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

A radioactive nucleus of mass $M$ emits a photon of frequency $v$ and the nucleus recoils. The recoil energy will be
  1. $h^2 v^2 / 2 M c^2$
  2. zero
  3. $h \mathrm{~V}$
  4. $M c^2-h v$

Solution

Momentum of a photon $p=\frac{h v}{c}$ Hence, Recoil energy $E=\frac{p^2}{2 M}$ $\begin{aligned} & \therefore \quad E=\frac{\left(\frac{h v}{c}\right)^2}{2 M} \\ & \text { or } \quad E=\frac{h^2 v^2}{2 M c^2} \\ & \end{aligned}$

Asked in: NEET 2011 (Screening)

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