A radium nucleus disintegrates into a nucleus of radon and an $\alpha$-particle. The forces leading to the decay are internal to the system and the external forces on the system are negligible.

The total linear momentum of the system is the same before and after decay, according to law of conservation of linear momentum.

For this, the radon nucleus and the $\alpha$-particle, move in different directions along the same path along which the original decaying radium nucleus was moving it is shown in figure $(a)$.

If we observe decay of the nucleus from the frame of reference whose centre of mass is at rest, the produced particles move near and opposite to each other such that their centre of mass is at rest. It is shown in figure $(b)$.

In many problems on the system of particles as in the above radioactive decay problem, it is convenient to work in the centre of mass frame rather than in the laboratory frame of reference.