Question

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.

Answer 1

Let $m$ masses of the parent nucleus and $m_1$ and $m_2$ be the respective 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 $m_2$.

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.