Physics - Modern Physics Question with Solution | TestHub

Let $m$ and $M$ be the masses of neutron and carbon nucleus (at rest) respectively. If $u$ and $v$ are the velocity of neutron before and after collision, then $K_i=\frac{1}{2}m{u}^2$ and $K_f=\frac{1}{2}m{v}^2$, But $v=\frac{(m-M)u}{m+M}$ $\begin{array}{rl}& \therefore K_f=\frac{1}{2}m{\left(\frac{m-M}{m+M}\right)}^2{u}^2\\ & \therefore \frac{K_f}{K_i}={\left(\frac{m-M}{m+M}\right)}^2\end{array}$ The fraction of kinetic energy transferred from the neutron to the carbon atom is $f=\frac{4mM}{(m+M{)}^2}$ But for carbon, $M=12\mathrm{m}$ $\therefore f=\frac{4m(12m)}{(m+12m{)}^2}=\frac{48}{169}$