Question

A radioactive nucleus of mass number A, initially at rest, emits an $\alpha$ - particle with a speed v. What will be the recoil speed of the daughter nucleus?

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

The total number of nucleons (i.e. protons + neutrons) in a nucleus is called its mass number. An α-particle is a helium nucleus having 2 protons and 2 neutrons. So the mass number of an $\alpha$ - particle = 4. When a nucleus of mass number A emits an $\alpha$ - particle, the mass number of the daughter nucleus reduces to (A – 4). If V is the recoil speed of the daughter nucleus, we have, from the law of conservation of momentum, (A – 4)V-4v = 0
or $V=\frac{4v}{A-4}$
Hence the correct choice is (c)