Question

In a $\gamma -$decay process, $\gamma -$rays of energy $E$ is emitted. Find the decrease in internal energy of mass $M$ (of nucleus).

• A. $\frac{E^2}{2M{c}^2}$
• B. $E-\frac{E^2}{2M{c}^2}$
• C. $E+\frac{E^2}{2M{c}^2}$
• D. $E+\frac{E^2}{M{c}^2}$

Answer 1

The correct option is C $E+\frac{E^2}{2M{c}^2}$

By momentum conservation:
$\frac{E}{c}=Mv$
$v=\frac{E}{Mc}$

Now, total decrease in internal energy $=$ Energy of $\gamma$ $+$ $KE$ of $M$
$=E+\frac{1}{2}M{v}^2$
$=E+\frac{E^2}{2M{c}^2}$