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 $\frac{E}{c}$ is emitted and the nucleus recoils.Find the decrease in internal energy.

Answer 1

K.E. of nucleus=$\left(\frac{1}{2}\right)m{v}^2$

=$\left(\frac{1}{2}\right)m{\left(\frac{E}{mc}\right)}^2=\frac{E^2}{2m{c}^2}$

Energy emitted by Gamma photon=E

Decrease in internal energy=$E+\frac{E^2}{2m{c}^2}$