Editing Beta decay (section)

===β<sup>−</sup> decay===
Consider the generic equation for beta decay
: {{Physics particle|TL={{mvar|A}}|BL={{mvar|Z}}|X}} → {{Physics particle|TL={{mvar|A}}|BL={{math|''Z''+1}}|X′}} + {{SubatomicParticle|Electron}} + {{math|{{SubatomicParticle|Electron Antineutrino}}}}.
The {{mvar|Q}} value for this decay is
:<math chem>Q=\left[m_N\left(\ce{^\mathit{A}_\mathit{Z}X}\right) - m_N\left(\ce{^\mathit{A}_{\mathit{Z}+1}X'}\right)-m_e-m_{\overline\nu_e}\right]c^2</math>,
where <math chem>m_N\left(\ce{^\mathit{A}_\mathit{Z}X}\right)</math> is the mass of the nucleus of the {{Physics particle|TL={{mvar|A}}|BL={{mvar|Z}}|X}} atom, <math chem>m_e</math> is the mass of the electron, and <math chem>m_{\overline\nu_e}</math> is the mass of the electron antineutrino. In other words, the total energy released is the mass energy of the initial nucleus, minus the mass energy of the final nucleus, electron, and antineutrino. The mass of the nucleus {{mvar|m<sub>N</sub>}} is related to the standard [[atomic mass]] {{mvar|m}} by
<math chem display="block">m\left(\ce{^\mathit{A}_\mathit{Z}X}\right)c^2=m_N\left(\ce{^\mathit{A}_\mathit{Z}X}\right)c^2 + Z m_e c^2-\sum_{i=1}^Z B_i.</math>
That is, the total atomic mass is the mass of the nucleus, plus the mass of the electrons, minus the sum of all ''electron'' binding energies {{mvar|B<sub>i</sub>}} for the atom. This equation is rearranged to find <math chem>m_N\left(\ce{^\mathit{A}_\mathit{Z}X}\right)</math>, and <math chem>m_N\left(\ce{^\mathit{A}_{\mathit{Z}+1}X'}\right)</math> is found similarly. Substituting these nuclear masses into the {{math|Q}}-value equation, while neglecting the nearly-zero antineutrino mass and the difference in electron binding energies, which is very small for high-{{mvar|Z}} atoms, we have
<math chem display="block">Q=\left[m\left(\ce{^\mathit{A}_\mathit{Z}X}\right)-m\left(\ce{^\mathit{A}_{\mathit{Z}+1}X'}\right)\right]c^2</math>
This energy is carried away as kinetic energy by the electron and antineutrino.

Because the reaction will proceed only when the {{mvar|Q}}&nbsp;value is positive, β<sup>−</sup> decay can occur when the mass of atom {{Physics particle|TL={{mvar|A}}|BL={{mvar|Z}}|X}} is greater than the mass of atom {{Physics particle|TL={{mvar|A}}|BL={{math|''Z''+1}}|X′}}.<ref name="Krane1987">{{cite book|author=Kenneth S. Krane|title=Introductory Nuclear Physics| url=https://books.google.com/books?id=ConwAAAAMAAJ|date=5 November 1987|publisher=Wiley|isbn=978-0-471-80553-3}}</ref>