You are viewing a free preview of this lesson.
Subscribe to unlock all 8 lessons in this course and every other course on LearningBro.
The previous lesson on nuclear fission and fusion introduced the basic physics: a slow neutron splits a U-235 nucleus into two fragments plus more neutrons, releasing ~200 MeV. This lesson digs into the engineering: how that single reaction is leashed into a sustained, controlled chain reaction inside a power-producing reactor; how moderator, control rods, coolant, and fuel cladding all combine to maintain a multiplication factor of exactly one; how spent fuel is handled and reprocessed; and what the environmental costs and benefits of fission power look like. The material is examined under AQA 7408 section 3.8.1.6 alongside the prerequisite fission physics from lesson 5.
Spec mapping (AQA 7408): This lesson covers induced fission of U-235 by thermal neutrons, the chain reaction and multiplication factor k, the role of moderator (slowing neutrons), control rods (absorbing neutrons), and coolant (heat transfer) in a thermal reactor, critical mass and prompt vs delayed neutrons, common reactor types (PWR, BWR, AGR), fuel-rod fabrication and the U-235 enrichment process, spent-fuel handling and reprocessing, and environmental considerations of fission power including waste storage and accident risk. It maps to AQA 7408 section 3.8.1.6 (nuclear reactors and energy production). (Refer to the official AQA specification document for exact wording.)
Synoptic links: (1) The thermal-neutron capture cross-section of U-235 follows a 1/v law at low energies, where v is the neutron speed — this is the synoptic bridge to kinetic theory (section 3.6) and the Maxwell-Boltzmann distribution. (2) The thermodynamic cycle converting reactor heat to electricity (typically a Rankine cycle in a PWR) connects to thermal physics (section 3.6) and the second law's restriction on thermal efficiency. (3) Reactor-safety engineering — negative temperature coefficients, passive cooling, defence in depth — applies the principles of feedback control and equilibrium covered in mechanics and electricity sections (3.4, 3.5).
A free thermal neutron with kinetic energy of about 0.025 eV (equivalent to room temperature, kT at 290 K) is absorbed by a U-235 nucleus, forming a highly excited U-236* compound nucleus. The excitation energy (~6 MeV) deforms the nucleus into an elongated shape that quickly snaps into two unequal fragments, releasing the energy stored in the binding-energy difference between U-236 and the lighter fragment pair (~200 MeV total). On average, 2.4 neutrons are released per fission event in U-235 fission, with a range of typically 0 to 5 depending on the specific fragmentation channel.
The probability that a neutron is absorbed by a U-235 nucleus (the capture cross-section, σ, measured in barns where 1 b = 10⁻²⁸ m²) varies strongly with neutron speed:
| Neutron energy | Speed (m s⁻¹) | σ for U-235 fission (b) |
|---|---|---|
| Thermal (0.025 eV) | ~2200 | ~580 |
| Epithermal (1 eV) | ~14 000 | ~100 |
| Fast (1 MeV) | ~1.4 × 10⁷ | ~1 |
Slow neutrons are about 600 times more likely to be captured by U-235 than fast neutrons. This is the central engineering reason why a thermal reactor uses a moderator to slow the fast neutrons released in fission down to thermal energies before they encounter the next U-235 nucleus.
Of the neutrons released per fission, the overwhelming majority — about 99 % — are emitted within ~10⁻¹⁴ s of the fission event itself; these are prompt neutrons. The remaining ~1 % are emitted seconds to minutes later by certain neutron-rich fission fragments after a beta decay; these are delayed neutrons.
The delayed-neutron fraction (β ≈ 0.0065 for U-235) is small, but it is what makes a reactor controllable. If only prompt neutrons existed, the reactor period (the time over which neutron population grows by a factor of e) would be ~10⁻⁴ s, far too short for any control system to react. The delayed neutrons stretch the effective reactor period to seconds, allowing control rods to be moved at human timescales. Prompt-critical operation (k_eff ≥ 1 with prompt neutrons alone) is what makes a nuclear weapon explosive; reactors are engineered to stay delayed-critical (k_eff = 1 only with the help of delayed neutrons).
The single most important parameter for reactor operation is the effective multiplication factor, k_eff:
k_eff = (number of neutrons in generation n+1) / (number in generation n)
The behaviour of the chain reaction depends entirely on k_eff:
| Condition | k_eff | Behaviour | Application |
|---|---|---|---|
| Subcritical | < 1 | Neutron population decays | Reactor shut down, or unsafe configuration |
| Critical | = 1 | Neutron population steady | Normal reactor operation |
| Supercritical | > 1 | Neutron population grows exponentially | Starting up; emergency excursion |
| Prompt-critical | > 1 with prompt neutrons alone | Uncontrollable, μs growth | Weapon physics |
In a power reactor, k_eff is held at 1.000 to within parts per thousand by automatic adjustment of the control rods. A small departure from k_eff = 1.000 causes the neutron flux (and therefore reactor power) to drift, which is corrected by inserting or withdrawing rods.
k_eff is conventionally decomposed into six contributions:
k_eff = η × f × p × ε × P_NL × P_FNL
where:
For a typical PWR at start-of-life, η ≈ 2.0, f ≈ 0.7, p ≈ 0.8, ε ≈ 1.03, with non-leakage close to 1 for a large core. The detail is beyond A-Level; what matters is that all six must work together to give k_eff = 1.
The fuel for a typical thermal reactor is uranium dioxide (UO₂) ceramic, formed into cylindrical pellets about 10 mm in diameter and 15 mm long. These pellets are stacked inside hollow tubes ("cladding") of zirconium alloy (Zircaloy-4 or Zirlo), each tube about 4 m long. Hundreds of these fuel rods are bundled into a fuel assembly, and hundreds of assemblies make up the reactor core.
Key properties:
The moderator slows fast neutrons (released from fission at ~2 MeV) down to thermal energies (~0.025 eV) by repeated elastic collisions. The fractional energy transferred in an elastic head-on collision between a neutron of mass m and a nucleus of mass M is 4mM/(m + M)². This fraction is maximised when M = m — i.e. the moderator nucleus is mass-matched to the neutron. Hydrogen (mass ~1 u) is therefore optimal but absorbs neutrons via n + p → ²H + γ; deuterium (mass 2 u) is nearly as efficient and absorbs far less. Common moderators:
| Moderator | M (u) | Slowing-down efficiency | Absorption | Where used |
|---|---|---|---|---|
| Light water (H₂O) | 18 (per molecule) | High (H atoms) | Moderate | PWR, BWR |
| Heavy water (D₂O) | 20 | High | Very low | CANDU |
| Graphite (C) | 12 | Moderate | Very low | AGR, RBMK |
| Beryllium | 9 | High | Low | Research reactors |
Control rods are inserted between the fuel assemblies to absorb excess neutrons. They are made from materials with very high thermal-neutron capture cross-sections:
A reactor "SCRAM" (emergency shutdown) drops all control rods fully into the core by gravity, halting the chain reaction in less than a second. The Three-Mile-Island accident (1979) and Fukushima accident (2011) both involved successful SCRAMs followed by decay-heat problems (the residual heat from short-lived fission products, ~6 % of full power immediately after shutdown, decreasing slowly over days).
The coolant transports thermal energy from the reactor core to the steam generator (in a PWR) or directly to the turbine (in a BWR or gas-cooled reactor). Coolant requirements: high specific heat capacity, low neutron absorption, chemical stability at high temperature and pressure, and compatibility with reactor materials.
| Coolant | Reactor types | Operating T (°C) | Operating P (bar) |
|---|---|---|---|
| Light water (pressurised) | PWR | ~325 | 155 |
| Light water (boiling) | BWR | ~285 | 70 |
| Heavy water | CANDU | ~310 | 100 |
| CO₂ | AGR, Magnox | ~650 | 40 |
| Liquid sodium | FBR | ~550 | 1 (low) |
| Molten salt | MSR (Gen IV) | ~700 | 1 |
In a PWR, the coolant (high-pressure liquid water) is also the moderator, giving an important passive safety property: if the coolant boils away or leaks, the moderator goes with it, and the chain reaction stops. This is the negative moderator-temperature coefficient that distinguishes water reactors from designs like the RBMK (Chernobyl), which had a positive coefficient under some conditions.
The reactor core sits inside a thick steel pressure vessel designed to contain the high-pressure coolant. The pressure vessel and primary cooling loop sit inside a much larger containment building — typically a steel-reinforced concrete dome designed to contain any radioactive release in the event of a core-damage accident. Modern Gen-III PWRs (AP1000, EPR) have double-walled containments with passive cooling.
graph TD
A["Containment building<br/>(steel-reinforced concrete)"] --> B["Pressure vessel<br/>(thick steel)"]
B --> C["Core: fuel + moderator + coolant"]
C --> D["Fuel assemblies<br/>(UO₂ in Zircaloy)"]
C --> E["Control rods<br/>(B₄C / Cd)"]
C --> F["Coolant<br/>(high-P water)"]
F --> G["Steam generator"]
G --> H["Turbine + generator<br/>→ grid"]
G --> I["Secondary loop<br/>(low radioactivity)"]
style B fill:#3498db,color:#fff
style G fill:#27ae60,color:#fff
style E fill:#e74c3c,color:#fff
The critical mass is the minimum amount of fissile material that can sustain a chain reaction. Below this mass, too many neutrons escape from the surface without causing further fissions; above it, leakage is small enough that k_eff ≥ 1 can be achieved.
Critical mass depends on:
For pure U-235 sphere, no reflector: ~52 kg. With a beryllium reflector: ~15 kg. For Pu-239, the figures are smaller still.
A power reactor operates with hundreds of kg of fissile material distributed over a large volume — far above the bare critical mass, but with the geometry (rods spaced in moderator) and control rods designed so that k_eff = 1.000 is the steady state.
A typical commercial PWR generates 1 GW of electrical power (about 3 GW of thermal power, given thermodynamic efficiency of ~33 %). Find:
(a) the rate at which U-235 is consumed.
Each fission releases 200 MeV = 200 × 1.60 × 10⁻¹³ J = 3.20 × 10⁻¹¹ J.
Required fission rate for 3 GW thermal = 3 × 10⁹ W / 3.20 × 10⁻¹¹ J per fission = 9.4 × 10¹⁹ fissions per second.
Mass per fission: 235 × 1.66 × 10⁻²⁷ kg = 3.90 × 10⁻²⁵ kg per nucleus consumed.
Rate of U-235 consumption: 9.4 × 10¹⁹ × 3.90 × 10⁻²⁵ kg s⁻¹ = 3.67 × 10⁻⁵ kg s⁻¹.
In a day: 3.67 × 10⁻⁵ × 86400 = 3.17 kg per day.
In a year: ~1160 kg or about 1.2 tonnes of U-235 per year.
For 3 % enriched fuel, this corresponds to roughly 40 tonnes of uranium per year loaded into the reactor (only a fraction of which is consumed before the fuel is removed as spent).
(b) Compare with a coal power station.
Subscribe to continue reading
Get full access to this lesson and all 8 lessons in this course.