When a U238 nucleus originally at rest decays by emitting an alpha particle having a speed ‘u’, the recoil speed of the residual nucleus is
−4u234
The momentum of the system remains the same before and after decay. This is in accordance with the principle of conservation of momentum.
Now, 4u+234v=238×0
or 234 v = – 4u or v=–4u234
So, (c) is the right choice.