Question

A nucleus of mass number '$A$' originally at rest emits an $\alpha$ particle with a speed '$v$' the recoil speed of the daughter nucleus is

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

Answer 1

The correct option is D $\frac{4v}{A-4}$

The initial momentum of the system is zero.
Using momentum conservation:
$mv+MV=0$
But, $m=4,M=A-4$
$\Rightarrow 4v+(A-4)V=0$
$\Rightarrow V=-\frac{4v}{A-4}$
$\Rightarrow Speed=V=\frac{4v}{A-4}$