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Summarizing Nuclear Decay and Conservation Laws

Nuclear Decay and Conservation Laws Summary

  • When a parent nucleus decays, it produces a daughter nucleus following rules and conservation laws. There are three major types of nuclear decay, called alpha \((\alpha ),\) beta \((\beta ),\) and gamma \((\gamma )\). The \(\alpha \) decay equation is

    \({}_{Z}^{A}{X}_{N}\to {}_{Z-2}^{A-4}{\text{Y}}_{N-2}+{}_{2}^{4}{\text{He}}_{2}.\)

  • Nuclear decay releases an amount of energy \(E\) related to the mass destroyed \(\Delta m\) by

    \(E=(\Delta m){c}^{2}.\)

  • There are three forms of beta decay. The \({\beta }^{-}\)decay equation is

    \({}_{Z}^{A}{X}_{N}\to {}_{Z+1}^{A}{\text{Y}}_{N-1}+{\beta }^{-}+{\overline{\nu }}_{e}.\)

  • The \({\beta }^{+}\) decay equation is

    \({}_{Z}^{A}{X}_{N}\to {}_{Z-1}^{A}{\text{Y}}_{N+1}+{\beta }^{+}+{\nu }_{e}.\)

  • The electron capture equation is

    \({}_{Z}^{A}{X}_{N}+{e}^{-}\to {}_{Z-1}^{A}{\text{Y}}_{N+1}+{\nu }_{e}.\)

  • \({\beta }^{-}\) is an electron, \({\beta }^{+}\) is an antielectron or positron, \({\nu }_{e}\) represents an electron’s neutrino, and \({\overline{\nu }}_{e}\) is an electron’s antineutrino. In addition to all previously known conservation laws, two new ones arise— conservation of electron family number and conservation of the total number of nucleons. The \(\gamma \) decay equation is

    \({}_{Z}{}^{A}\text{}{\text{X}}_{N}^{*}\to {}_{Z}{}^{A}\text{}{\text{X}}_{N}+{\gamma }_{1}+{\gamma }_{2}+\cdots \)

    \(\gamma \) is a high-energy photon originating in a nucleus.



the original state of nucleus before decay


the nucleus obtained when parent nucleus decays and produces another nucleus following the rules and the conservation laws


the particle that results from positive beta decay; also known as an antielectron


the process by which an atomic nucleus of an unstable atom loses mass and energy by emitting ionizing particles

alpha decay

type of radioactive decay in which an atomic nucleus emits an alpha particle

beta decay

type of radioactive decay in which an atomic nucleus emits a beta particle

gamma decay

type of radioactive decay in which an atomic nucleus emits a gamma particle

decay equation

the equation to find out how much of a radioactive material is left after a given period of time

nuclear reaction energy

the energy created in a nuclear reaction


an electrically neutral, weakly interacting elementary subatomic particle

electron’s antineutrino

antiparticle of electron’s neutrino

positron decay

type of beta decay in which a proton is converted to a neutron, releasing a positron and a neutrino


another term for positron

decay series

process whereby subsequent nuclides decay until a stable nuclide is produced

electron’s neutrino

a subatomic elementary particle which has no net electric charge


composed of antiparticles

electron capture

the process in which a proton-rich nuclide absorbs an inner atomic electron and simultaneously emits a neutrino

electron capture equation

equation representing the electron capture

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