Nuclear fission and fusionAQA A-Level Physics: Revision notes

Nuclear fission is the splitting of a heavy nucleus into two smaller nuclei, usually with the release of neutrons. Nuclear fusion is the joining of two light nuclei into a heavier one. Both release energy because the products have a higher average binding energy per nucleon than the reactants, so the total mass decreases.

Induced fission. A uranium-235 nucleus captures a thermal neutron (one with kinetic energy similar to that of the surrounding particles) and splits:

¹n + ²³⁵U → ¹⁴¹Ba + ⁹²Kr + 3 ¹n

The nucleon and proton numbers balance on both sides. About 200 MeV is released per fission, mostly as kinetic energy of the fragments, which becomes thermal energy. Slow neutrons are captured far more readily than fast ones.

The energy released is found from the decrease in mass:

energy released = (mass of reactants − mass of products) × c²

or, with masses in u, Δm × 931.5 MeV.

Worked example (fusion). ²H + ²H → ³He + ¹n. Nuclear masses: ²H 2.01355 u, ³He 3.01493 u, neutron 1.00867 u.

Δm = 2(2.01355) − (3.01493 + 1.00867) = 4.02710 − 4.02360 = 0.00350 u

Energy = 0.00350 × 931.5 = 3.26 MeV.

Use the masses of the nuclei, or atomic masses where the electrons balance on both sides.

Each fission of uranium-235 releases two or three neutrons. If at least one of them on average causes another fission, a chain reaction can be sustained. If more than one does, the rate rises rapidly and the reaction is uncontrolled.

In a small piece of fuel too many neutrons escape through the surface before being captured. The critical mass is the minimum mass of fissile material needed to sustain a chain reaction. Above it, with no control, the reaction can run away.

In a thermal reactor:

• the moderator slows fast fission neutrons to thermal energies so that they are likely to cause further fissions
• control rods absorb neutrons; lowering them into the core reduces the rate of fission, and raising them increases it. For steady power, on average one neutron per fission causes another fission
• the coolant flows through the core and carries thermal energy to a heat exchanger, where steam is made to drive turbines

Mechanical model of moderation. Treat a neutron as a ball hitting a stationary ball in an elastic collision (momentum and kinetic energy conserved). Colliding head-on with an object of equal mass, the neutron stops and passes on all its kinetic energy. With a much heavier object it rebounds and keeps nearly all of its kinetic energy. So moderators need nuclei of low mass, and many collisions slow the neutron to thermal speed.

• Moderator: low-mass nuclei to transfer most kinetic energy per collision, and low neutron absorption so neutrons are not wasted. Examples: graphite, water, heavy water.
• Control rods: high neutron absorption, solid at high temperature, resistant to corrosion. Examples: boron, cadmium.
• Coolant: high specific heat capacity, flows easily, low neutron absorption, does not corrode the core or become strongly radioactive. Examples: water, carbon dioxide, liquid sodium.

Details of particular reactors are not needed.

Knowing how fission and fusion work lets society make informed decisions about nuclear energy. For example, the physics shows how much energy comes from a kilogram of fuel, why control and shielding are needed, and why fusion is attractive but hard to achieve (nuclei must overcome electrostatic repulsion, needing very high temperatures). Governments and the public can weigh these facts against cost, safety and the alternatives.