Question

A nucleus of mass number A originally at rest emits $\alpha$-particle with speed v. The recoil speed of daughter nucleus is :

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

Answer 1

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

As $F_{net}=0,$ therefore momentum is conserved
$\overrightarrow{P_1}+\overrightarrow{P_2}=0$
or $|\overrightarrow{P_1}|=|\overrightarrow{P_2}|$
$m_1{v}_1=m_2{v}_2$
$(A-4)v_1=4v\Rightarrow v_1=\frac{4v}{(A-4)}$.