During a gamma decay process, a nucleus of mass M undergoes a...

By conservation of linear momentum, the momentum of the recoiling nucleus is equal in magnitude to the momentum of the emitted gamma photon.

$p = \dfrac{E}{c}$

The recoil kinetic energy of the nucleus is given by:

$K = \dfrac{p^2}{2M} = \dfrac{1}{2M} \left( \dfrac{E}{c} \right)^2 = \dfrac{E^2}{2Mc^2}$

By conservation of energy, the decrease in the internal energy of the nucleus $\Delta U$ is equal to the sum of the energy of the gamma photon and the recoil kinetic energy of the nucleus.

$\Delta U = E + K$

$\Delta U = E + \dfrac{E^2}{2Mc^2}$