A nucleus is at rest in the laboratory frame of reference.

solution:

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.