Students should have studied a simple mechanical model of moderation by…

The idea

Fission neutrons are released fast and must be slowed to sustain further fission. In a simple mechanical model, a neutron collides elastically with a stationary moderator nucleus. Conservation of momentum and kinetic energy show that the neutron loses the greatest fraction of its kinetic energy when the target nucleus has a mass similar to its own, as with hydrogen. A head-on collision with a nucleus of mass number A reduces the neutron speed by the factor (A − 1)/(A + 1), so a hydrogen nucleus can remove almost all the neutron energy in one collision, whereas a lead nucleus removes very little. The model treats nuclei as hard spheres and ignores binding and excitation, but it explains why light moderators are chosen.

What earns the marks

• State that fission neutrons are initially fast and must be moderated to increase the probability of further induced fission.
• Apply conservation of momentum and conservation of kinetic energy to a head-on elastic collision between a neutron and a stationary nucleus.
• Derive or use the speed ratio (A − 1)/(A + 1) for a head-on collision, where A is the mass number of the moderator nucleus.
• Explain that energy transfer is most efficient when the moderator nucleus mass is comparable to the neutron mass, so light nuclei such as hydrogen are effective.
• Compare moderators using the number of collisions needed to reduce neutron energy, linking smaller A to fewer collisions.
• Recognise the model's limitations: it ignores inelastic scattering, nuclear excitation and the random direction of collisions.

Common mistakes and how to put them right

• Treating the collision as perfectly inelastic and assuming the neutron and nucleus move together.

  Put it right by applying elastic collision equations that conserve kinetic energy as well as momentum.

• Assuming a heavy nucleus slows neutrons most because it is a large target.

  Put it right by explaining that a heavy nucleus recoils little, so the neutron retains most of its kinetic energy.

• Using the mass number A as a direct measure of energy transferred without deriving the speed ratio.

  Put it right by showing the head-on collision calculation and interpreting the ratio (A − 1)/(A + 1).

Exam tips

• Begin by stating the physical requirement: neutrons must be slowed from fast energies to thermal energies to sustain a chain reaction.
• Show the momentum and kinetic energy equations explicitly before quoting the speed ratio, so the reasoning is visible.
• Use the ratio to compare two named moderators, such as hydrogen and carbon, and state which needs fewer collisions and why.