Question

A radioactive nucleus of Mass M emits a photon of frequency and the nucleus recoils. The recoil will be

Answer 1

Energy of emitted photon (E)=hv

Photon it's momentum is given as $=\frac{E}{velocity of length}$

Which is not nothing but

$\frac{E}{c}or \frac{hv}{c}$

According to momentum conservation value of the momentum of recoiled nucleous should also be $\frac{hv}{c}$ But in opposite directions to make net momentum zero before and after emission

Recoil energy [E₂]=$\frac{P^2}{2m}$

P is recoil momentum putting

$P=\frac{hv}{c}$

We get recoil energy as

$E=\frac{h^2v^2}{2mc^2}$

Where $v\rightarrow frequency$