Nuclear Fission and Fusion

This lesson explores the practical aspects of nuclear fission and fusion — how they work, how nuclear reactors are designed, the conditions required for fusion, and the role of nucleosynthesis in stars. This material is assessed in AQA sections 3.8.1 and 3.2.1.

Spec mapping (AQA 7408): This lesson covers induced fission of U-235 by slow neutrons, the chain reaction and critical mass, the roles of moderator, control rods and coolant in a nuclear reactor, the conditions required for fusion (temperature, density, confinement time, Lawson criterion), the proton-proton chain in the Sun, stellar nucleosynthesis up to iron, and the supernova route to elements beyond iron. It maps to AQA 7408 sections 3.8.1.5 (fission and fusion) and 3.8.1.6 (nuclear reactors and energy production). (Refer to the official AQA specification document for exact wording.)

Synoptic links: (1) The energy released per fission and fusion event is computed using the mass-defect / binding-energy framework from the previous lesson — fission and fusion are the two energy-releasing routes up the BE/A curve. (2) Reactor moderation exploits the elastic-collision physics of section 3.4 (Mechanics) — the fractional energy transfer is maximum when colliding masses are equal, which is why hydrogen-rich moderators (water) thermalise neutrons so effectively. (3) The Lawson criterion for fusion connects to thermodynamics (kinetic theory and the Maxwell-Boltzmann distribution from section 3.6) — only the tail of the velocity distribution has enough energy to tunnel through the Coulomb barrier, so confinement time and density together determine net energy gain.

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Nuclear Fission

Nuclear fission is the splitting of a heavy nucleus into two lighter nuclei (roughly equal in size), accompanied by the release of neutrons and a large amount of energy.

Induced Fission

Fission can be induced (triggered) by the absorption of a neutron. Uranium-235 is the most commonly used fissile material:

²³⁵₉₂U + ¹₀n → ⁹²₃₆Kr + ¹⁴¹₅₆Ba + 3¹₀n + energy (~200 MeV)

The incoming neutron must be a thermal (slow) neutron — one with kinetic energy of about 0.025 eV (corresponding to room temperature). Fast neutrons are much less likely to be captured by U-235.

Key features of fission:

• The products (fission fragments) vary — many different pairs of daughter nuclei are possible.
• Typically 2 or 3 neutrons are released per fission event.
• The energy is released mainly as kinetic energy of the fission fragments and neutrons.
• The fission fragments are usually radioactive (neutron-rich) and undergo further beta decays.

Chain Reactions

Each fission event releases 2–3 neutrons. If at least one of these neutrons goes on to cause another fission event, a chain reaction is sustained.

• If exactly 1 neutron per fission causes another fission, the reaction is critical — the rate is constant and controlled. This is the condition maintained in a nuclear power reactor.
• If more than 1 neutron per fission causes another fission, the reaction is supercritical — the rate increases exponentially. This is the condition in a nuclear weapon.
• If fewer than 1 neutron per fission causes another fission, the reaction is subcritical — the rate decreases and the reaction dies out.

Critical Mass

The critical mass is the minimum mass of fissile material needed to sustain a chain reaction. Below this mass, too many neutrons escape from the surface without causing further fissions. The critical mass depends on:

• The type of fissile material (U-235, Pu-239, etc.)
• The shape of the material (a sphere has the smallest surface-area-to-volume ratio)
• The purity/enrichment of the material
• Whether a neutron reflector is used

For pure U-235 (unreflected sphere), the critical mass is approximately 52 kg.

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The Nuclear Fission Reactor

A nuclear fission reactor is designed to maintain a controlled, critical chain reaction. The key components are:

Fuel Rods

• Contain the fissile material, typically enriched uranium (3–5% U-235 in U-238) or sometimes plutonium-239.
• Natural uranium contains only 0.7% U-235 — enrichment increases this proportion.
• The fuel is formed into pellets and sealed in metal cladding (e.g., zirconium alloy) to contain the radioactive fission products.

Moderator

• Purpose: to slow down the fast neutrons released in fission to thermal energies, because U-235 has a much higher probability of capturing slow neutrons.
• Common moderators: graphite (carbon) or water (H₂O or heavy water D₂O).
• The moderator works by elastic collisions — neutrons bounce off moderator nuclei and transfer kinetic energy to them. The most effective moderation occurs when the moderator nuclei have a similar mass to the neutron (hence hydrogen/deuterium in water are very effective).
• The moderator must not absorb too many neutrons itself (otherwise the chain reaction cannot be sustained).

Control Rods

• Purpose: to absorb excess neutrons and control the rate of the chain reaction.
• Made from materials with a high neutron-absorption cross-section: boron or cadmium.
• Inserting the control rods further reduces the neutron population and slows the reaction.
• Withdrawing the control rods increases the neutron population and speeds up the reaction.
• In an emergency, the control rods are fully inserted (SCRAM) to shut down the reactor.

Coolant

• Purpose: to transfer thermal energy away from the reactor core to generate steam for electricity production.
• Common coolants: water, heavy water, CO₂ gas, or liquid sodium.
• In a pressurised water reactor (PWR), the same water acts as both moderator and coolant.

Exam Tip: The most common exam question on reactors asks you to explain the purpose of the moderator and control rods. Key points: the moderator slows neutrons (because U-235 is more likely to capture slow neutrons), and the control rods absorb neutrons to keep the reaction critical. Students often confuse these roles.

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Nuclear Fusion

Nuclear fusion is the joining of two light nuclei to form a heavier nucleus, accompanied by a release of energy. Fusion is the energy source of stars.

The Fusion Process

²₁H + ³₁H → ⁴₂He + ¹₀n + 17.6 MeV

This deuterium-tritium (D-T) reaction is the easiest fusion reaction to achieve because it has the lowest required temperature.

Conditions for Fusion

For fusion to occur, two positively charged nuclei must be brought close enough together (within ~10⁻¹⁵ m) for the strong nuclear force to take over and bind them. This requires overcoming the enormous Coulomb repulsion between the two positive charges. The conditions needed are:

1. Extremely high temperature — typically 10⁷ to 10⁸ K. At these temperatures, the fuel is a plasma (a gas of ions and free electrons). The high thermal energy gives the nuclei enough kinetic energy to overcome the Coulomb barrier.

2. Sufficient density — enough nuclei must be close together for collisions to be frequent.

3. Sufficient confinement time — the plasma must be held together long enough for enough fusion reactions to occur.

These three conditions are summarised by the Lawson criterion, which specifies the minimum product of density and confinement time needed for net energy gain.

Why Fusion Is Difficult on Earth

• No material container can withstand temperatures of 10⁸ K — the plasma would melt any wall it touched.
• Two approaches are being researched:
  • Magnetic confinement (e.g., tokamak reactors like ITER): powerful magnetic fields confine the plasma in a doughnut-shaped (toroidal) chamber.
  • Inertial confinement: powerful lasers compress a tiny pellet of fuel so quickly that fusion occurs before the fuel can fly apart.
• Achieving sustained, energy-positive fusion on Earth remains one of the greatest engineering challenges. As of current research, no fusion reactor has yet achieved sustained net energy gain in a commercially viable way.

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Stellar Nucleosynthesis

Stars generate energy through fusion. The specific fusion processes depend on the star's mass and stage of evolution.

The Proton-Proton Chain (Main Sequence Stars like the Sun)

The net effect is the fusion of four protons into one helium-4 nucleus:

4¹₁H → ⁴₂He + 2⁰₊₁e + 2νₑ + energy (26.7 MeV)

This process proceeds through several intermediate steps:

1. ¹₁H + ¹₁H → ²₁H + ⁰₊₁e + νₑ (two protons fuse, one converts to a neutron via beta-plus decay)
2. ²₁H + ¹₁H → ³₂He + γ
3. ³₂He + ³₂He → ⁴₂He + 2¹₁H

Beyond Helium — Heavier Elements

In more massive stars, once the hydrogen fuel is exhausted, the core contracts and heats up further, allowing fusion of heavier elements:

Stage	Fuel	Product	Approximate Temperature (K)
Hydrogen burning	H	He	1.5 × 10⁷
Helium burning	He	C, O	2 × 10⁸
Carbon burning	C	Ne, Na, Mg	8 × 10⁸
Neon burning	Ne	O, Mg	1.5 × 10⁹
Oxygen burning	O	Si, S	2 × 10⁹
Silicon burning	Si	Fe, Ni	3 × 10⁹

Fusion stops at iron (the peak of the binding energy per nucleon curve). Beyond iron, fusion is endothermic — it absorbs energy rather than releasing it.

Elements Heavier Than Iron

Elements heavier than iron are formed primarily during supernova explosions. The immense temperatures, densities, and neutron fluxes during a supernova provide enough energy to build nuclei beyond iron through rapid neutron capture (the r-process). This is why heavy elements like gold, platinum, and uranium are relatively rare.

Exam Tip: AQA expects you to understand that fusion in stars produces elements up to iron, and that elements heavier than iron are produced in supernovae. A common 6-mark question asks you to explain why fusion releases energy for light nuclei (they move up the binding energy per nucleon curve towards the peak) but not for nuclei heavier than iron.

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Comparing Fission and Fusion

Feature	Fission	Fusion
Process	Heavy nucleus splits	Light nuclei join
Fuel	U-235, Pu-239	H-2, H-3, He-3
Energy per reaction	~200 MeV	~17.6 MeV (D-T)
Energy per unit mass of fuel	~8 × 10¹³ J kg⁻¹	~3.4 × 10¹⁴ J kg⁻¹
Conditions	Room temperature, thermal neutrons	~10⁸ K, plasma
Waste	Long-lived radioactive fission products	Short-lived or stable products (mainly He)
Current status	Widely used in power stations	Under research (not yet commercially viable)
Where it occurs naturally	Extremely rare	In stars

Common Misconception: Students often think fusion releases more energy per reaction than fission. In fact, a single fission event (~200 MeV) releases more energy than a single D-T fusion event (~17.6 MeV). However, fusion releases far more energy per kilogram of fuel because the fuel nuclei are so much lighter.

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Specimen Exam Question

Specimen question modelled on the AQA 7408 paper format (9 marks):

Nuclear fission of U-235 and the deuterium-tritium fusion reaction

²³⁵₉₂U + ¹₀n → ⁹²₃₆Kr + ¹⁴¹₅₆Ba + 3 ¹₀n (≈ 200 MeV released)

²₁H + ³₁H → ⁴₂He + ¹₀n (17.6 MeV released)

are both energy-releasing nuclear reactions but differ profoundly in their physical conditions and engineering challenges.

(a) Compare the energy released per kilogram of fuel for U-235 fission and D-T fusion. Show numerical reasoning. (3 marks)

(b) Explain why fusion requires temperatures of ~10⁸ K while fission proceeds readily at room temperature. Refer to the Coulomb barrier and to the role of slow neutrons. (3 marks)

(c) State the function of the moderator, control rods, and coolant in a thermal fission reactor, and identify a suitable material for each. (3 marks)

AO Breakdown

Part	Marks	AO1	AO2	AO3
(a)	3	1 (energy-per-unit-mass concept)	2 (compute both numbers)	—
(b)	3	1 (recall Coulomb barrier; slow-neutron capture)	1 (link kinetic energy to temperature)	1 (contrast neutron-induced fission with charged-projectile fusion)
(c)	3	3 (recall three reactor roles and one material each)	—	—

For 9-mark "compare and explain" questions, examiners reward candidates who show calculation in (a), state the physical reason in (b) rather than just the empirical fact, and give paired role + material in (c) rather than dropping the material. The discriminating A* move is to link the temperature requirement in fusion back to the charged-projectile-vs-neutral-neutron contrast.

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Grade-Band Model Answers

Grade C response

(a) For U-235, 200 MeV per 235 u: 200 × 10⁶ × 1.6 × 10⁻¹⁹ / (235 × 1.66 × 10⁻²⁷) ≈ 8.2 × 10¹³ J/kg.

For D-T, 17.6 MeV per 5 u: 17.6 × 10⁶ × 1.6 × 10⁻¹⁹ / (5 × 1.66 × 10⁻²⁷) ≈ 3.4 × 10¹⁴ J/kg.

So D-T fusion gives about four times more energy per kg.

(b) Fusion needs two positive nuclei to come close together, but they repel each other electrically. Only at very high temperature do they have enough kinetic energy. Fission uses neutrons which have no charge so they don't repel.

(c) Moderator: slows neutrons; graphite or water. Control rods: absorb neutrons; boron. Coolant: removes heat; water.