Answer

a) Total momentum before the neutron is absorbed = 1.7 x 10^-27 kg x 1.4 x 10⁷ m s^-1 = 2.38 x 10^-20 kg m s^-1 (1).

Total momentum after the neutron is absorbed = 2.38 x 10^-10 kg m s^-1 (1)

Velocity of nucleus = p / m = 2.38 x 10^-20 kg m s^-1 / 4.017 x 10^-25 kg = 5.9 x 10⁴ m s^-1 (1) 

b) The velocity of the nucleus would be greater (1). The neutron would rebound and have a greater change in momentum (1) so the change in momentum of the nucleus would also be greater. (1)

c) E_k = 1/2mv² (1) = 1/2 x 1.7 x 10^-27 kg x (1.4 x 10⁷ m s^-1)²  (1) = 1.67 x 10^-13 J (1)