Q. A nucleus with mass number 220 initially at rest emits an $\alpha$-particle. If the $Q$ value of the reaction is $5.5\ MeV$, calculate the kinetic energy of the $\alpha$-particle
A) $10^{9}\ K$
B) $10^{7}\ K$
C) $10^{5}\ K$
D) $10^{3}\ K$
Explanation
(b) $Q$-value of the reaction is $5.5\ MeV$
$i.e.,k_{1} + k_{2} = 5.5\ MeV$ …(i)
By conservation of linear momentum
$p_{1} = p_{2} \Rightarrow \sqrt{2(216)/k_{1}} = \sqrt{2(4)k_{2}}$
$\Rightarrow k_{2} = 54\ k_{1}$ …(ii)
On solving equation (i) and (ii)
We get $k_{2} = 5.4\ MeV$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.