: According to law of conservation of linear momentum, we get

Where is the initial velocity of the neutron before collision and and are the velocities of the neutron and deuterium after collision

(i)

According to conservation of kinetic energy, we get

……(ii)

From eqs. (i) and (ii), it follows that

Substituting this in Eq. (i), we get

……(iii)

……..(iv)

The initial kinetic energy of the neutron is

Final kinetic energy of the deuterium is

(Using (iv))

Fraction of neutron’s energy transferred to deuterium is

For deuterium,