\( Q \)-values and separation energies

The above processes can be characterized by an energy difference called the \( Q \) value, defined as $$ Q=\sum_i M(N_i, Z_i)c^2-\sum_f M(N_f, Z_f)c^2=\sum_i BE(N_f, Z_f)-\sum_i BE(N_i, Z_i) $$ Spontaneous decay involves a single initial nuclear state and is allowed if \( Q > 0 \). In the decay, energy is released in the form of the kinetic energy of the final products. Reactions involving two initial nuclei are called endothermic (a net loss of energy) if \( Q < 0 \). The reactions are exothermic (a net release of energy) if \( Q > 0 \).