A radioactive nucleus of mass M emits a photo | vedclass

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(B) According to the law of conservation of momentum,the momentum of the emitted photon must be equal to the momentum of the recoiling nucleus.Momentu

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$\frac{h^2 v^2}{2Mc^2}$

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(B) According to the law of conservation of momentum,the momentum of the emitted photon must be equal to the momentum of the recoiling nucleus.Momentum of photon $p = \frac{hv}{c}$.Let $V$ be the recoil velocity of the nucleus. Then,the momentum of the nucleus is $p = MV$.Equating the two: $\frac{hv}{c} = MV$,which gives $V = \frac{hv}{Mc}$.The recoil kinetic energy of the nucleus is $K = \frac{1}{2}MV^2$.Substituting the value of $V$: $K = \frac{1}{2}M \left( \frac{hv}{Mc} \right)^2 = \frac{1}{2}M \frac{h^2 v^2}{M^2 c^2} = \frac{h^2 v^2}{2Mc^2}$.

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

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