Question

A radioactive nucleus of mass $M$ emits a photon of frequency $v$ and the nucleus recoils. The recoil energy will be

Answer 1

• Energy of emitted photon is $E=h\nu$
• For a photon its momentum is given as $\frac{Energy}{velocityoflight}$ which is nothing but $\frac{E}{c}$ or $\frac{h\nu }{c}$
• According to momentum conservation value of the momentum of recoiled nucleus should also be $\frac{h\nu }{c}$ but in opposite direction to make net momentum zero before and after emission.
• Now recoil energy $E_2$ = $\frac{p^2}{2M}$ where $p$ is recoil momentum putting $p$ $=$ $\frac{h\nu }{c}$ we get recoil energy as $\frac{h^2{\nu }^2}{2M{c}^2}$ i.e., option C