In a gamma decay process?

Question

In a gamma decay process, the internal energy of a nucleus of mass M decreases, a gamma photon of energy E and linear momentum E/c is emitted and the nucleus recoils. Find the decreases in internal energy.

Answer 1

Nucleus would acquire momentum equal to E/c in opposite direction to photon according to the law of momentum conservation. So the velocity of nucleus will be E/cM and kinetic energy of nucleus will be M(E/cM)^2/2=E^2/(2Mc^2)

So total decrease in energy is E+E^2/(2Mc^2).