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
- $h^2 v^2 / 2 M c^2$
- zero
- $h \mathrm{~V}$
- $M c^2-h v$
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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