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

Total initial momentum = Total final momentum

0=m1v1+m2+v2

$v_1=\frac{-m_2v_2}{m_1}$

the negative sign indicates that the fragments of the parent nucleus move in directions opposite to each other.