A radioactive nucleus of mass M emits a photo | vedclass

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(B) The momentum of the emitted photon is given by $p_{	ext{photon}} = \frac{hf}{c}$.According to the law of conservation of linear momentum,the magn

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$h^2f^2/2Mc^2$

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(B) The momentum of the emitted photon is given by $p_{	ext{photon}} = \frac{hf}{c}$.According to the law of conservation of linear momentum,the magnitude of the momentum of the recoiling nucleus must be equal to the momentum of the photon:$p_{	ext{nucleus}} = p_{	ext{photon}} = \frac{hf}{c}$.Let $v$ be the recoil speed of the nucleus. Then,$Mv = \frac{hf}{c}$,which gives $v = \frac{hf}{Mc}$.The recoil kinetic energy of the nucleus is given by $K = \frac{1}{2}Mv^2$.Substituting the value of $v$:$K = \frac{1}{2}M \left( \frac{hf}{Mc} ight)^2 = \frac{1}{2}M \left( \frac{h^2f^2}{M^2c^2} ight) = \frac{h^2f^2}{2Mc^2}$.

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

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