A nuclear reactor contains nuclei that fission when bombarded by slow neutrons. The fission reaction produces fast neutrons which need to be moderated (i.e. slowed down) in collisions before they can cause further fissions. In this problem we consider a reactor which uses graphite (i.e. carbon) as moderator. Assume the neutron and carbon nuclear masses are 1.67 ¡Ñ 10¡V27 kg and 20.0 ¡Ñ 10¡V27 kg respectively. Consider a head-on collision between a neutron with speed 15 Mm/s and a stationary carbon nucleus.

Question

A nuclear reactor contains nuclei that fission when bombarded by slow neutrons. The fission reaction produces fast neutrons which need to be moderated (i.e. slowed down) in collisions before they can cause further fissions. In this problem we consider a reactor which uses graphite (i.e. carbon) as moderator. Assume the neutron and carbon nuclear masses are 1.67 ¡Ñ 10¡V27 kg and 20.0 ¡Ñ 10¡V27 kg respectively. Consider a head-on collision between a neutron with speed 15 Mm/s and a stationary carbon nucleus.

(i) Calculate the speed of the neutron after the collision
(ii) Calculate the speed of the carbon nucleus after the collision

Answer 1

To calculate the speed of the neutron after the collision and the speed of the carbon nucleus, we can use the principle of conservation of momentum and kinetic energy.

(i) Calculate the speed of the neutron after the collision:

1. Calculate the initial momentum of the system before the collision:
- Momentum = mass × velocity
- Initial momentum = (mass of neutron) × (initial speed of neutron)
= (1.67 × 10^-27 kg) × (15 × 10^6 m/s)
= 25.05 × 10^-21 kg·m/s

2. Calculate the final momentum of the system after the collision:
- Since the neutron and carbon nucleus are initially at rest, the final momentum of the system will only be contributed by the neutron.
- Final momentum = (mass of neutron) × (final speed of neutron)

3. Apply the conservation of momentum:
- Initial momentum = Final momentum
- (1.67 × 10^-27 kg) × (15 × 10^6 m/s) = (1.67 × 10^-27 kg) × (final speed of neutron)
- Solve for the final speed of the neutron.

(ii) Calculate the speed of the carbon nucleus after the collision:

1. Apply the law of conservation of kinetic energy:
- The total kinetic energy of the system before the collision will be equal to the total kinetic energy of the system after the collision.
- Initial kinetic energy = Final kinetic energy

2. Calculate the initial kinetic energy:
- Initial kinetic energy = 0.5 × (mass of neutron) × (initial speed of neutron)^2
- Calculate the value.

3. Calculate the final kinetic energy:
- Final kinetic energy = 0.5 × (mass of neutron) × (final speed of neutron)^2 + 0.5 × (mass of carbon nucleus) × (final speed of carbon nucleus)^2
- Substitute the values and solve for the final speed of the carbon nucleus.

Remember to convert units to match the given values (Mm/s and kg).