A nucleus is at rest in the laboratory frame of reference. Show that if it disintegrates into two smaller nuclei the products must move in opposite directions.
A nucleus is at rest in the laboratory frame of reference. Show that if it disintegrates into two smaller nuclei the products must move in opposite directions.
Let $m, m_{1},$ and $m_{2}$ be the respective masses of the parent nucleus and the two daughter nuclei. The parent nucleus is at rest.
Initial momentum of the system (parent nucleus) $=0$
Let $v_{1}$ and $v_{2}$ be the respective velocities of the daughter nuclei having masses $m_{1}$ and $m_{2} .$
Total linear momentum of the system after disintegration $=m_{1} v_{1}+m_{2} v_{2}$
According to the law of conservation of momentum:
Total initial momentum $=$ Total final momentum
$0=m_{1} v_{1}+m_{2} v_{2}$
$v_{1}=\frac{-m_{2} v_{2}}{m_{1}}$
Here, the negative sign indicates that the fragments of the parent nucleus move in directions opposite to each other.
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