Question

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

• A. $4.4\text{MeV}$
• B. $5.4\text{MeV}$
• C. $5.6\text{MeV}$
• D. $6.5\text{MeV}$

Answer 1

The correct option is B $5.4\text{MeV}$

Given, $A=220;\text{Q-Energy}=5.5\text{MeV}$

Kinetic energy of the $\alpha$-particle is,

$K.E_{\alpha }=\left(\frac{A-4}{A}\right)\times Q$

$K.E_{\alpha }=\left(\frac{220-4}{220}\right)\times 5.5\times {10}^6$

$K.E_{\alpha }=5.4\times {10}^6\text{eV}\text{(or)}$

$K.E_{\alpha }=5.4\text{MeV}$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(B\right)$ is the correct answer.