li><a href="J._Robert_Oppenheimer" title="J. Robert Oppenheimer">Oppenheimer</a></li>

<li><a href="Alexandru_Proca" title="Alexandru Proca">Proca</a></li>

<li><a href="Edward_Mills_Purcell" title="Edward Mills Purcell">Purcell</a></li>

<li><a href="Ernest_Rutherford" title="Ernest Rutherford">Rutherford</a></li>

<li><a href="Frederick_Soddy" title="Frederick Soddy">Soddy</a></li>

<li><a href="Fritz_Strassmann" title="Fritz Strassmann">Strassmann</a></li>

<li><a href="W%C5%82adys%C5%82aw_%C5%9Awi%C4%85tecki_(physicist)" title="Władysław Świątecki (physicist)">Świątecki</a></li>

<li><a href="Le%C3%B3_Szil%C3%A1rd" class="mw-redirect" title="Leó Szilárd">Szilárd</a></li>

<li><a href="Edward_Teller" title="Edward Teller">Teller</a></li>

<li><a href="J._J._Thomson" title="J. J. Thomson">Thomson</a></li>

<li><a href="Ernest_Walton" title="Ernest Walton">Walton</a></li>

<li><a href="Eugene_Wigner" title="Eugene Wigner">Wigner</a></li></ul></div></div></td>

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</style></td></tr></tbody></table>Radioactive decay (also known as nuclear decay, radioactivity, radioactive disintegration, or nuclear disintegration) is the process by which an unstable <a href="Atomic_nucleus" title="Atomic nucleus">atomic nucleus</a> loses energy by <a href="Radiation" title="Radiation">radiation</a>. A material containing unstable nuclei is considered radioactive. Three of the most common types of decay are <a href="Alpha_decay" title="Alpha decay">alpha</a>, <a href="Beta_decay" title="Beta decay">beta</a>, and <a href="Gamma_ray" title="Gamma ray">gamma decay</a>. The <a href="Weak_force" class="mw-redirect" title="Weak force">weak force</a> is the <a href="Fundamental_interactions" class="mw-redirect" title="Fundamental interactions">mechanism</a> that is responsible for beta decay, while the other two are governed by the <a href="Electromagnetic_force" class="mw-redirect" title="Electromagnetic force">electromagnetic</a> and <a href="Nuclear_force" title="Nuclear force">nuclear forces</a>.<a href="#cite_note-edp-1">[1]</a>

Radioactive decay is a <a href="Randomness" title="Randomness">random</a> process at the level of single atoms. According to <a href="Quantum_mechanics" title="Quantum mechanics">quantum theory</a>, it is impossible to predict when a particular atom will decay, regardless of how long the atom has existed.<a href="#cite_note-IntroductionToHealthPhysics-2">[2]</a><a href="#cite_note-RadiationOncologyPrimer-3">[3]</a><a href="#cite_note-4">[4]</a> However, for a significant number of identical atoms, the overall decay rate can be expressed as a <a href="Decay_constant" class="mw-redirect" title="Decay constant">decay constant</a> or as a <a href="Half-life" title="Half-life">half-life</a>. The half-lives of radioactive atoms have a huge range: from nearly instantaneous to far longer than the <a href="Age_of_the_universe" title="Age of the universe">age of the universe</a>.

The decaying nucleus is called the parent <a href="Radionuclide" title="Radionuclide">radionuclide</a> (or parent <a href="Isotope#Isotope_vs._nuclide" title="Isotope">radioisotope</a>), and the process produces at least one <a href="Decay_product" title="Decay product">daughter nuclide</a>. Except for gamma decay or <a href="Internal_conversion" title="Internal conversion">internal conversion</a> from a nuclear <a href="Excited_state" title="Excited state">excited state</a>, the decay is a <a href="Nuclear_transmutation" title="Nuclear transmutation">nuclear transmutation</a> resulting in a daughter containing a different number of <a href="Proton" title="Proton">protons</a> or <a href="Neutron" title="Neutron">neutrons</a> (or both). When the number of protons changes, an atom of a different <a href="Chemical_element" title="Chemical element">chemical element</a> is created.

There are 28 naturally occurring chemical elements on Earth that are radioactive, consisting of 35 <a href="Radionuclide" title="Radionuclide">radionuclides</a> (seven elements have two different radionuclides each) that date before the time of formation of the <a href="Solar_System" title="Solar System">Solar System</a>. These 35 are known as <a href="Primordial_radionuclide" class="mw-redirect" title="Primordial radionuclide">primordial radionuclides</a>. Well-known examples are <a href="Uranium" title="Uranium">uranium</a> and <a href="Thorium" title="Thorium">thorium</a>, but also included are naturally occurring long-lived radioisotopes, such as <a href="Potassium-40" title="Potassium-40">potassium-40</a>. Each of the heavy <a href="Primordial_nuclide" title="Primordial nuclide">primordial radionuclides</a> participates in one of the four <a href="Decay_chain" title="Decay chain">decay chains</a>.

<div class="mw-heading mw-heading2"><h2 id="History_of_discovery">History of discovery</h2></div>

<a href="Henri_Poincar%C3%A9" title="Henri Poincaré">Henri Poincaré</a> laid the seeds for the discovery of radioactivity through his interest in and studies of <a href="X-ray" title="X-ray">X-rays</a>, which significantly influenced physicist <a href="Henri_Becquerel" title="Henri Becquerel">Henri Becquerel</a>.<a href="#cite_note-5">[5]</a> Radioactivity was discovered in 1896 by Becquerel and independently by <a href="Marie_Curie" title="Marie Curie">Marie Curie</a>, while working with <a href="Phosphorescence" title="Phosphorescence">phosphorescent</a> materials.<a href="#cite_note-6">[6]</a><a href="#cite_note-7">[7]</a><a href="#cite_note-8">[8]</a><a href="#cite_note-9">[9]</a><a href="#cite_note-10">[10]</a> These materials glow in the dark after exposure to light, and Becquerel suspected that the glow produced in <a href="Cathode-ray_tube" title="Cathode-ray tube">cathode-ray tubes</a> by X-rays might be associated with phosphorescence. He wrapped a photographic plate in black paper and placed various phosphorescent <a href="Salt_(chemistry)" title="Salt (chemistry)">salts</a> on it. All results were negative until he used <a href="Uranium" title="Uranium">uranium</a> salts. The uranium salts caused a blackening of the plate in spite of the plate being wrapped in black paper.<a href="#cite_note-PaisInward-11">[11]</a>: 48 Curie named the radiation rayons de Becquerel, "Becquerel Rays" and showed these rays were a property of atoms.<a href="#cite_note-PaisInward-11">[11]</a>: 54

While X-rays were produced using electrical energy, the source of energy for radiation was a mystery.

In 1899, <a href="Julius_Elster" title="Julius Elster">Julius Elster</a> and <a href="Hans_Geitel" title="Hans Geitel">Hans Geitel</a> performed key experiments to find the energy source for radioactivity, excluding extraction of energy from air by measurements in a vacuum and extraction of energy from outer space by measurements 300m down a mine in the <a href="Harz_mountains" class="mw-redirect" title="Harz mountains">Harz mountains</a>.<a href="#cite_note-PaisInward-11">[11]</a>: 100 If the atoms themselves were the source of energy, this meant the seemingly immutable atoms must be altered when emitting the rays. In 1900 Curie summarized the puzzle of radioactivity as a choice between two equally unlikely possibilities: either energy was not conserved or chemical elements could be transmuted.<a href="#cite_note-PaisInward-11">[11]</a>: 112

Rutherford was the first to realize that all such elements decay in accordance with the same mathematical exponential formula. Rutherford and his student <a href="Frederick_Soddy" title="Frederick Soddy">Frederick Soddy</a> were the first to realize that many decay processes resulted in the <a href="Nuclear_transmutation" title="Nuclear transmutation">transmutation</a> of one element to another. Subsequently, the <a href="Radioactive_displacement_law_of_Fajans_and_Soddy" title="Radioactive displacement law of Fajans and Soddy">radioactive displacement law of Fajans and Soddy</a> was formulated to describe the products of alpha and <a href="Beta_decay" title="Beta decay">beta decay</a>.<a href="#cite_note-12">[12]</a><a href="#cite_note-13">[13]</a>

The early researchers also discovered that many other <a href="Chemical_element" title="Chemical element">chemical elements</a>, besides uranium, have radioactive isotopes. A systematic search for the total radioactivity in uranium ores also guided Pierre and Marie Curie to isolate two new elements: <a href="Polonium" title="Polonium">polonium</a> and <a href="Radium" title="Radium">radium</a>. Except for the radioactivity of radium, the chemical similarity of radium to <a href="Barium" title="Barium">barium</a> made these two elements difficult to distinguish.

Marie and Pierre Curie's study of radioactivity is an important factor in science and medicine. After their research on Becquerel's rays led them to the discovery of both radium and polonium, they coined the term "radioactivity"<a href="#cite_note-L'Annunziata-2007-14">[14]</a> to define the emission of <a href="Ionizing_radiation" title="Ionizing radiation">ionizing radiation</a> by some heavy elements.<a href="#cite_note-15">[15]</a> (Later the term was generalized to all elements.) Their research on the penetrating rays in uranium and the discovery of radium launched an era of using radium for the treatment of cancer. Their exploration of radium could be seen as the first peaceful use of nuclear energy and the start of modern <a href="Nuclear_medicine" title="Nuclear medicine">nuclear medicine</a>.<a href="#cite_note-L'Annunziata-2007-14">[14]</a>

<div class="mw-heading mw-heading2"><h2 id="Early_health_dangers">Early health dangers</h2></div>

<div role="note" class="hatnote navigation-not-searchable">Main article: <a href="Ionizing_radiation" title="Ionizing radiation">Ionizing radiation</a></div>

The dangers of <a href="Ionizing_radiation" title="Ionizing radiation">ionizing radiation</a> due to radioactivity and X-rays were not immediately recognized.

The discovery of X‑rays by <a href="Wilhelm_R%C3%B6ntgen" title="Wilhelm Röntgen">Wilhelm Röntgen</a> in 1895 led to widespread experimentation by scientists, physicians, and inventors. Many people began recounting stories of burns, hair loss and worse in technical journals as early as 1896. In February of that year, Professor Daniel and Dr. Dudley of <a href="Vanderbilt_University" title="Vanderbilt University">Vanderbilt University</a> performed an experiment involving X-raying Dudley's head that resulted in his hair loss. A report by Dr. H.D. Hawks, of his suffering severe hand and chest burns in an X-ray demonstration, was the first of many other reports in Electrical Review.<a href="#cite_note-SansareKhanna2011-16">[16]</a>

Other experimenters, including <a href="Elihu_Thomson" title="Elihu Thomson">Elihu Thomson</a> and <a href="Nikola_Tesla" title="Nikola Tesla">Nikola Tesla</a>, also reported burns. Thomson deliberately exposed a finger to an X-ray tube over a period of time and suffered pain, swelling, and blistering.<a href="#cite_note-physics.isu.edu-17">[17]</a> Other effects, including ultraviolet rays and ozone, were sometimes blamed for the damage,<a href="#cite_note-18">[18]</a> and many physicians still claimed that there were no effects from X-ray exposure at all.<a href="#cite_note-physics.isu.edu-17">[17]</a>

Despite this, there were some early systematic hazard investigations, and as early as 1902 <a href="William_Herbert_Rollins" title="William Herbert Rollins">William Herbert Rollins</a> wrote almost despairingly that his warnings about the dangers involved in the careless use of X-rays were not being heeded, either by industry or by his colleagues. By this time, Rollins had proved that X-rays could kill experimental animals, could cause a pregnant guinea pig to abort, and that they could kill a foetus. He also stressed that "animals vary in susceptibility to the external action of X-light" and warned that these differences be considered when patients were treated by means of X-rays.

<div class="mw-heading mw-heading3"><h3 id="Radioactive_substances">Radioactive substances</h3></div>

However, the biological effects of radiation due to radioactive substances were less easy to gauge. This gave the opportunity for many physicians and corporations to market radioactive substances as <a href="Patent_medicine" title="Patent medicine">patent medicines</a>. Examples were radium <a href="Enema" title="Enema">enema</a> treatments, and radium-containing waters to be drunk as tonics. Marie Curie protested against this sort of treatment, warning that "radium is dangerous in untrained hands".<a href="#cite_note-19">[19]</a> Curie later died from <a href="Aplastic_anaemia" class="mw-redirect" title="Aplastic anaemia">aplastic anaemia</a>, likely caused by exposure to ionizing radiation. By the 1930s, after a number of cases of bone necrosis and death of radium treatment enthusiasts, radium-containing medicinal products had been largely removed from the market (<a href="Radioactive_quackery" title="Radioactive quackery">radioactive quackery</a>).

<div class="mw-heading mw-heading3"><h3 id="Radiation_protection">Radiation protection</h3></div>

<div role="note" class="hatnote navigation-not-searchable">Main article: <a href="Radiation_protection" title="Radiation protection">Radiation protection</a></div>

<div role="note" class="hatnote navigation-not-searchable">See also: <a href="Sievert" title="Sievert">Sievert</a> and <a href="Ionizing_radiation" title="Ionizing radiation">Ionizing radiation</a></div>

Only a year after <a href="Wilhelm_R%C3%B6ntgen" title="Wilhelm Röntgen">Röntgen</a>'s discovery of X-rays, the American engineer <a href="Wolfram_Conrad_Fuchs" title="Wolfram Conrad Fuchs">Wolfram Fuchs</a> (1896) gave what is probably the first protection advice, but it was not until 1925 that the first <a href="International_Congress_of_Radiology" title="International Congress of Radiology">International Congress of Radiology</a> (ICR) was held and considered establishing international protection standards. The effects of radiation on genes, including the effect of cancer risk, were recognized much later. In 1927, <a href="Hermann_Joseph_Muller" title="Hermann Joseph Muller">Hermann Joseph Muller</a> published research showing genetic effects and, in 1946, was awarded the <a href="Nobel_Prize_in_Physiology_or_Medicine" title="Nobel Prize in Physiology or Medicine">Nobel Prize in Physiology or Medicine</a> for his findings.

The second ICR was held in Stockholm in 1928 and proposed the adoption of the <a href="Roentgen_(unit)" title="Roentgen (unit)">röntgen</a> unit, and the <a href="International_X-ray_and_Radium_Protection_Committee" class="mw-redirect" title="International X-ray and Radium Protection Committee">International X-ray and Radium Protection Committee</a> (IXRPC) was formed. <a href="Rolf_Maximilian_Sievert" title="Rolf Maximilian Sievert">Rolf Sievert</a> was named chairman, but a driving force was <a href="G._W._C._Kaye" title="G. W. C. Kaye">George Kaye</a> of the British <a href="National_Physical_Laboratory_(United_Kingdom)" title="National Physical Laboratory (United Kingdom)">National Physical Laboratory</a>. The committee met in 1931, 1934, and 1937.

After <a href="World_War_II" title="World War II">World War II</a>, the increased range and quantity of radioactive substances being handled as a result of military and civil nuclear programs led to large groups of occupational workers and the public being potentially exposed to harmful levels of ionising radiation. This was considered at the first post-war ICR convened in London in 1950, when the present <a href="International_Commission_on_Radiological_Protection" title="International Commission on Radiological Protection">International Commission on Radiological Protection</a> (ICRP) was born.<a href="#cite_note-20">[20]</a>

Since then the ICRP has developed the present international system of radiation protection, covering all aspects of radiation hazards.

In 2020, Hauptmann and another 15 international researchers from eight nations (among them: Institutes of Biostatistics, Registry Research, Centers of Cancer Epidemiology, Radiation Epidemiology, and also the <a href="National_Cancer_Institute" title="National Cancer Institute">U.S. National Cancer Institute</a> (NCI), <a href="International_Agency_for_Research_on_Cancer" title="International Agency for Research on Cancer">International Agency for Research on Cancer</a> (IARC) and the <a href="Radiation_Effects_Research_Foundation" title="Radiation Effects Research Foundation">Radiation Effects Research Foundation of Hiroshima</a>) studied definitively through <a href="Meta-analysis" title="Meta-analysis">meta-analysis</a> the damage resulting from the "low doses" that have afflicted survivors of the <a href="Atomic_bombings_of_Hiroshima_and_Nagasaki" title="Atomic bombings of Hiroshima and Nagasaki">atomic bombings of Hiroshima and Nagasaki</a> and also in numerous <a href="Nuclear_and_radiation_accidents_and_incidents" title="Nuclear and radiation accidents and incidents">accidents at nuclear plants</a> that have occurred. These scientists reported, in JNCI Monographs: Epidemiological Studies of Low Dose Ionizing Radiation and Cancer Risk, that the new epidemiological studies directly support excess cancer risks from low-dose ionizing radiation.<a href="#cite_note-21">[21]</a> In 2021, Italian researcher Sebastiano Venturi reported the first correlations between radio-caesium and <a href="Pancreatic_cancer" title="Pancreatic cancer">pancreatic cancer</a> with the role of <a href="Caesium" title="Caesium">caesium</a> in biology, in pancreatitis and in diabetes of pancreatic origin.<a href="#cite_note-22">[22]</a>

<div class="mw-heading mw-heading2"><h2 id="Units">Units</h2></div>

The <a href="International_System_of_Units" title="International System of Units">International System of Units</a> (SI) unit of radioactive activity is the <a href="Becquerel" title="Becquerel">becquerel</a> (Bq), named in honor of the scientist <a href="Henri_Becquerel" title="Henri Becquerel">Henri Becquerel</a>. One Bq is defined as one transformation (or decay or disintegration) per second.

An older unit of radioactivity is the <a href="Curie_(unit)" title="Curie (unit)">curie</a>, Ci, which was originally defined as "the quantity or mass of <a href="Radium_emanation" class="mw-redirect" title="Radium emanation">radium emanation</a> in <a href="Secular_equilibrium" title="Secular equilibrium">equilibrium</a> with one gram of <a href="Radium" title="Radium">radium</a> (element)".<a href="#cite_note-23">[23]</a> Today, the curie is defined as 3.7×1010 disintegrations per second, so that 1 <a href="Curie_(unit)" title="Curie (unit)">curie</a> (Ci) = 3.7×1010 Bq.

For radiological protection purposes, although the United States Nuclear Regulatory Commission permits the use of the unit curie alongside SI units,<a href="#cite_note-24">[24]</a> the <a href="European_Union" title="European Union">European Union</a> <a href="European_units_of_measurement_directives" title="European units of measurement directives">European units of measurement directives</a> required that its use for "public health ... purposes" be phased out by 31 December 1985.<a href="#cite_note-25">[25]</a>

The effects of ionizing radiation are often measured in units of <a href="Gray_(unit)" title="Gray (unit)">gray</a> for mechanical or <a href="Sievert" title="Sievert">sievert</a> for damage to tissue.

<div class="mw-heading mw-heading2"><h2 id="Types">Types</h2></div>

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Radioactive decay results in a reduction of summed rest <a href="Mass" title="Mass">mass</a>, once the released energy (the disintegration energy) has escaped in some way. Although <a href="Decay_energy" title="Decay energy">decay energy</a> is sometimes defined as associated with the difference between the mass of the parent nuclide products and the mass of the decay products, this is true only of rest mass measurements, where some energy has been removed from the product system. This is true because the decay energy must always carry mass with it, wherever it appears (see <a href="Mass_in_special_relativity" title="Mass in special relativity">mass in special relativity</a>) according to the formula <a href="E%3Dmc2" class="mw-redirect" title="E=mc2">E = mc2</a>. The decay energy is initially released as the energy of emitted photons plus the kinetic energy of massive emitted particles (that is, particles that have rest mass). If these particles come to <a href="Thermal_equilibrium" title="Thermal equilibrium">thermal equilibrium</a> with their surroundings and photons are absorbed, then the decay energy is transformed to thermal energy, which retains its mass.

Decay energy, therefore, remains associated with a certain measure of the mass of the decay system, called <a href="Invariant_mass" title="Invariant mass">invariant mass</a>, which does not change during the decay, even though the energy of decay is distributed among decay particles. The energy of photons, the kinetic energy of emitted particles, and, later, the thermal energy of the surrounding matter, all contribute to the <a href="Invariant_mass" title="Invariant mass">invariant mass</a> of the system. Thus, while the sum of the rest masses of the particles is not conserved in radioactive decay, the system mass and system invariant mass (and also the system total energy) is conserved throughout any decay process. This is a restatement of the equivalent laws of <a href="Conservation_of_energy" title="Conservation of energy">conservation of energy</a> and <a href="Conservation_of_mass" title="Conservation of mass">conservation of mass</a>.

<div class="mw-heading mw-heading3"><h3 id="Alpha,_beta_and_gamma_decay">Alpha, beta and gamma decay</h3></div>

<div role="note" class="hatnote navigation-not-searchable">Main articles: <a href="Alpha_decay" title="Alpha decay">Alpha decay</a>, <a href="Beta_decay" title="Beta decay">Beta decay</a>, and <a href="Gamma_decay" class="mw-redirect" title="Gamma decay">Gamma decay</a></div>

Early researchers found that an <a href="Electric_field" title="Electric field">electric</a> or <a href="Magnetic_field" title="Magnetic field">magnetic field</a> could split radioactive emissions into three types of beams. The rays were given the names <a href="Alpha_particle" title="Alpha particle">alpha</a>, <a href="Beta_particle" title="Beta particle">beta</a>, and gamma, in increasing order of their ability to penetrate matter. Alpha decay is observed only in heavier elements of atomic number 52 (<a href="Tellurium" title="Tellurium">tellurium</a>) and greater, with the exception of <a href="Beryllium-8" title="Beryllium-8">beryllium-8</a> (which decays to two alpha particles). The other two types of decay are observed in all the elements. Lead, <a href="Atomic_number" title="Atomic number">atomic number</a> 82, is the heaviest element to have any isotopes stable (to the limit of measurement) to radioactive decay. Radioactive decay is seen in all isotopes of all elements of atomic number 83 (<a href="Bismuth" title="Bismuth">bismuth</a>) or greater. <a href="Bismuth-209" title="Bismuth-209">Bismuth-209</a>, however, is only very slightly radioactive, with a half-life greater than the age of the universe; radioisotopes with extremely long half-lives are considered effectively stable for practical purposes.

In analyzing the nature of the decay products, it was obvious from the direction of the <a href="Electromagnetic_force" class="mw-redirect" title="Electromagnetic force">electromagnetic forces</a> applied to the radiations by external magnetic and electric fields that alpha particles carried a positive charge, beta particles carried a negative charge, and gamma rays were neutral. From the magnitude of deflection, it was clear that <a href="Alpha_particles" class="mw-redirect" title="Alpha particles">alpha particles</a> were much more massive than <a href="Beta_particles" class="mw-redirect" title="Beta particles">beta particles</a>. Passing alpha particles through a very thin glass window and trapping them in a <a href="Neon_lamp" title="Neon lamp">discharge tube</a> allowed researchers to study the <a href="Emission_spectrum" title="Emission spectrum">emission spectrum</a> of the captured particles, and ultimately proved that alpha particles are <a href="Helium" title="Helium">helium</a> nuclei. Other experiments showed beta radiation, resulting from decay and <a href="Cathode_ray" title="Cathode ray">cathode rays</a>, were high-speed <a href="Electrons" class="mw-redirect" title="Electrons">electrons</a>. Likewise, gamma radiation and X-rays were found to be high-energy <a href="Electromagnetic_radiation" title="Electromagnetic radiation">electromagnetic radiation</a>.

The relationship between the types of decays also began to be examined: For example, gamma decay was almost always found to be associated with other types of decay, and occurred at about the same time, or afterwards. Gamma decay as a separate phenomenon, with its own half-life (now termed <a href="Isomeric_transition" class="mw-redirect" title="Isomeric transition">isomeric transition</a>), was found in natural radioactivity to be a result of the gamma decay of excited metastable <a href="Nuclear_isomer" title="Nuclear isomer">nuclear isomers</a>, which were in turn created from other types of decay. Although alpha, beta, and gamma radiations were most commonly found, other types of emission were eventually discovered. Shortly after the discovery of the <a href="Positron" title="Positron">positron</a> in cosmic ray products, it was realized that the same process that operates in classical beta decay can also produce positrons (<a href="Positron_emission" title="Positron emission">positron emission</a>), along with <a href="Neutrino" title="Neutrino">neutrinos</a> (classical beta decay produces antineutrinos).

<div class="mw-heading mw-heading3"><h3 id="Electron_capture">Electron capture</h3></div>

<div role="note" class="hatnote navigation-not-searchable">Main article: <a href="Electron_capture" title="Electron capture">Electron capture</a></div>

In electron capture, some proton-rich nuclides were found to capture their own atomic electrons instead of emitting positrons, and subsequently, these nuclides emit only a neutrino and a gamma ray from the excited nucleus (and often also <a href="Auger_electron" class="mw-redirect" title="Auger electron">Auger electrons</a> and <a href="Characteristic_X-ray" title="Characteristic X-ray">characteristic X-rays</a>, as a result of the re-ordering of electrons to fill the place of the missing captured electron). These types of decay involve the nuclear capture of electrons or emission of electrons or positrons, and thus acts to move a nucleus toward the ratio of neutrons to protons that has the least energy for a given total number of <a href="Nucleon" title="Nucleon">nucleons</a>. This consequently produces a more stable (lower energy) nucleus.

A hypothetical process of positron capture, analogous to electron capture, is theoretically possible in antimatter atoms, but has not been observed, as complex antimatter atoms beyond <a href="Antihelium" class="mw-redirect" title="Antihelium">antihelium</a> are not experimentally available.<a href="#cite_note-26">[26]</a> Such a decay would require antimatter atoms at least as complex as <a href="Beryllium-7" class="mw-redirect" title="Beryllium-7">beryllium-7</a>, which is the lightest known isotope of normal matter to undergo decay by electron capture.<a href="#cite_note-27">[27]</a>

<div class="mw-heading mw-heading3"><h3 id="Nucleon_emission">Nucleon emission</h3></div>

<div role="note" class="hatnote navigation-not-searchable">Main articles: <a href="Neutron_emission" title="Neutron emission">Neutron emission</a>, <a href="Cluster_emission" class="mw-redirect" title="Cluster emission">Cluster emission</a>, and <a href="Nuclear_fission" title="Nuclear fission">Nuclear fission</a></div>

Shortly after the discovery of the neutron in 1932, <a href="Enrico_Fermi" title="Enrico Fermi">Enrico Fermi</a> realized that certain rare beta-decay reactions immediately yield neutrons as an additional decay particle, so called beta-delayed <a href="Neutron_emission" title="Neutron emission">neutron emission</a>. Neutron emission usually happens from nuclei that are in an excited state, such as the excited 17O* produced from the beta decay of 17N. The neutron emission process itself is controlled by the <a href="Nuclear_force" title="Nuclear force">nuclear force</a> and therefore is extremely fast, sometimes referred to as "nearly instantaneous". Isolated <a href="Proton_emission" title="Proton emission">proton emission</a> was eventually observed in some elements. It was also found that some heavy elements may undergo <a href="Spontaneous_fission" title="Spontaneous fission">spontaneous fission</a> into products that vary in composition. In a phenomenon called <a href="Cluster_decay" title="Cluster decay">cluster decay</a>, specific combinations of neutrons and protons other than alpha particles (helium nuclei) were found to be spontaneously emitted from atoms.

<div class="mw-heading mw-heading3"><h3 id="More_exotic_types_of_decay">More exotic types of decay</h3></div>

Other types of radioactive decay were found to emit previously seen particles but via different mechanisms. An example is <a href="Internal_conversion" title="Internal conversion">internal conversion</a>, which results in an initial electron emission, and then often further <a href="Characteristic_X-ray" title="Characteristic X-ray">characteristic X-rays</a> and <a href="Auger_electron" class="mw-redirect" title="Auger electron">Auger electrons</a> emissions, although the internal conversion process involves neither beta nor gamma decay. A neutrino is not emitted, and none of the electron(s) and photon(s) emitted originate in the nucleus, even though the energy to emit all of them does originate there. Internal conversion decay, like <a href="Isomeric_transition" class="mw-redirect" title="Isomeric transition">isomeric transition</a> gamma decay and neutron emission, involves the release of energy by an excited nuclide, without the transmutation of one element into another.

Rare events that involve a combination of two beta-decay-type events happening simultaneously are known (see below). Any decay process that does not violate the conservation of energy or momentum laws (and perhaps other particle conservation laws) is permitted to happen, although not all have been detected. An interesting example discussed in a final section, is <a href="Beta_decay#Bound-state_β−_decay" title="Beta decay">bound state beta decay</a> of <a href="Rhenium-187" class="mw-redirect" title="Rhenium-187">rhenium-187</a>. In this process, the beta electron-decay of the parent nuclide is not accompanied by beta electron emission, because the beta particle has been captured into the K-shell of the emitting atom. An antineutrino is emitted, as in all negative beta decays.

If energy circumstances are favorable, a given radionuclide may undergo many competing types of decay, with some atoms decaying by one route, and others decaying by another. An example is <a href="Copper-64" title="Copper-64">copper-64</a>, which has 29 protons, and 35 neutrons, which decays with a half-life of 12.7004(13) hours.<a href="#cite_note-NUBASE2020-28">[28]</a> This isotope has one unpaired proton and one unpaired neutron, so either the proton or the neutron can decay to the other particle, which has opposite <a href="Isospin" title="Isospin">isospin</a>. This particular nuclide (though not all nuclides in this situation) is more likely to decay through <a href="Beta_plus_decay" class="mw-redirect" title="Beta plus decay">beta plus decay</a> (61.52(26)%<a href="#cite_note-NUBASE2020-28">[28]</a>) than through <a href="Electron_capture" title="Electron capture">electron capture</a> (38.48(26)%<a href="#cite_note-NUBASE2020-28">[28]</a>). The excited energy states resulting from these decays which fail to end in a ground energy state, also produce later internal conversion and <a href="Gamma_decay" class="mw-redirect" title="Gamma decay">gamma decay</a> in almost 0.5% of the time.

<div class="mw-heading mw-heading3"><h3 id="List_of_decay_modes">List of decay modes </h3></div>

<caption>Decay modes in NUBASE2020<a href="#cite_note-NUBASE2020-28">[28]</a>

</caption>

<th>Mode

</th>

<th>Name

</th>

<th style="max-width:30%;">Action

</th>

<th>Nucleus changes

</th></tr>

<tr>

/* start https://en.wikipedia.org/ */

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</style><div class="plainlist" style="text-align: center;font-size:120%"><ul><li>α</li></ul></div>

</td>

<td><a href="Alpha_decay" title="Alpha decay">alpha emission</a>

</td>

<td>An <a href="Alpha_particle" title="Alpha particle">alpha particle</a> (A = 4, Z = 2) emitted from nucleus

</td>

<td>(A − 4, Z − 2)

</td></tr>

<tr>

</td>

<td><a href="Proton_emission" title="Proton emission">proton emission</a>

</td>

<td>A <a href="Proton" title="Proton">proton</a> ejected from nucleus

</td>

<td>(A − 1, Z − 1)

</td></tr>

<tr>

</td>

<td><a href="Proton_emission" title="Proton emission">2-proton emission</a>

</td>

<td>Two protons ejected from nucleus simultaneously

</td>

<td>(A − 2, Z − 2)

</td></tr>

<tr>

</td>

<td><a href="Neutron_emission" title="Neutron emission">neutron emission</a>

</td>

<td>A <a href="Neutron" title="Neutron">neutron</a> ejected from nucleus

</td>

<td>(A − 1, Z)

</td></tr>

<tr>

</td>

<td><a href="Neutron_emission" title="Neutron emission">2-neutron emission</a>

</td>

<td>Two neutrons ejected from nucleus simultaneously

</td>

<td>(A − 2, Z)

</td></tr>

<tr>

</td>

<td><a href="Electron_capture" title="Electron capture">electron capture</a>

</td>

<td>A nucleus captures an orbiting electron and emits a neutrino; the daughter nucleus is left in an excited unstable state

</td>

<td>(A, Z − 1)

</td></tr>

<tr>

</td>

<td><a href="Positron_emission" title="Positron emission">positron emission</a>

</td>

<td>A nuclear proton converts to a neutron by emitting a positron and an electron neutrino

</td>

<td>(A, Z − 1)

</td></tr>

<tr>

</td>

<td><a href="Positron_emission" title="Positron emission">positron emission</a>

</td>

<td>In NUBASE2020, ß+ refers to the combined rate of electron capture (ε) and positron emission (e+): ß+ = ε + e+

</td>

<td>(A, Z − 1)

</td></tr>

<tr>

</td>

<td><a href="Beta_decay" title="Beta decay">β− decay</a>

</td>

<td>A nucleus emits an <a href="Electron" title="Electron">electron</a> and an <a href="Electron_antineutrino" class="mw-redirect" title="Electron antineutrino">electron antineutrino</a>

</td>

<td>(A, Z + 1)

</td></tr>

<tr>

</td>

<td><a href="Double_beta_decay" title="Double beta decay">double β− decay</a>

</td>

<td>A nucleus emits two electrons and two antineutrinos

</td>

<td>(A, Z + 2)

</td></tr>

<tr>

</td>

<td><a href="Double_beta_decay" title="Double beta decay">double β+ decay</a>

</td>

<td>A nucleus emits two positrons and two neutrinos

</td>

<td>(A, Z − 2)

</td></tr>

<tr>

</td>

<td><a href="Delayed_neutron" title="Delayed neutron">β−-delayed neutron emission</a>

</td>

<td>A nucleus decays by β− emission to an excited state, which then emits a neutron

</td>

<td>(A − 1, Z + 1)

</td></tr>

<tr>

</td>

<td>β−-delayed 2-neutron emission

</td>

<td>A nucleus decays by β− emission to an excited state, which then emits two neutrons

</td>

<td>(A − 2, Z + 1)

</td></tr>

<tr>

</td>

<td>β−-delayed 3-neutron emission

</td>

<td>A nucleus decays by β− emission to an excited state, which then emits three neutrons

</td>

<td>(A − 3, Z + 1)

</td></tr>

<tr>

</td>

<td>β+-delayed proton emission

</td>

<td>A nucleus decays by β+ emission to an excited state, which then emits a proton

</td>

<td>(A − 1, Z − 2)

</td></tr>

<tr>

</td>

<td>β+-delayed 2-proton emission

</td>

<td>A nucleus decays by β+ emission to an excited state, which then emits two protons

</td>

<td>(A − 2, Z − 3)

</td></tr>

<tr>

</td>

<td>β+-delayed 3-proton emission

</td>

<td>A nucleus decays by β+ emission to an excited state, which then emits three protons

</td>

<td>(A − 3, Z − 4)

</td></tr>

<tr>

</td>

<td>β−-delayed alpha emission

</td>

<td>A nucleus decays by β− emission to an excited state, which then emits an α particle

</td>

<td>(A − 4, Z − 1)

</td></tr>

<tr>

</td>

<td>β+-delayed alpha emission

</td>

<td>A nucleus decays by β+ emission to an excited state, which then emits an a particle

</td>

<td>(A − 4, Z − 3)

</td></tr>

<tr>

</td>

<td>β−-delayed deuteron emission

</td>

<td>A nucleus decays by β− emission to an excited state, which then emits a deuteron

</td>

<td>(A − 2, Z)

</td></tr>

<tr>

</td>

<td>β−-delayed triton emission

</td>

<td>A nucleus decays by β− emission to an excited state, which then emits a triton

</td>

<td>(A − 3, Z)

</td></tr>

<tr>

</td>

<td><a href="Cluster_decay" title="Cluster decay">cluster decay</a>

</td>

<td>A nucleus emits a specific type of smaller nucleus (A1, Z1) which is larger than an alpha particle (e.g. 14C, 24Ne)

</td>

<td>(A − A1, Z − Z1) & (A1, Z1)

</td></tr>

<tr>

</td>

<td><a href="Nuclear_isomer#Decay_processes" title="Nuclear isomer">internal (isomeric) transition</a>

</td>

<td>A nucleus in a metastable state drops to a lower energy state by emitting a photon or ejecting an electron

</td>

<td>(A, Z)

</td></tr>

<tr>

</td>

<td><a href="Spontaneous_fission" title="Spontaneous fission">spontaneous fission</a>

</td>

<td>A nucleus disintegrates into two or more smaller nuclei and other particles, all of which may vary with each decay

</td>

<td>variable

</td></tr>

<tr>

</td>

<td>β+-delayed fission

</td>

<td>A nucleus decays by β+ emission to an excited state, which then undergoes spontaneous fission

</td>

<td>β+ & variable

</td></tr>

<tr>

</td>

<td>β−-delayed fission

</td>

<td>A nucleus decays by β− emission to an excited state, which then undergoes spontaneous fission

</td>

<td>β− & variable

</td></tr></tbody></table>

<div class="mw-heading mw-heading3"><h3 id="Decay_chains_and_multiple_modes">Decay chains and multiple modes</h3></div>

<div role="note" class="hatnote navigation-not-searchable">See also: <a href="Valley_of_stability" title="Valley of stability">Valley of stability</a></div>

The daughter nuclide of a decay event may also be unstable (radioactive). In this case, it too will decay, producing radiation. The resulting second daughter nuclide may also be radioactive. This can lead to a sequence of several decay events called a <a href="Decay_chain" title="Decay chain">decay chain</a> (see this article for specific details of important natural decay chains). Eventually, a stable nuclide is produced. Any decay daughters that are the result of an alpha decay will also result in helium atoms being created.

Some radionuclides may have several different paths of decay. For example, 35.94(6)%<a href="#cite_note-NUBASE2020-28">[28]</a> of <a href="Bismuth-212" class="mw-redirect" title="Bismuth-212">bismuth-212</a> decays, through alpha-emission, to <a href="Thallium-208" class="mw-redirect" title="Thallium-208">thallium-208</a> while 64.06(6)%<a href="#cite_note-NUBASE2020-28">[28]</a> of <a href="Bismuth-212" class="mw-redirect" title="Bismuth-212">bismuth-212</a> decays, through beta-emission, to <a href="Polonium-212" class="mw-redirect" title="Polonium-212">polonium-212</a>. Both <a href="Thallium-208" class="mw-redirect" title="Thallium-208">thallium-208</a> and <a href="Polonium-212" class="mw-redirect" title="Polonium-212">polonium-212</a> are radioactive daughter products of bismuth-212, and both decay directly to stable <a href="Lead-208" class="mw-redirect" title="Lead-208">lead-208</a>.

<div class="mw-heading mw-heading2"><h2 id="Occurrence_and_applications">Occurrence and applications</h2></div>

<div role="note" class="hatnote navigation-not-searchable">See also: <a href="Nuclear_drip_line" title="Nuclear drip line">Nuclear drip line</a></div>

According to the <a href="Big_Bang_theory" class="mw-redirect" title="Big Bang theory">Big Bang theory</a>, stable isotopes of the lightest three elements (<a href="Hydrogen" title="Hydrogen">H</a>, He, and traces of <a href="Lithium" title="Lithium">Li</a>) were produced very shortly after the emergence of the universe, in a process called <a href="Big_Bang_nucleosynthesis" title="Big Bang nucleosynthesis">Big Bang nucleosynthesis</a>. These lightest stable nuclides (including <a href="Deuterium" title="Deuterium">deuterium</a>) survive to today, but any radioactive isotopes of the light elements produced in the Big Bang (such as <a href="Tritium" title="Tritium">tritium</a>) have long since decayed. Isotopes of elements heavier than boron were not produced at all in the Big Bang, and these first five elements do not have any long-lived radioisotopes. Thus, all radioactive nuclei are, therefore, relatively young with respect to the birth of the universe, having formed later in various other types of <a href="Nucleosynthesis" title="Nucleosynthesis">nucleosynthesis</a> in <a href="Star" title="Star">stars</a> (in particular, <a href="Supernova" title="Supernova">supernovae</a>), and also during ongoing interactions between stable isotopes and energetic particles. For example, <a href="Carbon-14" title="Carbon-14">carbon-14</a>, a radioactive nuclide with a half-life of only 5700(30) years,<a href="#cite_note-NUBASE2020-28">[28]</a> is constantly produced in Earth's upper atmosphere due to interactions between cosmic rays and nitrogen.

Nuclides that are produced by radioactive decay are called <a href="Radiogenic_nuclide" title="Radiogenic nuclide">radiogenic nuclides</a>, whether they themselves are <a href="Stable_isotope" class="mw-redirect" title="Stable isotope">stable</a> or not. There exist stable radiogenic nuclides that were formed from short-lived <a href="Extinct_radionuclide" title="Extinct radionuclide">extinct radionuclides</a> in the early Solar System.<a href="#cite_note-29">[29]</a><a href="#cite_note-30">[30]</a> The extra presence of these stable radiogenic nuclides (such as xenon-129 from extinct <a href="Iodine-129" title="Iodine-129">iodine-129</a>) against the background of primordial <a href="Stable_nuclide" title="Stable nuclide">stable nuclides</a> can be inferred by various means.

Radioactive decay has been put to use in the technique of <a href="Radioisotopic_labeling" class="mw-redirect" title="Radioisotopic labeling">radioisotopic labeling</a>, which is used to track the passage of a chemical substance through a complex system (such as a living <a href="Organism" title="Organism">organism</a>). A sample of the substance is synthesized with a high concentration of unstable atoms. The presence of the substance in one or another part of the system is determined by detecting the locations of decay events.

On the premise that radioactive decay is truly <a href="Random" class="mw-redirect" title="Random">random</a> (rather than merely <a href="Chaos_theory" title="Chaos theory">chaotic</a>), it has been used in <a href="Hardware_random-number_generator" class="mw-redirect" title="Hardware random-number generator">hardware random-number generators</a>. Because the process is not thought to vary significantly in mechanism over time, it is also a valuable tool in estimating the absolute ages of certain materials. For geological materials, the radioisotopes and some of their decay products become trapped when a rock solidifies, and can then later be used (subject to many well-known qualifications) to estimate the date of the solidification. These include checking the results of several simultaneous processes and their products against each other, within the same sample. In a similar fashion, and also subject to qualification, the rate of formation of carbon-14 in various eras, the date of formation of organic matter within a certain period related to the isotope's half-life may be estimated, because the carbon-14 becomes trapped when the organic matter grows and incorporates the new carbon-14 from the air. Thereafter, the amount of carbon-14 in organic matter decreases according to decay processes that may also be independently cross-checked by other means (such as checking the carbon-14 in individual tree rings, for example).

<div class="mw-heading mw-heading3"><h3 id="Szilard–Chalmers_effect">Szilard–Chalmers effect</h3></div>

The Szilard–Chalmers effect is the breaking of a chemical bond as a result of a kinetic energy imparted from radioactive decay. It operates by the absorption of neutrons by an atom and subsequent emission of gamma rays, often with significant amounts of kinetic energy. This kinetic energy, by <a href="Newton's_laws_of_motion" title="Newton's laws of motion">Newton's third law</a>, pushes back on the decaying atom, which causes it to move with enough speed to break a chemical bond.<a href="#cite_note-31">[31]</a> This effect can be used to separate isotopes by chemical means.

The Szilard–Chalmers effect was discovered in 1934 by <a href="Le%C3%B3_Szil%C3%A1rd" class="mw-redirect" title="Leó Szilárd">Leó Szilárd</a> and Thomas A. Chalmers.<a href="#cite_note-32">[32]</a> They observed that after bombardment by neutrons, the breaking of a bond in liquid ethyl iodide allowed radioactive iodine to be removed.<a href="#cite_note-33">[33]</a>

<div class="mw-heading mw-heading3"><h3 id="Origins_of_radioactive_nuclides">Origins of radioactive nuclides</h3></div>

<div role="note" class="hatnote navigation-not-searchable">Main article: <a href="Nucleosynthesis" title="Nucleosynthesis">Nucleosynthesis</a></div>

Radioactive <a href="Primordial_nuclide" title="Primordial nuclide">primordial nuclides</a> found in the <a href="Earth" title="Earth">Earth</a> are residues from ancient <a href="Supernova_nucleosynthesis" title="Supernova nucleosynthesis">supernova</a> explosions that occurred before the formation of the <a href="Solar_System" title="Solar System">Solar System</a>. They are the fraction of radionuclides that survived from that time, through the formation of the primordial solar <a href="Nebula" title="Nebula">nebula</a>, through planet <a href="Accretion_(astrophysics)" title="Accretion (astrophysics)">accretion</a>, and up to the present time. The naturally occurring short-lived <a href="Radiogenic" class="mw-redirect" title="Radiogenic">radiogenic</a> radionuclides found in today's <a href="Rock_(geology)" title="Rock (geology)">rocks</a>, are the daughters of those radioactive primordial nuclides. Another minor source of naturally occurring radioactive nuclides are <a href="Cosmogenic_nuclide" title="Cosmogenic nuclide">cosmogenic nuclides</a>, that are formed by cosmic ray bombardment of material in the Earth's <a href="Atmosphere" title="Atmosphere">atmosphere</a> or <a href="Crust_(geology)" title="Crust (geology)">crust</a>. The decay of the radionuclides in rocks of the Earth's <a href="Mantle_(geology)" title="Mantle (geology)">mantle</a> and <a href="Crust_(geology)" title="Crust (geology)">crust</a> contribute significantly to <a href="Earth's_internal_heat_budget" title="Earth's internal heat budget">Earth's internal heat budget</a>.

<div class="mw-heading mw-heading2"><h2 id="Aggregate_processes">Aggregate processes</h2></div>

While the underlying process of radioactive decay is subatomic, historically and in most practical cases it is encountered in bulk materials with very large numbers of atoms. This section discusses models that connect events at the atomic level to observations in aggregate.

<div class="mw-heading mw-heading3"><h3 id="Terminology">Terminology</h3></div>

The decay rate, or activity, of a radioactive substance is characterized by the following time-independent parameters:

<ul><li>The <a href="Half-life" title="Half-life">half-life</a>, t1/2, is the time taken for the activity of a given amount of a <a href="List_of_nuclides" title="List of nuclides">radioactive substance</a> to decay to half of its initial value.</li>

<li>The <a href="Decay_constant" class="mw-redirect" title="Decay constant">decay constant</a>, λ "<a href="Lambda" title="Lambda">lambda</a>", the reciprocal of the mean lifetime (in s−1), sometimes referred to as simply decay rate.</li>

<li>The <a href="Mean_lifetime" class="mw-redirect" title="Mean lifetime">mean lifetime</a>, τ "<a href="Tau" title="Tau">tau</a>", the average lifetime (1/<a href="E_(mathematical_constant)" title="E (mathematical constant)">e</a> life) of a radioactive particle before decay.</li></ul>

Although these are constants, they are associated with the <a href="Statistical_mechanics" title="Statistical mechanics">statistical behavior of populations</a> of atoms. In consequence, predictions using these constants are less accurate for minuscule samples of atoms.

In principle a half-life, a third-life, or even a (1/√2)-life, could be used in exactly the same way as half-life; but the mean life and half-life t1/2 have been adopted as standard times associated with exponential decay.

Those parameters can be related to the following time-dependent parameters:

<ul><li><a href="Total_activity" class="mw-redirect" title="Total activity">Total activity</a> (or just activity), A, is the number of decays per unit time of a radioactive sample.</li>

<li><a href="Number_of_particles" class="mw-redirect" title="Number of particles">Number of particles</a>, N, in the sample.</li>

<li><a href="Specific_activity" title="Specific activity">Specific activity</a>, a, is the number of decays per unit time per amount of substance of the sample at time set to zero (t = 0). "Amount of substance" can be the mass, volume or moles of the initial sample.</li></ul>

These are related as follows:

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<annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}t_{1/2}&={\frac {\ln(2)}{\lambda }}=\tau \ln(2)\\[2pt]A&=-{\frac {\mathrm {d} N}{\mathrm {d} t}}=\lambda N={\frac {\ln(2)}{t_{1/2}}}N\\[2pt]S_{A}a_{0}&=-{\frac {\mathrm {d} N}{\mathrm {d} t}}{\bigg |}_{t=0}=\lambda N_{0}\end{aligned}}}</annotation>

</semantics>

</math><img src="./08fd79adb91a3896db0855d30c72096055431cbf.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -9.005ex; width:32.451ex; height:19.176ex;" alt="{\displaystyle {\begin{aligned}t_{1/2}&={\frac {\ln(2)}{\lambda }}=\tau \ln(2)\\[2pt]A&=-{\frac {\mathrm {d} N}{\mathrm {d} t}}=\lambda N={\frac {\ln(2)}{t_{1/2}}}N\\[2pt]S_{A}a_{0}&=-{\frac {\mathrm {d} N}{\mathrm {d} t}}{\bigg |}_{t=0}=\lambda N_{0}\end{aligned}}}" loading="lazy"></dd></dl>

where N0 is the initial amount of active substance — substance that has the same percentage of unstable particles as when the substance was formed.

<div class="mw-heading mw-heading3"><h3 id="Assumptions">Assumptions</h3></div>

The mathematics of radioactive decay depend on a key assumption that a nucleus of a radionuclide has no "memory" or way of translating its history into its present behavior. A nucleus does not "age" with the passage of time. Thus, the probability of its breaking down does not increase with time but stays constant, no matter how long the nucleus has existed. This constant probability may differ greatly between one type of nucleus and another, leading to the many different observed decay rates. However, whatever the probability is, it does not change over time. This is in marked contrast to complex objects that do show aging, such as automobiles and humans. These aging systems do have a chance of breakdown per unit of time that increases from the moment they begin their existence.

Aggregate processes, like the radioactive decay of a lump of atoms, for which the single-event probability of realization is very small but in which the number of time-slices is so large that there is nevertheless a reasonable rate of events, are modelled by the <a href="Poisson_distribution" title="Poisson distribution">Poisson distribution</a>, which is discrete. Radioactive decay and <a href="Nuclear_reaction" title="Nuclear reaction">nuclear particle reactions</a> are two examples of such aggregate processes.<a href="#cite_note-leofish-34">[34]</a> The mathematics of <a href="Poisson_processes" class="mw-redirect" title="Poisson processes">Poisson processes</a> reduce to the law of <a href="Exponential_decay" title="Exponential decay">exponential decay</a>, which describes the statistical behaviour of a large number of nuclei, rather than one individual nucleus. In the following formalism, the number of nuclei or the nuclei population N, is of course a discrete variable (a <a href="Natural_number" title="Natural number">natural number</a>)—but for any physical sample N is so large that it can be treated as a continuous variable. <a href="Differential_calculus" title="Differential calculus">Differential calculus</a> is used to model the behaviour of nuclear decay.

<div class="mw-heading mw-heading4"><h4 id="One-decay_process">One-decay process</h4></div>

<div role="note" class="hatnote navigation-not-searchable">For the mathematical details of exponential decay in general context, see <a href="Exponential_decay" title="Exponential decay">exponential decay</a>.</div>

Consider the case of a nuclide A that decays into another B by some process A → B (emission of other particles, like <a href="Electron_neutrino" title="Electron neutrino">electron neutrinos</a> ν e and <a href="Electron" title="Electron">electrons</a> e− as in <a href="Beta_decay" title="Beta decay">beta decay</a>, are irrelevant in what follows). The decay of an unstable nucleus is entirely random in time so it is impossible to predict when a particular atom will decay. However, it is equally likely to decay at any instant in time. Therefore, given a sample of a particular radioisotope, the number of decay events −dN expected to occur in a small interval of time dt is proportional to the number of atoms present N, that is<a href="#cite_note-Patel-35">[35]</a>

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<annotation encoding="application/x-tex">{\displaystyle -{\frac {\mathrm {d} N}{\mathrm {d} t}}\propto N}</annotation>

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</math><img src="./6890621e95338c399e18448391fc92dbe3ca18eb.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:11.162ex; height:5.509ex;" alt="{\displaystyle -{\frac {\mathrm {d} N}{\mathrm {d} t}}\propto N}" loading="lazy"></dd></dl>

Particular radionuclides decay at different rates, so each has its own decay constant λ. The expected decay −dN/N is proportional to an increment of time, dt:

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<annotation encoding="application/x-tex">{\displaystyle -{\frac {\mathrm {d} N}{N}}=\lambda \mathrm {d} t}</annotation>

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</math><img src="./65be9c78630bf2f8468874170cbe591f272d47d0.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:12.586ex; height:5.343ex;" alt="{\displaystyle -{\frac {\mathrm {d} N}{N}}=\lambda \mathrm {d} t}" loading="lazy">

</div>

The negative sign indicates that N decreases as time increases, as the decay events follow one after another. The solution to this first-order <a href="Differential_equation" title="Differential equation">differential equation</a> is the <a href="Mathematical_function" class="mw-redirect" title="Mathematical function">function</a>:

<msub>

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</msub>

<msup>

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<annotation encoding="application/x-tex">{\displaystyle N(t)=N_{0}\,e^{-{\lambda }t}}</annotation>

</semantics>

</math><img src="./2709c8f04fa7f7062192da2fe2af75554b3caa76.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:15.265ex; height:3.176ex;" alt="{\displaystyle N(t)=N_{0}\,e^{-{\lambda }t}}" loading="lazy"></dd></dl>

where N0 is the value of N at time t = 0, with the decay constant expressed as λ<a href="#cite_note-Patel-35">[35]</a>

We have for all time t:

<msub>

</mrow>

</msub>

<msub>

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</msub>

<msub>

<mtext>total</mtext>

</mrow>

</msub>

<msub>

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<annotation encoding="application/x-tex">{\displaystyle N_{A}+N_{B}=N_{\text{total}}=N_{A0},}</annotation>

</semantics>

</math><img src="./363f7608f8e686130be84e079bc258e4d8258beb.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:25.993ex; height:2.509ex;" alt="{\displaystyle N_{A}+N_{B}=N_{\text{total}}=N_{A0},}" loading="lazy"></dd></dl>

where Ntotal is the constant number of particles throughout the decay process, which is equal to the initial number of A nuclides since this is the initial substance.

If the number of non-decayed A nuclei is:

<msub>

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</msub>

<msub>

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</msub>

<msup>

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</msup>

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<annotation encoding="application/x-tex">{\displaystyle N_{A}=N_{A0}e^{-\lambda t}}</annotation>

</semantics>

</math><img src="./2f418457e5436a681336b35addd364ce61ce97f9.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:14.729ex; height:3.009ex;" alt="{\displaystyle N_{A}=N_{A0}e^{-\lambda t}}" loading="lazy"></dd></dl>

then the number of nuclei of B (i.e. the number of decayed A nuclei) is

<msub>

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</msub>

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<msub>

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<msup>

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</msup>

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</msub>

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<annotation encoding="application/x-tex">{\displaystyle N_{B}=N_{A0}-N_{A}=N_{A0}-N_{A0}e^{-\lambda t}=N_{A0}\left(1-e^{-\lambda t}\right).}</annotation>

</semantics>

</math><img src="./1a3f60a7a06a0e7fffc884aa8ea2607bb11af890.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:54.111ex; height:3.343ex;" alt="{\displaystyle N_{B}=N_{A0}-N_{A}=N_{A0}-N_{A0}e^{-\lambda t}=N_{A0}\left(1-e^{-\lambda t}\right).}" loading="lazy"></dd></dl>

The number of decays observed over a given interval obeys <a href="Poisson_statistics" class="mw-redirect" title="Poisson statistics">Poisson statistics</a>. If the average number of decays is ⟨N⟩, the probability of a given number of decays N is<a href="#cite_note-Patel-35">[35]</a>

<mfrac>

<mrow>

<msup>

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</msup>

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<annotation encoding="application/x-tex">{\displaystyle P(N)={\frac {\langle N\rangle ^{N}\exp(-\langle N\rangle )}{N!}}.}</annotation>

</semantics>

</math><img src="./39a337d1b5d849e24c557e5f1bee0fe26f0ba28c.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:27.194ex; height:6.009ex;" alt="{\displaystyle P(N)={\frac {\langle N\rangle ^{N}\exp(-\langle N\rangle )}{N!}}.}" loading="lazy"></dd></dl>

<div class="mw-heading mw-heading4"><h4 id="Chain-decay_processes">Chain-decay processes</h4></div>

<div role="note" class="hatnote navigation-not-searchable">For the analogous mathematics in 1st order chemical reactions, see <a href="Rate_equation#Consecutive_reactions" title="Rate equation">consecutive reactions</a>.</div>

<div class="mw-heading mw-heading5"><h5 id="Chain_of_two_decays">Chain of two decays</h5></div>

Now consider the case of a chain of two decays: one nuclide A decaying into another B by one process, then B decaying into another C by a second process, i.e. A → B → C. The previous equation cannot be applied to the decay chain, but can be generalized as follows. Since A decays into B, then B decays into C, the activity of A adds to the total number of B nuclides in the present sample, before those B nuclides decay and reduce the number of nuclides leading to the later sample. In other words, the number of second generation nuclei B increases as a result of the first generation nuclei decay of A, and decreases as a result of its own decay into the third generation nuclei C.<a href="#cite_note-Introductory_Nuclear_Physics_1988-36">[36]</a> The sum of these two terms gives the law for a decay chain for two nuclides:

<mfrac>

<mrow>

</mrow>

<msub>

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<msub>

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</msub>

<msub>

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<msub>

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<annotation encoding="application/x-tex">{\displaystyle {\frac {\mathrm {d} N_{B}}{\mathrm {d} t}}=-\lambda _{B}N_{B}+\lambda _{A}N_{A}.}</annotation>

</semantics>

</math><img src="./7e360bcb58678e105101a1caa1c0b79cd71f362f.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:26.2ex; height:5.509ex;" alt="{\displaystyle {\frac {\mathrm {d} N_{B}}{\mathrm {d} t}}=-\lambda _{B}N_{B}+\lambda _{A}N_{A}.}" loading="lazy"></dd></dl>

The rate of change of NB, that is dNB/dt, is related to the changes in the amounts of A and B, NB can increase as B is produced from A and decrease as B produces C.

Re-writing using the previous results:

<mfrac>

<mrow>

</mrow>

<msub>

</mrow>

</msub>

</mrow>

<mrow>

</mrow>

</mrow>

</mfrac>

</mrow>

<msub>

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</msub>

<msub>

</mrow>

</msub>

<msub>

</mrow>

</msub>

<msub>

</mrow>

</msub>

<msup>

<msub>

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</msub>

</mrow>

</msup>

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</mrow>

<annotation encoding="application/x-tex">{\displaystyle {\frac {\mathrm {d} N_{B}}{\mathrm {d} t}}=-\lambda _{B}N_{B}+\lambda _{A}N_{A0}e^{-\lambda _{A}t}}</annotation>

</semantics>

</math><img src="./599ed253439ab4951bb51cb0cb886a0e661638fd.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:31.686ex; height:5.509ex;" alt="{\displaystyle {\frac {\mathrm {d} N_{B}}{\mathrm {d} t}}=-\lambda _{B}N_{B}+\lambda _{A}N_{A0}e^{-\lambda _{A}t}}" loading="lazy">

</div>

The subscripts simply refer to the respective nuclides, i.e. NA is the number of nuclides of type A; NA0 is the initial number of nuclides of type A; λA is the decay constant for A – and similarly for nuclide B. Solving this equation for NB gives:

<msub>

</mrow>

</msub>

<mfrac>

<mrow>

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</msub>

<msub>

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<msup>

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</msub>

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<msup>

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</mrow>

<annotation encoding="application/x-tex">{\displaystyle N_{B}={\frac {N_{A0}\lambda _{A}}{\lambda _{B}-\lambda _{A}}}\left(e^{-\lambda _{A}t}-e^{-\lambda _{B}t}\right).}</annotation>

</semantics>

</math><img src="./3180ac1277d1853b7b83ddef1cb5c56c015b0228.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:32.801ex; height:5.843ex;" alt="{\displaystyle N_{B}={\frac {N_{A0}\lambda _{A}}{\lambda _{B}-\lambda _{A}}}\left(e^{-\lambda _{A}t}-e^{-\lambda _{B}t}\right).}" loading="lazy"></dd></dl>

In the case where B is a stable nuclide (λB = 0), this equation reduces to the previous solution:

<msub>

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</munder>

<mrow>

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<mfrac>

<mrow>

<msub>

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</msub>

<msub>

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<msup>

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<annotation encoding="application/x-tex">{\displaystyle \lim _{\lambda _{B}\rightarrow 0}\left[{\frac {N_{A0}\lambda _{A}}{\lambda _{B}-\lambda _{A}}}\left(e^{-\lambda _{A}t}-e^{-\lambda _{B}t}\right)\right]={\frac {N_{A0}\lambda _{A}}{0-\lambda _{A}}}\left(e^{-\lambda _{A}t}-1\right)=N_{A0}\left(1-e^{-\lambda _{A}t}\right),}</annotation>

</semantics>

</math><img src="./982ae50245eea1305c63a7b97be54ea1e2a19ccf.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:75.62ex; height:6.176ex;" alt="{\displaystyle \lim _{\lambda _{B}\rightarrow 0}\left[{\frac {N_{A0}\lambda _{A}}{\lambda _{B}-\lambda _{A}}}\left(e^{-\lambda _{A}t}-e^{-\lambda _{B}t}\right)\right]={\frac {N_{A0}\lambda _{A}}{0-\lambda _{A}}}\left(e^{-\lambda _{A}t}-1\right)=N_{A0}\left(1-e^{-\lambda _{A}t}\right),}" loading="lazy"></dd></dl>

as shown above for one decay. The solution can be found by the <a href="Integrating_factor" title="Integrating factor">integration factor</a> method, where the integrating factor is eλBt. This case is perhaps the most useful since it can derive both the one-decay equation (above) and the equation for multi-decay chains (below) more directly.

<div class="mw-heading mw-heading5"><h5 id="Chain_of_any_number_of_decays">Chain of any number of decays</h5></div>

For the general case of any number of consecutive decays in a decay chain, i.e. A1 → A2 ··· → Ai ··· → AD, where D is the number of decays and i is a dummy index (i = 1, 2, 3, ..., D), each nuclide population can be found in terms of the previous population. In this case N2 = 0, N3 = 0, ..., ND = 0. Using the above result in a recursive form:

<mfrac>

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<annotation encoding="application/x-tex">{\displaystyle {\frac {\mathrm {d} N_{j}}{\mathrm {d} t}}=-\lambda _{j}N_{j}+\lambda _{j-1}N_{(j-1)0}e^{-\lambda _{j-1}t}.}</annotation>

</semantics>

</math><img src="./d297c8b3a107a1f54865232f96cf4251593d0bcd.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:36.248ex; height:5.843ex;" alt="{\displaystyle {\frac {\mathrm {d} N_{j}}{\mathrm {d} t}}=-\lambda _{j}N_{j}+\lambda _{j-1}N_{(j-1)0}e^{-\lambda _{j-1}t}.}" loading="lazy"></dd></dl>

The general solution to the recursive problem is given by Bateman's equations:<a href="#cite_note-general_solution_of_Bateman-37">[37]</a>

<div class="equation-box" style="margin: 0 0 0 1.6em;padding: 5px; border-width:2px; border-style: solid; border-color: #0073CF; color: inherit;text-align: center; display: table">'Bateman's equations'

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<annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}N_{D}&={\frac {N_{1}(0)}{\lambda _{D}}}\sum _{i=1}^{D}\lambda _{i}c_{i}e^{-\lambda _{i}t}\\[3pt]c_{i}&=\prod _{j=1,i\neq j}^{D}{\frac {\lambda _{j}}{\lambda _{j}-\lambda _{i}}}\end{aligned}}}</annotation>

</semantics>

</math><img src="./4cd85cd77b00707ebf272a4cb25d5b2768e2ab39.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -7.338ex; width:26.899ex; height:15.843ex;" alt="{\displaystyle {\begin{aligned}N_{D}&={\frac {N_{1}(0)}{\lambda _{D}}}\sum _{i=1}^{D}\lambda _{i}c_{i}e^{-\lambda _{i}t}\\[3pt]c_{i}&=\prod _{j=1,i\neq j}^{D}{\frac {\lambda _{j}}{\lambda _{j}-\lambda _{i}}}\end{aligned}}}" loading="lazy">

</div>

<div class="mw-heading mw-heading4"><h4 id="Multiple_products">Multiple products</h4></div>

In all of the above examples, the initial nuclide decays into just one product.<a href="#cite_note-38">[38]</a> Consider the case of one initial nuclide that can decay into either of two products, that is A → B and A → C in parallel. For example, in a sample of <a href="Potassium-40" title="Potassium-40">potassium-40</a>, 89.3% of the nuclei decay to <a href="Calcium-40" class="mw-redirect" title="Calcium-40">calcium-40</a> and 10.7% to <a href="Argon-40" class="mw-redirect" title="Argon-40">argon-40</a>. We have for all time t:

<msub>

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<msub>

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<annotation encoding="application/x-tex">{\displaystyle N=N_{A}+N_{B}+N_{C}}</annotation>

</semantics>

</math><img src="./435b0bcb1bc5c003bab1641554f2446a3de8aa5d.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:20.867ex; height:2.509ex;" alt="{\displaystyle N=N_{A}+N_{B}+N_{C}}" loading="lazy"></dd></dl>

which is constant, since the total number of nuclides remains constant. Differentiating with respect to time:

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<annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}{\frac {\mathrm {d} N_{A}}{\mathrm {d} t}}&=-\left({\frac {\mathrm {d} N_{B}}{\mathrm {d} t}}+{\frac {\mathrm {d} N_{C}}{\mathrm {d} t}}\right)\\-\lambda N_{A}&=-N_{A}\left(\lambda _{B}+\lambda _{C}\right)\\\end{aligned}}}</annotation>

</semantics>

</math><img src="./42722672716dbbaff15cdba6e535700ba01e23a4.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.005ex; width:29.752ex; height:9.176ex;" alt="{\displaystyle {\begin{aligned}{\frac {\mathrm {d} N_{A}}{\mathrm {d} t}}&=-\left({\frac {\mathrm {d} N_{B}}{\mathrm {d} t}}+{\frac {\mathrm {d} N_{C}}{\mathrm {d} t}}\right)\\-\lambda N_{A}&=-N_{A}\left(\lambda _{B}+\lambda _{C}\right)\\\end{aligned}}}" loading="lazy"></dd></dl>

defining the total decay constant λ in terms of the sum of partial decay constants λB and λC:

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<annotation encoding="application/x-tex">{\displaystyle \lambda =\lambda _{B}+\lambda _{C}.}</annotation>

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</math><img src="./e95e72479f18bca1469b30a6df1fd3f51fef5390.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:13.612ex; height:2.509ex;" alt="{\displaystyle \lambda =\lambda _{B}+\lambda _{C}.}" loading="lazy"></dd></dl>

Solving this equation for NA:

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<annotation encoding="application/x-tex">{\displaystyle N_{A}=N_{A0}e^{-\lambda t}.}</annotation>

</semantics>

</math><img src="./df5b95c6a5ad1eff55fa92904d7fc465aaa95d41.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:15.376ex; height:3.009ex;" alt="{\displaystyle N_{A}=N_{A0}e^{-\lambda t}.}" loading="lazy"></dd></dl>

where NA0 is the initial number of nuclide A. When measuring the production of one nuclide, one can only observe the total decay constant λ. The decay constants λB and λC determine the probability for the decay to result in products B or C as follows:

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<annotation encoding="application/x-tex">{\displaystyle N_{B}={\frac {\lambda _{B}}{\lambda }}N_{A0}\left(1-e^{-\lambda t}\right),}</annotation>

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</math><img src="./5ef8424c8985617449660101cbc3c714fa52bc0f.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:25.968ex; height:5.509ex;" alt="{\displaystyle N_{B}={\frac {\lambda _{B}}{\lambda }}N_{A0}\left(1-e^{-\lambda t}\right),}" loading="lazy"></dd></dl>

<msub>

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<annotation encoding="application/x-tex">{\displaystyle N_{C}={\frac {\lambda _{C}}{\lambda }}N_{A0}\left(1-e^{-\lambda t}\right).}</annotation>

</semantics>

</math><img src="./6d99cc749c93f1c24ef2618d86e85608b859a1fc.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:25.971ex; height:5.509ex;" alt="{\displaystyle N_{C}={\frac {\lambda _{C}}{\lambda }}N_{A0}\left(1-e^{-\lambda t}\right).}" loading="lazy"></dd></dl>

because the fraction λB/λ of nuclei decay into B while the fraction λC/λ of nuclei decay into C.

<div class="mw-heading mw-heading3"><h3 id="Corollaries_of_laws">Corollaries of laws</h3></div>

The above equations can also be written using quantities related to the number of nuclide particles N in a sample;

<ul><li>The activity: A = λN.</li>

<li>The <a href="Amount_of_substance" title="Amount of substance">amount of substance</a>: n = N/NA.</li>

where NA = 6.02214076×1023 mol−1‍<a href="#cite_note-physconst-NA-39">[39]</a> is the <a href="Avogadro_constant" title="Avogadro constant">Avogadro constant</a>, M is the <a href="Molar_mass" title="Molar mass">molar mass</a> of the substance in kg/mol, and the amount of the substance n is in <a href="Mole_(unit)" title="Mole (unit)">moles</a>.

<div class="mw-heading mw-heading3"><h3 id="Decay_timing:_definitions_and_relations">Decay timing: definitions and relations</h3></div>

<div class="mw-heading mw-heading4"><h4 id="Time_constant_and_mean-life">Time constant and mean-life</h4></div>

For the one-decay solution A → B:

<msub>

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</msub>

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</msub>

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<annotation encoding="application/x-tex">{\displaystyle N=N_{0}\,e^{-{\lambda }t}=N_{0}\,e^{-t/\tau },\,\!}</annotation>

</semantics>

</math><img src="./26927776582294591c8d1d4460fb7d035cd183f9.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.387ex; width:24.916ex; height:3.176ex;" alt="{\displaystyle N=N_{0}\,e^{-{\lambda }t}=N_{0}\,e^{-t/\tau },\,\!}" loading="lazy"></dd></dl>

the equation indicates that the decay constant λ has units of t−1, and can thus also be represented as 1/τ, where τ is a characteristic time of the process called the <a href="Time_constant" title="Time constant">time constant</a>.

In a radioactive decay process, this time constant is also the <a href="Mean_lifetime" class="mw-redirect" title="Mean lifetime">mean lifetime</a> for decaying atoms. Each atom "lives" for a finite amount of time before it decays, and it may be shown that this mean lifetime is the <a href="Arithmetic_mean" title="Arithmetic mean">arithmetic mean</a> of all the atoms' lifetimes, and that it is τ, which again is related to the decay constant as follows:

<mfrac>

</mfrac>

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<annotation encoding="application/x-tex">{\displaystyle \tau ={\frac {1}{\lambda }}.}</annotation>

</semantics>

</math><img src="./b76039d8bdae097486ea0430b191f607a1873231.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:7.139ex; height:5.343ex;" alt="{\displaystyle \tau ={\frac {1}{\lambda }}.}" loading="lazy"></dd></dl>

This form is also true for two-decay processes simultaneously A → B + C, inserting the equivalent values of decay constants (as given above)

<msub>

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</msub>

<msub>

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<annotation encoding="application/x-tex">{\displaystyle \lambda =\lambda _{B}+\lambda _{C}\,}</annotation>

</semantics>

</math><img src="./9f74e4913f1161959a08c0512b7b3bc8c3164a24.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:13.352ex; height:2.509ex;" alt="{\displaystyle \lambda =\lambda _{B}+\lambda _{C}\,}" loading="lazy"></dd></dl>

into the decay solution leads to:

<mfrac>

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<msub>

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</msub>

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</msub>

<mfrac>

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</mrow>

<annotation encoding="application/x-tex">{\displaystyle {\frac {1}{\tau }}=\lambda =\lambda _{B}+\lambda _{C}={\frac {1}{\tau _{B}}}+{\frac {1}{\tau _{C}}}\,}</annotation>

</semantics>

</math><img src="./75363f26f174d74ffa721d5d98fda34a4a50fa80.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:31.093ex; height:5.509ex;" alt="{\displaystyle {\frac {1}{\tau }}=\lambda =\lambda _{B}+\lambda _{C}={\frac {1}{\tau _{B}}}+{\frac {1}{\tau _{C}}}\,}" loading="lazy"></dd></dl>

<div role="note" class="hatnote navigation-not-searchable">For related derivations with some further details, see <a href="Half-life" title="Half-life">half-life</a>.</div>

A more commonly used parameter is the half-life T1/2. Given a sample of a particular radionuclide, the half-life is the time taken for half the radionuclide's atoms to decay. For the case of one-decay nuclear reactions:

<msub>

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<annotation encoding="application/x-tex">{\displaystyle N=N_{0}\,e^{-{\lambda }t}=N_{0}\,e^{-t/\tau },\,\!}</annotation>

</semantics>

</math><img src="./26927776582294591c8d1d4460fb7d035cd183f9.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.387ex; width:24.916ex; height:3.176ex;" alt="{\displaystyle N=N_{0}\,e^{-{\lambda }t}=N_{0}\,e^{-t/\tau },\,\!}" loading="lazy"></dd></dl>

the half-life is related to the decay constant as follows: set N = N0/2 and t = T1/2 to obtain

<msub>

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</mrow>

</msub>

<mfrac>

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</mrow>

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</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle t_{1/2}={\frac {\ln 2}{\lambda }}=\tau \ln 2.}</annotation>

</semantics>

</math><img src="./937374af2b4db7f946bd223a44c2559a8c034e94.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:19.785ex; height:5.509ex;" alt="{\displaystyle t_{1/2}={\frac {\ln 2}{\lambda }}=\tau \ln 2.}" loading="lazy"></dd></dl>

This relationship between the half-life and the decay constant shows that highly radioactive substances are quickly spent, while those that radiate weakly endure longer. <a href="List_of_radioactive_nuclides_by_half-life" title="List of radioactive nuclides by half-life">Half-lives of known radionuclides</a> vary by almost 54 orders of magnitude, from more than 2.25(9)×1024 years (6.9×1031 sec) for the very nearly stable nuclide <a href="Isotopes_of_tellurium" title="Isotopes of tellurium">128Te</a>, to 8.6(6)×10−23 seconds for the highly unstable nuclide <a href="Isotopes_of_hydrogen" title="Isotopes of hydrogen">5H</a>.<a href="#cite_note-NUBASE2020-28">[28]</a>

The factor of ln(2) in the above relations results from the fact that the concept of "half-life" is merely a way of selecting a different base other than the natural base e for the lifetime expression. The time constant τ is the e −1 -life, the time until only 1/e remains, about 36.8%, rather than the 50% in the half-life of a radionuclide. Thus, τ is longer than t1/2. The following equation can be shown to be valid:

<msub>

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</msub>

<msup>

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</msup>

<msub>

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</mrow>

<annotation encoding="application/x-tex">{\displaystyle N(t)=N_{0}\,e^{-t/\tau }=N_{0}\,2^{-t/t_{1/2}}.\,\!}</annotation>

</semantics>

</math><img src="./e6102327b6aa6ef4aad8555050b6afefcc1dd823.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-right: -0.387ex; width:30.267ex; height:3.343ex;" alt="{\displaystyle N(t)=N_{0}\,e^{-t/\tau }=N_{0}\,2^{-t/t_{1/2}}.\,\!}" loading="lazy"></dd></dl>

Since radioactive decay is exponential with a constant probability, each process could as easily be described with a different constant time period that (for example) gave its "(1/3)-life" (how long until only 1/3 is left) or "(1/10)-life" (a time period until only 10% is left), and so on. Thus, the choice of τ and t1/2 for marker-times, are only for convenience, and from convention. They reflect a fundamental principle only in so much as they show that the same proportion of a given radioactive substance will decay, during any time-period that one chooses.

Mathematically, the nth life for the above situation would be found in the same way as above—by setting N = N0/n, t = T1/n and substituting into the decay solution to obtain

<msub>

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</mrow>

</msub>

<mfrac>

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</mstyle>

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<annotation encoding="application/x-tex">{\displaystyle t_{1/n}={\frac {\ln n}{\lambda }}=\tau \ln n.}</annotation>

</semantics>

</math><img src="./adedff1071f83854a0f6fddfcde6af18ae384f83.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:20.413ex; height:5.509ex;" alt="{\displaystyle t_{1/n}={\frac {\ln n}{\lambda }}=\tau \ln n.}" loading="lazy"></dd></dl>

<div class="mw-heading mw-heading3"><h3 id="Example_for_carbon-14">Example for carbon-14</h3></div>

<a href="Carbon-14" title="Carbon-14">Carbon-14</a> has a half-life of 5700(30) years<a href="#cite_note-NUBASE2020-28">[28]</a> and a decay rate of 14 disintegrations per minute (dpm) per gram of natural carbon.

If an artifact is found to have radioactivity of 4 dpm per gram of its present C, we can find the approximate age of the object using the above equation:

<msub>

</mrow>

</msub>

<msup>

</mrow>

</mrow>

</msup>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle N=N_{0}\,e^{-t/\tau },}</annotation>

</semantics>

</math><img src="./a3d1ed36cc35720df145e80a3b7de5cbc5d5b7fe.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:13.976ex; height:3.176ex;" alt="{\displaystyle N=N_{0}\,e^{-t/\tau },}" loading="lazy"></dd></dl>

where:

<mtr>

<mtd>

<mfrac>

<msub>

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</mfrac>

</mrow>

</mtd>

<mtd>

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<mfrac>

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<mtext> years</mtext>

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<mtd>

</mtd>

<mtd>

<mfrac>

<msub>

</mrow>

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<mtext> years</mtext>

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<annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}{\frac {N}{N_{0}}}&=4/14\approx 0.286,\\\tau &={\frac {T_{1/2}}{\ln 2}}\approx 8267{\text{ years}},\\t&=-\tau \,\ln {\frac {N}{N_{0}}}\approx 10356{\text{ years}}.\end{aligned}}}</annotation>

</semantics>

</math><img src="./a27e637cbf673d28d41e6082bda888934630202c.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -8.171ex; width:32.862ex; height:17.509ex;" alt="{\displaystyle {\begin{aligned}{\frac {N}{N_{0}}}&=4/14\approx 0.286,\\\tau &={\frac {T_{1/2}}{\ln 2}}\approx 8267{\text{ years}},\\t&=-\tau \,\ln {\frac {N}{N_{0}}}\approx 10356{\text{ years}}.\end{aligned}}}" loading="lazy"></dd></dl>

<div class="mw-heading mw-heading3"><h3 id="Changing_rates">Changing rates</h3></div>

The radioactive decay modes of electron capture and internal conversion are known to be slightly sensitive to chemical and environmental effects that change the electronic structure of the atom, which in turn affects the presence of 1s and 2s electrons that participate in the decay process. A small number of nuclides are affected.<a href="#cite_note-40">[40]</a> For example, <a href="Chemical_bonds" class="mw-redirect" title="Chemical bonds">chemical bonds</a> can affect the rate of electron capture to a small degree (in general, less than 1%) depending on the proximity of electrons to the nucleus. In 7Be, a difference of 0.9% has been observed between half-lives in metallic and insulating environments.<a href="#cite_note-WangYan2006-41">[41]</a> This relatively large effect is because beryllium is a small atom whose valence electrons are in 2s <a href="Atomic_orbital" title="Atomic orbital">atomic orbitals</a>, which are subject to electron capture in 7Be because (like all s atomic orbitals in all atoms) they naturally penetrate into the nucleus.

In 1992, Jung et al. of the Darmstadt Heavy-Ion Research group observed an accelerated β− decay of 163Dy66+. Although neutral 163Dy is a stable isotope, the fully ionized 163Dy66+ undergoes β− decay <a href="Bound-state_beta_decay" class="mw-redirect" title="Bound-state beta decay">into the K and L shells</a> to 163Ho66+ with a half-life of 47 days.<a href="#cite_note-JungBosch1992-42">[42]</a>

<a href="Rhenium-187" class="mw-redirect" title="Rhenium-187">Rhenium-187</a> is another spectacular example. 187Re normally undergoes beta decay to 187Os with a half-life of 41.6 billion years,<a href="#cite_note-43">[43]</a> but studies using fully ionised 187<a href="Rhenium" title="Rhenium">Re</a> atoms (bare nuclei) have found that this can decrease to only 32.9 years.<a href="#cite_note-44">[44]</a> This is attributed to "<a href="Beta_decay#Bound-state_β−_decay" title="Beta decay">bound-state β− decay</a>" of the fully ionised atom – the electron is emitted into the "K-shell" (1s atomic orbital), which cannot occur for neutral atoms in which all low-lying bound states are occupied.<a href="#cite_note-Bosch1996-45">[45]</a>

A number of experiments have found that decay rates of other modes of artificial and naturally occurring radioisotopes are, to a high degree of precision, unaffected by external conditions such as temperature, pressure, the chemical environment, and electric, magnetic, or gravitational fields.<a href="#cite_note-46">[46]</a> Comparison of laboratory experiments over the last century, studies of the Oklo <a href="Natural_nuclear_fission_reactor" title="Natural nuclear fission reactor">natural nuclear reactor</a> (which exemplified the effects of thermal neutrons on nuclear decay), and astrophysical observations of the luminosity decays of distant supernovae (which occurred far away so the light has taken a great deal of time to reach us), for example, strongly indicate that unperturbed decay rates have been constant (at least to within the limitations of small experimental errors) as a function of time as well.

Recent results suggest the possibility that decay rates might have a weak dependence on environmental factors. It has been suggested that measurements of decay rates of <a href="Silicon-32" class="mw-redirect" title="Silicon-32">silicon-32</a>, <a href="Manganese-54" class="mw-redirect" title="Manganese-54">manganese-54</a>, and <a href="Radium-226" title="Radium-226">radium-226</a> exhibit small seasonal variations (of the order of 0.1%).<a href="#cite_note-47">[47]</a><a href="#cite_note-48">[48]</a><a href="#cite_note-49">[49]</a> However, such measurements are highly susceptible to systematic errors, and a subsequent paper<a href="#cite_note-50">[50]</a> has found no evidence for such correlations in seven other isotopes (22Na, 44Ti, 108Ag, 121Sn, 133Ba, 241Am, 238Pu), and sets upper limits on the size of any such effects. The decay of <a href="Radon-222" title="Radon-222">radon-222</a> was once reported to exhibit large 4% peak-to-peak seasonal variations (see plot),<a href="#cite_note-SturrockSteinitz2012-51">[51]</a> which were proposed to be related to either <a href="Solar_flare" title="Solar flare">solar flare</a> activity or the distance from the Sun, but detailed analysis of the experiment's design flaws, along with comparisons to other, much more stringent and systematically controlled, experiments refute this claim.<a href="#cite_note-52">[52]</a>

<div class="mw-heading mw-heading4"><h4 id="GSI_anomaly">GSI anomaly</h4></div>

<div role="note" class="hatnote navigation-not-searchable">Main article: <a href="GSI_anomaly" title="GSI anomaly">GSI anomaly</a></div>

An unexpected series of experimental results for the rate of decay of heavy <a href="Highly_charged_ion" title="Highly charged ion">highly charged</a> radioactive <a href="Ion" title="Ion">ions</a> circulating in a <a href="Storage_ring" title="Storage ring">storage ring</a> has provoked theoretical activity in an effort to find a convincing explanation. The rates of <a href="Weak_interaction" title="Weak interaction">weak</a> decay of two radioactive species with half-lives of about 40 s and 200 s are found to have a significant <a href="Oscillation" title="Oscillation">oscillatory</a> <a href="Modulation" class="mw-redirect" title="Modulation">modulation</a>, with a period of about 7 s.<a href="#cite_note-KienleBosch2013-53">[53]</a>

The observed phenomenon is known as the <a href="GSI_anomaly" title="GSI anomaly">GSI anomaly</a>, as the storage ring is a facility at the <a href="GSI_Helmholtz_Centre_for_Heavy_Ion_Research" title="GSI Helmholtz Centre for Heavy Ion Research">GSI Helmholtz Centre for Heavy Ion Research</a> in <a href="Darmstadt" title="Darmstadt">Darmstadt</a>, <a href="Germany" title="Germany">Germany</a>. As the decay process produces an <a href="Electron_neutrino" title="Electron neutrino">electron neutrino</a>, some of the proposed explanations for the observed rate oscillation invoke neutrino properties. Initial ideas related to <a href="Neutrino#Flavor_oscillations" title="Neutrino">flavour oscillation</a> met with skepticism.<a href="#cite_note-Giunti2009-54">[54]</a> A more recent proposal involves mass differences between neutrino mass <a href="Eigenstates" class="mw-redirect" title="Eigenstates">eigenstates</a>.<a href="#cite_note-Gal2016-55">[55]</a>

<div class="mw-heading mw-heading2"><h2 id="Nuclear_processes">Nuclear processes</h2></div>

A nuclide is considered to "exist" if it has a half-life greater than 2x10−14s. This is an arbitrary boundary; shorter half-lives are considered resonances, such as a system undergoing a nuclear reaction. This time scale is characteristic of the <a href="Strong_interaction" title="Strong interaction">strong interaction</a> which creates the <a href="Nuclear_force" title="Nuclear force">nuclear force</a>. Only nuclides are considered to decay and produce radioactivity.<a href="#cite_note-Pfutzner2012-56">[56]</a>: 568

Nuclides can be stable or unstable. Unstable nuclides decay, possibly in several steps, until they become stable. There are 251 known <a href="Stable_nuclide" title="Stable nuclide">stable nuclides</a>. The number of unstable nuclides discovered has grown, with about 3000 known in 2006.<a href="#cite_note-Pfutzner2012-56">[56]</a>

The most common and consequently historically the most important forms of natural radioactive decay involve the emission of alpha-particles, beta-particles, and gamma rays. Each of these correspond to a <a href="Fundamental_interaction" title="Fundamental interaction">fundamental interaction</a> predominantly responsible for the radioactivity:<a href="#cite_note-PaisInwardBound-57">[57]</a>: 142

<ul><li><a href="Alpha-decay" class="mw-redirect" title="Alpha-decay">alpha-decay</a> -> <a href="Strong_interaction" title="Strong interaction">strong interaction</a>,</li>

<li><a href="Beta-decay" class="mw-redirect" title="Beta-decay">beta-decay</a> -> <a href="Weak_interaction" title="Weak interaction">weak interaction</a>,</li>

<li><a href="Gamma-decay" class="mw-redirect" title="Gamma-decay">gamma-decay</a> -> <a href="Electromagnetism" title="Electromagnetism">electromagnetism</a>.</li></ul>

In alpha decay, a particle containing two protons and two neutrons, equivalent to a He nucleus, breaks out of the parent nucleus. The process represents a competition between the electromagnetic repulsion between the protons in the nucleus and attractive <a href="Nuclear_force" title="Nuclear force">nuclear force</a>, a residual of the strong interaction. The alpha particle is an especially strongly bound nucleus, helping it win the competition more often.<a href="#cite_note-Ohanian1994-58">[58]</a>: 872 However some nuclei break up or <a href="Nuclear_fission" title="Nuclear fission">fission</a> into larger particles and artificial nuclei decay with the emission of

single protons, double protons, and other combinations.<a href="#cite_note-Pfutzner2012-56">[56]</a>

Beta decay transforms a neutron into proton or vice versa. When a neutron inside a parent nuclide decays to a proton, an electron, a <a href="Anti-neutrino" class="mw-redirect" title="Anti-neutrino">anti-neutrino</a>, and nuclide with high atomic number results. When a proton in a parent nuclide transforms to a neutron, a <a href="Positron" title="Positron">positron</a>, a <a href="Neutrino" title="Neutrino">neutrino</a>, and nuclide with a lower atomic number results. These changes are a direct manifestation of the weak interaction.<a href="#cite_note-Ohanian1994-58">[58]</a>: 874

Gamma decay resembles other kinds of electromagnetic emission: it corresponds to transitions between an excited quantum state and lower energy state. Any of the particle decay mechanisms often leave the daughter in an excited state, which then decays via gamma emission.<a href="#cite_note-Ohanian1994-58">[58]</a>: 876

Other forms of decay include <a href="Neutron_emission" title="Neutron emission">neutron emission</a>, <a href="Electron_capture" title="Electron capture">electron capture</a>, <a href="Internal_conversion" title="Internal conversion">internal conversion</a>, <a href="Cluster_decay" title="Cluster decay">cluster decay</a>.<a href="#cite_note-59">[59]</a>

<div class="mw-heading mw-heading2"><h2 id="Hazard_warning_signs">Hazard warning signs</h2></div>

<div class="gallerytext">The trefoil symbol used to warn of presence of radioactive material or ionising radiation</div>

</li>

<div class="gallerytext">2007 ISO radioactivity <a href="Hazard_symbol" title="Hazard symbol">hazard symbol</a> intended for IAEA Category 1, 2 and 3 sources defined as dangerous sources capable of death or serious injury<a href="#cite_note-60">[60]</a></div>

</li>

<div class="gallerytext">One of several dangerous goods transport classification signs for radioactive materials</div>

</li>

</ul>

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<ul><li><a href="Actinides_in_the_environment" title="Actinides in the environment">Actinides in the environment</a></li>

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<li><a href="Transient_equilibrium" title="Transient equilibrium">Transient equilibrium</a></li></ul>

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<div class="mw-heading mw-heading2"><h2 id="Notes">Notes</h2></div>

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<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>

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<li id="cite_note-Pfutzner2012-56">^ <a href="#cite_ref-Pfutzner2012_56-0">a</a> <a href="#cite_ref-Pfutzner2012_56-1">b</a> <a href="#cite_ref-Pfutzner2012_56-2">c</a> <cite id="CITEREFPfütznerKarnyGrigorenkoRiisager2012" class="citation journal cs1">Pfützner, M.; Karny, M.; Grigorenko, L. V.; Riisager, K. (30 April 2012). <a rel="nofollow" class="external text" href="https://link.aps.org/doi/10.1103/RevModPhys.84.567">"Radioactive decays at limits of nuclear stability"</a>. Reviews of Modern Physics. 84 (2): 567–619. <a href="ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<a rel="nofollow" class="external text" href="https://arxiv.org/abs/1111.0482">1111.0482</a>. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2012RvMP...84..567P">2012RvMP...84..567P</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FRevModPhys.84.567">10.1103/RevModPhys.84.567</a>. <a href="ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0034-6861">0034-6861</a>.</cite>

</li>

<cite id="CITEREFPais2002" class="citation book cs1">Pais, Abraham (2002). Inward bound: of matter and forces in the physical world (Reprint ed.). Oxford: Clarendon Press [u.a.] <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0-19-851997-3</bdi>.</cite>

</li>

<li id="cite_note-Ohanian1994-58">^ <a href="#cite_ref-Ohanian1994_58-0">a</a> <a href="#cite_ref-Ohanian1994_58-1">b</a> <a href="#cite_ref-Ohanian1994_58-2">c</a> <cite id="CITEREFOhanian1994" class="citation book cs1">Ohanian, Hans C. (1994). Principles of physics (1 ed.). New York: W.W. Norton. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0-393-95773-0</bdi>. <a href="OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/1311044116">1311044116</a>.</cite>

</li>

<li id="cite_note-59"><a href="#cite_ref-59">^</a> <cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.arpansa.gov.au/understanding-radiation/what-is-radiation/ionising-radiation/radiation-decay">"Other types of radioactive decay"</a>. Australian Radiation Protection and Nuclear Safety Agency.</cite>

</li>

<li id="cite_note-60"><a href="#cite_ref-60">^</a> <a rel="nofollow" class="external text" href="http://www.iaea.org/newscenter/news/2007/radiationsymbol.html">IAEA news release Feb 2007</a>

</li>

</ol></div></div>

<div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2></div>

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<div class="side-box-text plainlist">The Wikibook <a href="https://en.wikibooks.org/wiki/Historical_Geology" class="extiw external" title="wikibooks:Historical Geology">Historical Geology</a> has a page on the topic of: <a href="https://en.wikibooks.org/wiki/Historical_Geology/Radioactive_decay" class="extiw external" title="wikibooks:Historical Geology/Radioactive decay">Radioactive decay</a></div></div>

</div>

<div class="side-box-text plainlist">Look up <a href="https://en.wiktionary.org/wiki/radioactivity" class="extiw external" title="wiktionary:radioactivity">radioactivity</a> in Wiktionary, the free dictionary.</div></div>

</div>

<div class="side-box-text plainlist">English <a href="Wikisource" title="Wikisource">Wikisource</a> has original text related to this article:

<div style="margin-left: 10px;"><a href="https://en.wikisource.org/wiki/en:1911_Encyclop%C3%A6dia_Britannica/Radioactivity" class="extiw external" title="s:en:1911 Encyclopædia Britannica/Radioactivity">Radioactivity</a></div></div></div>

</div>

<ul><li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20130108122246/http://ie.lbl.gov/toi/abouttoi.htm">The Lund/LBNL Nuclear Data Search</a> – Contains tabulated information on radioactive decay types and energies.</li>

<li><a rel="nofollow" class="external text" href="http://www.radiochemistry.org/nomenclature/">Nomenclature of nuclear chemistry</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20150212024753/http://www.radiochemistry.org/nomenclature/">Archived</a> 12 February 2015 at the <a href="Wayback_Machine" title="Wayback Machine">Wayback Machine</a></li>

<li><a rel="nofollow" class="external text" href="http://www.iem-inc.com/prhlfr.html">Specific activity and related topics</a>.</li>

<li><a rel="nofollow" class="external text" href="http://www-nds.iaea.org/livechart">The Live Chart of Nuclides – IAEA</a></li>

<li><a rel="nofollow" class="external text" href="http://www.nndc.bnl.gov/chart/">Interactive Chart of Nuclides</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20181010070007/http://www.nndc.bnl.gov/chart/">Archived</a> 10 October 2018 at the <a href="Wayback_Machine" title="Wayback Machine">Wayback Machine</a></li>

<li><a rel="nofollow" class="external text" href="http://www.radiationanswers.org/">Health Physics Society Public Education Website</a></li>

<li><cite id="CITEREFBeach1914" class="citation encyclopaedia cs1">Beach, Chandler B., ed. (1914). <a class="external text external" href="https://en.wikisource.org/wiki/The_New_Student%27s_Reference_Work/Becquerel_Rays">"Becquerel Rays" </a>. <a class="external text external" href="https://en.wikisource.org/wiki/The_New_Student%27s_Reference_Work">The New Student's Reference Work </a>. Chicago: F. E. Compton and Co.</cite></li>

<li><a rel="nofollow" class="external text" href="http://alsos.wlu.edu/qsearch.aspx?browse=science/Radioactivity">Annotated bibliography for radioactivity from the Alsos Digital Library for Nuclear Issues</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20101007075539/http://alsos.wlu.edu/qsearch.aspx?browse=science%2FRadioactivity">Archived</a> 7 October 2010 at the <a href="Wayback_Machine" title="Wayback Machine">Wayback Machine</a></li>

<li>"Henri Becquerel: The Discovery of Radioactivity", Becquerel's 1896 articles online and analyzed on <a rel="nofollow" class="external text" href="http://www.bibnum.education.fr/physique/radioactivite/sur-les-radiations-invisibles-emises-par-les-corps-phosphorescents">BibNum</a> [click 'à télécharger' for English version].</li>

<li>"Radioactive change", Rutherford & Soddy article (1903), online and analyzed on <a rel="nofollow" class="external text" href="http://www.bibnum.education.fr/physique/radioactivite/la-transformation-radioactive">Bibnum</a> [click 'à télécharger' for English version]</li></ul>

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</style></div><div role="navigation" class="navbox" aria-labelledby="Radiation_(physics_and_health)439" style="padding:3px"><table class="nowraplinks mw-collapsible uncollapsed navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Radiation_(physics_and_health)439" style="font-size:114%;margin:0 4em"><a href="Radiation" title="Radiation">Radiation</a> (physics and health)</div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Main articles</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Non-ionizing_radiation" title="Non-ionizing radiation">Non-ionizing radiation</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Acoustic_radiation_force" title="Acoustic radiation force">Acoustic radiation force</a></li>

<li><a href="Infrared" title="Infrared">Infrared</a></li>

<li><a href="Light" title="Light">Light</a></li>

<li><a href="Starlight" title="Starlight">Starlight</a></li>

<li><a href="Sunlight" title="Sunlight">Sunlight</a></li>

<li><a href="Microwave" title="Microwave">Microwave</a></li>

<li><a href="Radio_wave" title="Radio wave">Radio waves</a></li>

<li><a href="Ultraviolet" title="Ultraviolet">Ultraviolet</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Ionizing_radiation" title="Ionizing radiation">Ionizing radiation</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul>

<li><a href="Cluster_decay" title="Cluster decay">Cluster decay</a></li>

<li><a href="Background_radiation" title="Background radiation">Background radiation</a></li>

<li><a href="Alpha_particle" title="Alpha particle">Alpha particle</a></li>

<li><a href="Beta_particle" title="Beta particle">Beta particle</a></li>

<li><a href="Gamma_ray" title="Gamma ray">Gamma ray</a></li>

<li><a href="Cosmic_ray" title="Cosmic ray">Cosmic ray</a></li>

<li><a href="Neutron_radiation" title="Neutron radiation">Neutron radiation</a></li>

<li><a href="Nuclear_fission" title="Nuclear fission">Nuclear fission</a></li>

<li><a href="Nuclear_fusion" title="Nuclear fusion">Nuclear fusion</a></li>

<li><a href="Nuclear_reactor" title="Nuclear reactor">Nuclear reactors</a></li>

<li><a href="Nuclear_weapon" title="Nuclear weapon">Nuclear weapons</a></li>

<li><a href="Particle_accelerator" title="Particle accelerator">Particle accelerators</a></li>

<li><a href="Radionuclide" title="Radionuclide">Radioactive materials</a></li>

</div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Earth's_energy_budget" title="Earth's energy budget">Earth's energy budget</a></li>

<li><a href="Electromagnetic_radiation" title="Electromagnetic radiation">Electromagnetic radiation</a></li>

<li><a href="Synchrotron_radiation" title="Synchrotron radiation">Synchrotron radiation</a></li>

<li><a href="Thermal_radiation" title="Thermal radiation">Thermal radiation</a></li>

<li><a href="Black-body_radiation" title="Black-body radiation">Black-body radiation</a></li>

<li><a href="Particle_radiation" title="Particle radiation">Particle radiation</a></li>

<li><a href="Gravitational_radiation" class="mw-redirect" title="Gravitational radiation">Gravitational radiation</a></li>

<li><a href="Cosmic_background_radiation" title="Cosmic background radiation">Cosmic background radiation</a></li>

<li><a href="Cherenkov_radiation" title="Cherenkov radiation">Cherenkov radiation</a></li>

<li><a href="Askaryan_radiation" title="Askaryan radiation">Askaryan radiation</a></li>

<li><a href="Bremsstrahlung" title="Bremsstrahlung">Bremsstrahlung</a></li>

<li><a href="Unruh_radiation" class="mw-redirect" title="Unruh radiation">Unruh radiation</a></li>

<li><a href="Dark_radiation" title="Dark radiation">Dark radiation</a></li>

<li><a href="Radiation_exposure" title="Radiation exposure">Radiation exposure</a></li></ul>

</div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Radiation and health</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li>Radiation syndrome

<ul><li><a href="Acute_radiation_syndrome" title="Acute radiation syndrome">acute</a></li>

<li><a href="Chronic_radiation_syndrome" title="Chronic radiation syndrome">chronic</a></li></ul></li>

<li><a href="Health_physics" title="Health physics">Health physics</a></li>

<li><a href="Dosimetry" title="Dosimetry">Dosimetry</a></li>

<li><a href="Electromagnetic_radiation_and_health" title="Electromagnetic radiation and health">Electromagnetic radiation and health</a></li>

<li><a href="Laser_safety" title="Laser safety">Laser safety</a></li>

<li><a href="Lasers_and_aviation_safety" title="Lasers and aviation safety">Lasers and aviation safety</a></li>

<li><a href="Medical_radiography" class="mw-redirect" title="Medical radiography">Medical radiography</a></li>

<li><a href="Radiation_protection" title="Radiation protection">Radiation protection</a></li>

<li><a href="Radiation_therapy" title="Radiation therapy">Radiation therapy</a></li>

<li><a href="Radiation_damage" title="Radiation damage">Radiation damage</a></li>

<li><a href="Radioactivity_in_the_life_sciences" title="Radioactivity in the life sciences">Radioactivity in the life sciences</a></li>

<li><a href="Radioactive_contamination" title="Radioactive contamination">Radioactive contamination</a></li>

<li><a href="Radiobiology" title="Radiobiology">Radiobiology</a></li>

<li><a href="Sievert" title="Sievert">Biological dose units and quantities</a></li>

<li><a href="Wireless_device_radiation_and_health" title="Wireless device radiation and health">Wireless device radiation and health</a></li>

<li><a href="Wireless_electronic_devices_and_health" class="mw-redirect" title="Wireless electronic devices and health">Wireless electronic devices and health</a></li>

<li><a href="Heat_transfer" title="Heat transfer">Radiation heat-transfer</a></li>

<li><a href="Linear_energy_transfer" title="Linear energy transfer">Linear energy transfer</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Radiation incidents</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="List_of_civilian_radiation_accidents" title="List of civilian radiation accidents">List of civilian radiation accidents</a></li>

<li><a href="1996_San_Juan_de_Dios_radiotherapy_accident" title="1996 San Juan de Dios radiotherapy accident">1996 Costa Rica accident</a></li>

<li><a href="Goi%C3%A2nia_accident" title="Goiânia accident">1987 Goiânia accident</a></li>

<li><a href="1984_Moroccan_radiation_accident" title="1984 Moroccan radiation accident">1984 Moroccan accident</a></li>

<li><a href="1990_Clinic_of_Zaragoza_radiotherapy_accident" class="mw-redirect" title="1990 Clinic of Zaragoza radiotherapy accident">1990 Zaragoza accident</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related articles</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<li><a href="Nuclear_physics" title="Nuclear physics">Nuclear physics</a></li>

<li><a href="Radioactive_source" title="Radioactive source">Radioactive source</a></li>

<li><a href="Radiation_hardening" title="Radiation hardening">Radiation hardening</a></li></ul>

</div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div></div></td></tr></tbody></table></div>

<div class="navbox-styles"></div><div role="navigation" class="navbox" aria-labelledby="Marie_and_Pierre_Curie129" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Marie_and_Pierre_Curie129" style="font-size:114%;margin:0 4em"><a href="Marie_Curie" title="Marie Curie"> Marie</a> and <a href="Pierre_Curie" title="Pierre Curie"> Pierre</a> Curie</div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Discoveries</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Curie's_law" title="Curie's law">Curie's law</a></li>

<li><a href="Curie%E2%80%93Weiss_law" title="Curie–Weiss law">Curie–Weiss law</a></li>

<li><a href="Curie_temperature" title="Curie temperature">Curie temperature</a></li>

<li><a href="Mean-field_theory" title="Mean-field theory">Mean-field theory</a></li>

<li><a href="Piezoelectricity" title="Piezoelectricity">Piezoelectricity</a></li>

<li><a href="Polonium" title="Polonium">Polonium</a></li>

<li><a href="Radium" title="Radium">Radium</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Publications</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Curie's_principle" title="Curie's principle">Curie's principle</a></li>

<li><a href="Treatise_on_Radioactivity" title="Treatise on Radioactivity">Treatise on Radioactivity</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Museums</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Maria_Sk%C5%82odowska-Curie_Museum" title="Maria Skłodowska-Curie Museum">Maria Skłodowska-Curie Museum</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Curie_family" title="Curie family">Family</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Ir%C3%A8ne_Joliot-Curie" title="Irène Joliot-Curie">Irène Joliot-Curie</a> (daughter)</li>

<li><a href="%C3%88ve_Curie" title="Ève Curie">Ève Curie</a> (daughter)</li>

<li><a href="H%C3%A9l%C3%A8ne_Langevin-Joliot" title="Hélène Langevin-Joliot">Hélène Langevin-Joliot</a> (granddaughter)</li>

<li><a href="Pierre_Joliot" title="Pierre Joliot">Pierre Joliot</a> (grandson)</li>

<li><a href="Jacques_Curie" title="Jacques Curie">Jacques Curie</a> (Pierre's brother)</li>

<li><a href="Fr%C3%A9d%C3%A9ric_Joliot-Curie" title="Frédéric Joliot-Curie">Frédéric Joliot-Curie</a> (son-in-law)</li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Namesakes</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Curie_Institute_(Paris)" title="Curie Institute (Paris)">Curie Institute</a></li>

<li><a href="Curie_(unit)" title="Curie (unit)">Curie</a></li>

<li><a href="Curium" title="Curium">Curium</a></li>

<li><a href="IEEE_Marie_Sklodowska-Curie_Award" title="IEEE Marie Sklodowska-Curie Award">IEEE Marie Sklodowska-Curie Award</a></li>

<li><a href="Marie_Curie_Medal" class="mw-redirect" title="Marie Curie Medal">Marie Curie Medal</a></li>

<li><a href="Maria_Sk%C5%82odowska-Curie_Bridge%2C_Warsaw" title="Maria Skłodowska-Curie Bridge, Warsaw">Maria Skłodowska-Curie Bridge</a></li>

<li><a href="Maria_Sk%C5%82odowska-Curie_Park" title="Maria Skłodowska-Curie Park">Maria Skłodowska-Curie Park</a></li>

<li><a href="Maria_Curie-Sk%C5%82odowska_University" title="Maria Curie-Skłodowska University">Maria Curie-Skłodowska University</a></li>

<li><a href="Pierre_and_Marie_Curie_University" title="Pierre and Marie Curie University">Pierre and Marie Curie University</a></li>

<li><a href="Maria_Sk%C5%82odowska-Curie_National_Research_Institute_of_Oncology" title="Maria Skłodowska-Curie National Research Institute of Oncology">Maria Skłodowska-Curie National Research Institute of Oncology</a></li>

<li><a href="Curie_Island" title="Curie Island">Curie Island</a></li>

<li><a href="7000_Curie" class="mw-redirect" title="7000 Curie">7000 Curie</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Depictions</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Maria_Sk%C5%82odowska-Curie_Monument_(Lublin)" title="Maria Skłodowska-Curie Monument (Lublin)">Maria Skłodowska-Curie Monument in Lublin</a></li>

<li><a href="Maria_Sk%C5%82odowska-Curie_Monument_(Downtown%2C_Warsaw)" title="Maria Skłodowska-Curie Monument (Downtown, Warsaw)">Maria Skłodowska-Curie Monument in Warsaw (Downtown)</a></li>

<li><a href="Maria_Sk%C5%82odowska-Curie_Monument_(Ochota)" title="Maria Skłodowska-Curie Monument (Ochota)">Maria Skłodowska-Curie Monument in Warsaw (Ochota)</a></li>

<li><a href="Marie_Curie_Gargoyle" title="Marie Curie Gargoyle">Marie Curie Gargoyle</a></li>

<li><a href="Maria_Sk%C5%82odowska-Curie_Medallion" title="Maria Skłodowska-Curie Medallion">Maria Skłodowska-Curie Medallion</a></li>

<li><a href="Madame_Curie_(film)" title="Madame Curie (film)">Madame Curie</a> (1943 film)</li>

<li><a href="Les_Palmes_de_M._Schutz" title="Les Palmes de M. Schutz">Les Palmes de M. Schutz</a> (1997 film)</li>

<li><a href="Marie_Curie%2C_une_femme_sur_le_front" title="Marie Curie, une femme sur le front">Marie Curie, une femme sur le front</a> (2014 film)</li>

<li><a href="Marie_Curie%3A_The_Courage_of_Knowledge" title="Marie Curie: The Courage of Knowledge">Marie Curie: The Courage of Knowledge</a> (2016 film)</li>

<li><a href="Radioactive_(film)" title="Radioactive (film)">Radioactive</a> (2019 film)</li></ul>

</div></td></tr></tbody></table></div>

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