$A$ 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.

(N/A) 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.