A neutron in a nuclear reactor collides head on elastically with the nucleus of a carbon atom initially at rest. The fraction of kinetic energy transferred from the neutron to the carbon atom is?

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
Ki = 1/2 mu² and Kf = 1/2 mv²
But v = (m - M)u / (m + M)
∴ Kf = 1/2 m ((m - M)u / (m + M))²
∴ Kf/Ki = (m - M)² / (m + M)²
The fraction of kinetic energy transferred from the neutron to the carbon atom is
f = 4mM / (m + M)²
But for carbon, M = 12m
∴ f = 4m(12m) / (m + 12m)² = 48/169.