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 decrease in internal energy.

Answer 1

$M\stackrel{radiation}{\to }{M}^1+E\begin{array}{cc}ApplymomentumConservation& \\ M^{1}V=\frac{E}{}C& \\ V_1=\frac{E}{M^{1}C}& \end{array}|\begin{array}{cc}\Delta m{C}^2=E& \\ \Delta m=\frac{E}{C^2}=M-M^1& \\ \Rightarrow M^1=(M-\frac{E}{C^2})& \end{array}=\frac{E}{(M-\frac{E}{MC-\frac{E}{C}})}$
Recoil velocity $\frac{E}{(MC-\frac{E}{C})}$