Explain the conservation of linear momentum for the radioactive decay of a radium nucleus.

(N/A) radium nucleus $(Ra)$ disintegrates into a radon nucleus $(Rn)$ and an $\alpha$-particle $(He)$. The forces leading to the decay are internal to the system,and the external forces on the system are negligible.
According to the law of conservation of linear momentum,the total linear momentum of the system remains constant before and after the decay.
In the laboratory frame of reference,if the original radium nucleus was moving,the radon nucleus and the $\alpha$-particle move in different directions such that their combined momentum equals the initial momentum of the radium nucleus,as shown in figure $(a)$.
If we observe the decay of the nucleus from the centre of mass frame of reference,the produced particles move in opposite directions such that their total momentum is zero,keeping the centre of mass at rest. This is shown in figure $(b)$.
In many problems involving a system of particles,such as the radioactive decay problem,it is more convenient to perform calculations in the centre of mass frame rather than in the laboratory frame of reference.