Question

A nucleus with mass number $220$ initially at rest emits an $\alpha -$particle. If the $Q$ value of the reaction is $5.5\text{MeV}$ then the kinetic energy $\left(\text{in MeV}\right)$ of the $\alpha -$particle is

• A. $6.5$
• B. $5.6$
• C. $4.4$
• D. $5.4$

Answer 1

The correct option is D $5.4$

Given:
$Q=5.5\text{MeV}$
Mass number of parent atom, $A=220$
Mass number of daughter atom, $A_d=216$
Mass number of $\alpha -$ particle, $A_{\alpha }=4$

As we know that, kinetic energy of $\alpha -$ particle,

$K{E}_{\alpha }=\frac{A_d}{A_d+A_{\alpha }}Q=\frac{216}{216+4}\times 5.5$

$\therefore K{E}_{\alpha }=5.4\text{MeV}$

Hence, option $\left(\text{D}\right)$ is correct.