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.
We suppose,
Mass of the parent nucleus as M and the mass of two daughter nuclei as m1 and m2 .
The final velocities of the respective two daughter nuclei after disintegration as v1,v2 respectively.
Since, the parent nucleus before disintegration was at rest,
Initial momentum of the system i.e. parent nucleus = 0
Final momentum of the system i.e. daughter nuclei = m1v1+m2v2
According to the law of conservation of linear momentum:
Total initial momentum = Total final momentum
Therefore,
0 = m1v1+m2v2
⇒ v1 = - (m1/m2)× v2
The negative sign indicates that both the velocities of the daughter nuclei are in opposite directions.