Q. A neutron travelling with a velocity $v$ and K.E. $E$ collides perfectly elastically head on with the nucleus of an atom of mass number $A$ at rest. The fraction of total energy retained by neutron is
A) $\left( \frac{A - 1}{A + 1} \right)^{2}$
B) $\left( \frac{A + 1}{A - 1} \right)^{2}$
C) $\left( \frac{A - 1}{A} \right)^{2}$
D) $\left( \frac{A + 1}{A} \right)^{2}$
Explanation
(a) $\left( \frac{\mathrm{\Delta}k}{k} \right)_{retained} = \left( \frac{m_{1} - m_{2}}{m_{1} + m_{2}} \right)^{2} = \left( \frac{1 - A}{1 + A} \right)^{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.