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Nuclear fission is the splitting of a heavy nucleus into two lighter nuclei, accompanied by the release of a large amount of energy. It is the process that powers nuclear power stations and was used in the first atomic weapons. Understanding fission requires bringing together everything we have learned about binding energy, the strong nuclear force, and mass-energy equivalence.
Fission can occur spontaneously in some very heavy isotopes, but the fission used in nuclear reactors is induced fission — triggered by a neutron striking a heavy nucleus.
The most important fission fuel is uranium-235. When a U-235 nucleus absorbs a slow-moving (thermal) neutron, it briefly becomes uranium-236 in a highly excited state. This compound nucleus is so unstable that it immediately splits into two medium-mass fission fragments plus two or three additional neutrons:
²³⁵₉₂U + ¹₀n → ²³⁶₉₂U → fission fragments + neutrons + energy*
A typical fission reaction:
²³⁵₉₂U + ¹₀n → ¹⁴¹₅₆Ba + ⁹²₃₆Kr + 3¹₀n + ~200 MeV
The exact fission fragments vary — there are many possible ways for the uranium nucleus to split. The fragments are almost always unequal in mass and are themselves radioactive (neutron-rich), undergoing a chain of beta decays to reach stability.
U-235 undergoes fission most readily with slow (thermal) neutrons — neutrons with kinetic energies around 0.025 eV, corresponding to room temperature. This is because slow neutrons spend more time near the nucleus, increasing the probability of absorption. Fast neutrons tend to pass through or scatter off the nucleus without being captured.
The probability of a neutron causing fission is described by the fission cross-section, measured in barns (1 barn = 10⁻²⁸ m²):
| Isotope | Thermal neutron fission cross-section | Fast neutron fission cross-section |
|---|---|---|
| U-235 | ~585 barns | ~1.2 barns |
| U-238 | ~0 barns (not fissile) | ~0.3 barns (above ~1 MeV only) |
| Pu-239 | ~748 barns | ~1.8 barns |
The enormous difference between thermal and fast cross-sections for U-235 explains why moderators are essential in thermal reactors.
Each fission event releases approximately 200 MeV of energy. This can be understood from the binding energy per nucleon curve:
This energy appears as:
Problem: A nuclear reactor operates at 1.0 GW thermal power. How many fission events per second are needed?
Energy per fission = 200 MeV = 200 × 10⁶ × 1.6 × 10⁻¹⁹ J = 3.2 × 10⁻¹¹ J
Fissions per second = Power / Energy per fission = 1.0 × 10⁹ / 3.2 × 10⁻¹¹ = 3.125 × 10¹⁹
That is approximately 3 × 10¹⁹ fission events every second. Despite this enormous number, the mass of U-235 consumed per day is only about 1 kg.
Daily energy = 1.0 × 10⁹ × 86400 = 8.64 × 10¹³ J
Using E = mc²: Δm = E/c² = 8.64 × 10¹³ / (3 × 10⁸)² = 0.096 kg
This 96 g is the actual mass converted to energy. The total mass of U-235 consumed is much larger (about 1.1 kg/day), because only a fraction of the rest-mass energy is released — the binding energy difference, not the total mass.
Each fission event produces 2–3 neutrons. If these neutrons go on to cause further fissions, each of those produces another 2–3 neutrons, and so on. This is a chain reaction.
The behaviour of a chain reaction depends on the multiplication factor k:
| Condition | k value | Meaning |
|---|---|---|
| Subcritical | k < 1 | Each generation has fewer fissions than the previous one; the reaction dies out |
| Critical | k = 1 | Each generation has exactly the same number of fissions; the reaction is self-sustaining at a constant rate |
| Supercritical | k > 1 | Each generation has more fissions; the reaction rate increases exponentially |
A nuclear reactor operates at k = 1 (critical). A nuclear weapon requires k >> 1 (supercritical) for a very brief time.
A chain reaction can only be sustained if there is enough fissile material for the neutrons to find another U-235 nucleus before escaping from the surface. The minimum amount of fissile material needed is the critical mass. For pure U-235, the critical mass is about 52 kg (a sphere roughly 17 cm in diameter).
Below the critical mass, too many neutrons escape without causing further fissions, and the chain reaction fizzles out.
A nuclear power station converts the kinetic energy of fission fragments into thermal energy, which is used to generate steam, which drives turbines connected to generators. The key components of a nuclear reactor are:
The fuel is typically enriched uranium — natural uranium (99.3% U-238, 0.7% U-235) with the proportion of U-235 increased to about 3–5%. The fuel is formed into ceramic pellets and loaded into long metal tubes (cladding) to form fuel rods. The cladding prevents fission products from escaping into the coolant.
The neutrons produced by fission are fast (high energy), but U-235 fissions most effectively with slow (thermal) neutrons. A moderator is a material that slows the neutrons down through elastic collisions without absorbing too many of them.
Effective moderators have low mass number (so the neutron transfers maximum kinetic energy per collision) and low neutron absorption cross-section:
A neutron is slowed from about 2 MeV to 0.025 eV through multiple collisions with moderator atoms — a process called thermalisation.
The average fractional energy loss per elastic collision depends on the moderator mass number A_mod:
| Moderator | A_mod | Average collisions to thermalise |
|---|---|---|
| Water (hydrogen) | 1 | ~18 |
| Heavy water (deuterium) | 2 | ~25 |
| Graphite (carbon) | 12 | ~115 |
Hydrogen is the most efficient per collision, but it also absorbs more neutrons than deuterium or carbon.
Control rods are made of materials that readily absorb neutrons, such as boron or cadmium. By inserting or withdrawing the control rods, operators adjust the number of neutrons available for fission, keeping the multiplication factor k = 1.
In an emergency, all control rods are fully inserted rapidly (SCRAM) to shut the reactor down.
The coolant transfers thermal energy from the reactor core to the steam generators. Common coolants include:
The heated coolant passes through a heat exchanger, where it boils water in a separate circuit to produce steam.
Nuclear reactors incorporate multiple safety systems:
Induced fission occurs when a thermal neutron is absorbed by U-235, forming an unstable compound nucleus that splits into two fission fragments plus 2–3 neutrons and ~200 MeV. The released neutrons can trigger further fissions in a chain reaction. A reactor maintains k = 1 using control rods (neutron absorbers), a moderator (to slow neutrons), fuel rods (enriched uranium), and a coolant (to transfer thermal energy). Critical mass is the minimum amount of fissile material needed to sustain a chain reaction. Each fission event converts about 0.1% of the uranium’s rest mass into energy.
Edexcel 9PH0 specification Topic 8 — Nuclear and Particle Physics, with crossover into Topic 11 — Nuclear Radiation covers the induced fission of heavy nuclei, the conditions for a self-sustaining chain reaction, the role of moderators and control rods in thermal reactors, and the calculation of energy released from a mass defect using E=mc2 (refer to the official specification document for exact wording). Although fission sits in the second-year content for the Edexcel A-Level Physics route, the underlying mass–energy equivalence is introduced in Topic 4 (Materials and energy) at AS, and the binding-energy-per-nucleon framework on which fission analysis rests is built in Topic 8 itself. The Edexcel formula and data booklet supplies c, NA, the unified atomic mass unit u=1.66×10−27 kg, and the conversion 1u≡931.5 MeV, so candidates do not need to memorise these constants — but they must use them confidently. Fission is examined principally in Paper 2 (Physics on the Move and beyond) but appears synoptically in Paper 3 short-answer items as well.
Question (8 marks):
A thermal neutron induces fission in a uranium-235 nucleus according to:
92235U+01n→56141Ba+3692Kr+301n+Q
Atomic masses (in u): U-235 = 235.04393; n = 1.00867; Ba-141 = 140.91440; Kr-92 = 91.92616.
(a) Show that the equation conserves both nucleon (baryon) number and proton (charge) number. (2)
(b) Calculate the energy released per fission, Q, in MeV. (4)
(c) Estimate the energy released per kilogram of U-235 consumed, in J kg−1. (2)
Solution with mark scheme:
(a) Step 1 — check nucleon number.
LHS: 235+1=236. RHS: 141+92+3(1)=236. Balanced.
LHS proton number: 92+0=92. RHS: 56+36+3(0)=92. Balanced.
B1 — both balances stated explicitly, with arithmetic shown.
B1 — explicit conclusion that the equation is consistent with conservation of nucleon and charge number.
A common slip is to count only one side and assert balance without showing the sum on the other; examiners want both sides demonstrated.
(b) Step 1 — calculate the mass defect Δm.
Total reactant mass: 235.04393+1.00867=236.05260 u.
Total product mass: 140.91440+91.92616+3×1.00867=235.86657 u.
Mass defect: Δm=236.05260−235.86657=0.18603 u.
M1 — correct method (reactants minus products) using all five mass terms, including the three product neutrons.
A1 — Δm≈0.186 u (allow rounding to 3 s.f. or better).
Step 2 — convert mass defect to energy.
Using 1u≡931.5 MeV from the data booklet:
Q=0.18603×931.5≈173MeV
M1 — applying the u-to-MeV conversion (or equivalently E=Δmc2 in SI then dividing by 1.6×10−13).
A1 — Q≈173 MeV (accept 170–175 MeV depending on rounding).
(c) Step 1 — number of nuclei per kg.
Number of U-235 nuclei in 1 kg =235×1.66×10−27kg1kg≈2.56×1024.
M1 — using the molar mass M=235 g mol−1 with Avogadro's number, or equivalently 1/(235u).
Step 2 — total energy.
Energy per fission in joules: 173×106×1.6×10−19≈2.77×10−11 J.
Energy per kg: 2.56×1024×2.77×10−11≈7.1×1013 J kg−1.
A1 — answer in the range 7–8×1013 J kg−1.
Total: 8 marks (B2 M3 A3, split as shown). Compare this with the chemical energy density of a fossil fuel (∼5×107 J kg−1 for petrol): fission is roughly a million times more energy-dense, the synoptic comparison most often reached for in extended-prose questions.
Question (6 marks): A thermal-neutron reactor uses U-235 fuel rods, a graphite moderator, and boron control rods.
(a) State why fast neutrons emitted from a fission event are unlikely to induce further fission, and explain how the moderator addresses this. (3)
(b) Explain how moving the control rods further out of the core changes the value of the reproduction constant k, and describe the consequence for reactor power. (3)
Mark scheme decomposition by AO:
(a)
(b)
Total: 6 marks split AO1 = 3, AO2 = 2, AO3 = 1. This is a classic "physics in context" question pattern: AO1 marks for naming components and stating their function, AO2 marks for explaining the underlying mechanism, AO3 marks for predicting the time-dependent behaviour.
Connects to:
Topic 8 — Binding energy per nucleon: the curve peaks near A≈56 (iron). Fission of U-235 (A=235) produces fragments near A≈100–140, all of which have higher binding energy per nucleon than the parent. The energy released per fission is approximately (A_\text{parent})\Delta(BE/A)\), giving the right order of magnitude (\sim 200$ MeV) without any explicit mass-defect arithmetic.
Topic 4 / Topic 8 — E=mc2: the energy released is the mass defect times c2. The number "200 MeV per fission" is roughly 0.1% of a uranium rest-mass energy; emphasising "0.1% of mass becomes energy" is a high-impact synoptic comparison with fusion (∼0.7%) and chemical reactions (∼10−9%).
Topic 11 — Radioactive decay: fission fragments are neutron-rich and undergo β− decay chains until reaching stability. The half-lives span microseconds to millions of years, which is why spent fuel must be cooled and shielded for centuries.
Topic 8 — Particle physics and conservation laws: charge, baryon number and lepton number are conserved at every stage. Even the prompt neutrons emitted in fission obey these conservation rules, identical in spirit to the conservation laws governing meson decay.
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