Question

A nucleus with mass number $220$ initially at rest emits an $\alpha$-particle. lf the $Q$ value of the reaction is $5.5$ $MeV$, calculate the kinetic energy of the $\alpha$-particle.

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

Answer 1

The correct option is B $5.4MeV$

Let the velocity of alpha particle be $v$.

Mass of the alpha nucleus is 4amu.

From conservation of momentum,

$216\left(v_{atom}\right)=4v$

$⟹v_{atom}=\frac{v}{54}$

Total energy $=Q=5.5MeV=\frac{1}{2}\left(4\right)v^2+\frac{1}{2}\left(216\right)(\frac{v}{54}{)}^2$
Solving gives KE of alpha particle $=\frac{1}{2}\left(4\right)v^2=5.4MeV$