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, m₁, and m₂ 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 v₁ and v₂ be the respective velocities of the daughter nuclei having masses m₁ and m₂.
Total linear momentum of the system after disintegration=m₁v₁+m₂v₂

According to the law of conservation of momentum:
Total initial momentum = Total final momentum​

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