Question

A radioactive nucleus emits an $\alpha$-particle and a neutron simultaneously with speed but in opposite direction in order to form a stable nuclei. If the speed of emitted particles is $v$ and $A$ is the mass number of radioactive nucleus, then speed of stable nucleus is:

• A. $\frac{3v}{A-5}$
• B. $\frac{2v}{A-5}$
• C. $\frac{4v}{A-5}$
• D. $\frac{2v}{A+5}$

Answer 1

The correct option is A $\frac{3v}{A-5}$

The mass number of stable nucleus $=A-5$ (as mass of a particle $=4u$ and neutron $=1$u)

Applying conservation of momentum we have:

Initial momentum of the system $\left(p_i\right)=$ final momentum of the system $\left(p_f\right)$

$\Rightarrow 0=p_{nucleus}+p_{neutron}+P_{\alpha }$

As neutron and $\alpha$ particle move in opposite directions so:

$0=(A-5)v_{nucleus}+1\left(v\right)-4v$ (considering neutron to move in $+x$ direction)

$\Rightarrow v_{nucleus}=\frac{3v}{A-5}$ is the speed of the stable nucleus.