• Tags: Q-value, exothermic, endothermic
• Difficulty: Moderate

The Q-value of a nuclear reaction = (total mass of reactants - total mass of products) x $c^2$ = (total mass of reactants - total mass of products) x 931.5 MeV. If Q > 0, the reaction is exothermic (energy released); if Q < 0, it's endothermic (energy must be supplied). For exothermic reactions, Q appears as kinetic energy of the products. For endothermic reactions, the minimum KE of the projectile needed is not Q but the threshold energy: $KE_{threshold}$ = |Q| x (1 + $m_{projectile}$/$m_{target}$) due to conservation of momentum (some KE goes into center-of-mass motion). Q-value can also be calculated using binding energies: Q = BE(products) - BE(reactants). This is opposite in sign to the mass formula because higher binding energy means lower mass. For alpha decay: Q = BE(daughter) + BE(He-4) - BE(parent). The Q-value determines whether a decay is energetically possible.