A nucleus of mass number A, originally at rest, emits an   α-particle with speed v. The daughter nucleus  recoils with a speed

The emission of an α-particle from the atom of an element reduces its atomic number by 2 and mass number by 4. Hence, the radioactive emission is as follows :X A Z →α-particleY A-4 Z-2 +He 4 Z     (α-particle)Also from law of conservation of momentum,m x 0=myvy+mαvα           =A-4vy+4v ⇒vy=4vA-4