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Q.
A radioactive nucleus of mass $M$ emits a photon of frequency $\upsilon$ and the nucleus recoils. The recoil energy will be
AIPMTAIPMT 2011Nuclei
Solution:
$F _{ ex }=\frac{ d P }{ dt }=0 $
$\Rightarrow dP =0 $
$\Rightarrow P =$ constant
$\vec{ P }_{ i }=\vec{ P }_{ f }$
$0=\vec{ P }_{ Nu }+\vec{ P }_{ Ph }$
$\left|\vec{ P }_{ Nu }\right|=\left|\vec{ P }_{ Ph }\right|=\frac{ h }{\lambda}=\frac{ hv }{ c }$
Recoil $K.E$. of nucleus $K . E _{ Nu }=\frac{ P _{ Nu }^{2}}{2 M _{ Nu }}$
$K.E _{\cdot Nu }=\frac{( hv / c )^{2}}{2 M }=\frac{ h ^{2} v^{2}}{2 Mc ^{2}}$
