Question

A radioactive nucleus of mass number A undergoes $\alpha -$emission to form a stable element. What will be the recoil velocity of the daughter nucleus if v is the velocity of $\alpha -$emission?

• A. $\frac{4v}{A-4}$
• B. $\frac{2v}{A-4}$
• C. $\frac{4v}{A+4}$
• D. $\frac{2v}{A+4}$

Answer 1

The correct option is A

$\frac{4v}{A-4}$

Mass of daughter nucleus $=A-4$

Mass of $\alpha -$particle $=4$

By conservation of momentum

$(A-4)v^{{}^{\prime }}=4v$ or $v^{{}^{\prime }}=\frac{4v}{A-4}$