Consider the generic equation for beta decay
The  value for this decay is
where  is the mass of the nucleus of the  atom,  is the mass of the electron, and  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  is related to the standard atomic mass  by
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  for the atom. This equation is rearranged to find , and  is found similarly. Substituting these nuclear masses into the -value equation, while neglecting the nearly-zero antineutrino mass and the difference in electron binding energies, which is very small for high- atoms, we have
This energy is carried away as kinetic energy by the electron and antineutrino.
Because the reaction will proceed only when the  value is positive, β decay can occur when the mass of atom  is greater than the mass of atom .