OCR A Level Physics A: Mass-energy, binding energy, fission and fusion (H556) – Revision Notes

These notes condense section 6.4.4 (Nuclear fission and fusion), outcomes (a) to (k), of the OCR A Level Physics A (H556) specification, Version 3.0 (March 2026). The study guide has the fuller explanations and longer examples. For timed practice, try the practice questions, the course hub, the printable checklist and the free diagnostics.

Key definitions

Term	Meaning
Mass defect	Total mass of the free protons and neutrons, less the nucleus mass
Binding energy	Energy required to pull a nucleus apart into free nucleons; equal to mass defect × c²
Binding energy per nucleon	Binding energy ÷ nucleon number A; higher means more stable
Pair creation	A photon becomes a particle and its antiparticle
Annihilation	A particle and its antiparticle become photons
Induced fission	A nucleus, usually U-235, splits after absorbing a neutron
Chain reaction	Neutrons from one fission cause further fissions
Fusion	Light nuclei join to make a heavier nucleus

Equations and conversions

Quantity	Relationship	Units
Mass-energy	ΔE = Δmc²	J, kg, m s⁻¹
Pair creation threshold	photon energy ≥ 2mc²	J
Photon energy	E = hc/λ	J, m
Energy released	(mass before − mass after) × c²	J
Energy from binding energies	total of products − total of reactants	MeV
Mean kinetic energy	(3/2)kT	J, K
Electronvolt	1 MeV = 1.60 × 10⁻¹³ J
Mass equivalent	1 MeV = 1.78 × 10⁻³⁰ kg (with c = 3.00 × 10⁸ m s⁻¹)

Use the constants given in the question. Converting 1 u = 1.661 × 10⁻²⁷ kg with c = 3.00 × 10⁸ m s⁻¹ gives 934 MeV, while 931.5 MeV is the value from more precise constants. Do not mix the two in one answer.

Method: binding energy from masses

1. Mass of nucleons = Z × m(proton) + (A − Z) × m(neutron).
2. Mass defect = mass of nucleons − mass of nucleus.
3. Convert to kilograms if needed, then ΔE = Δmc².
4. Per nucleon: divide by A.

With atomic masses, replace each proton by a hydrogen atom so that the electron masses cancel.

Worked reminder. Iron-56 has a binding energy per nucleon of 8.79 MeV.

total binding energy = 56 × 8.79 = 492 MeV
= 492 × 1.60e-13 = 7.87 × 10⁻¹¹ J
mass defect = 7.87e-11 / (3.00e8)² = 8.75 × 10⁻²⁸ kg

Method: energy released in a reaction

1. Write a balanced equation (A and Z both balance).
2. Total the masses on each side, using nuclear masses or atomic masses consistently.
3. Subtract: reactants minus products. A positive result means energy is released; a negative one means energy is absorbed.
4. Convert with ΔE = Δmc² (or 931.5 MeV per u if that is the value you are given).

Worked reminder. ²₁H + ²₁H → ³₁H + ¹₁H. Atomic masses: H-2 2.014102 u, H-3 3.016049 u, H-1 1.007825 u.

before = 2 × 2.014102 = 4.028204 u
after  = 3.016049 + 1.007825 = 4.023874 u
Δm = 0.004330 u, so energy released = 0.004330 × 931.5 = 4.03 MeV

Pair creation and annihilation

• Electron rest energy is about 0.51 MeV. An electron-positron pair needs a photon of at least about 1.02 MeV.
• Annihilation at rest gives two photons in opposite directions, each carrying one rest energy, so momentum stays zero.
• Photon energy above the threshold becomes kinetic energy of the pair.

Binding energy per nucleon curve

BE per nucleon
 8.8 |            . . Fe-56 peak
     |        . .       . . .
     |      .                   . . . U
     |    .
     |  . He-4 (local peak)
     +--------------------------------- nucleon number A

Region	Process that releases energy	Why
Left of A = 56	Fusion	Product has a higher binding energy per nucleon
Right of A = 56	Fission	Fragments have a higher binding energy per nucleon

Near iron no further gain is possible by joining or splitting.

Fission reactor in steps

1. A thermal neutron is absorbed by U-235 in a fuel rod.
2. The nucleus splits into two fragments plus two or three fast neutrons, releasing energy.
3. The moderator slows the fast neutrons so they are likely to cause further fission.
4. Control rods absorb neutrons: in to slow the reaction, out to speed it up. A steady reaction needs one neutron per fission to cause another.
5. A coolant carries the thermal energy to a heat exchanger that raises steam for turbines.

Part	Typical material	Must have
Fuel rods	Enriched uranium	Fissile nuclei
Moderator	Water, graphite	Light nuclei, low neutron absorption
Control rods	Boron, cadmium	Strong neutron absorption

Nuclear waste

• Hazards: ionising radiation, heat, very long half-lives for some nuclides, leaks and security during transport and storage.
• Handling: cooling ponds, sealing in glass, shielded containers, deep geological storage.
• Benefits to weigh: no carbon dioxide from fission in operation, small volume of waste.
• Judgement: give an advantage and a disadvantage, each with a reason.

Fusion and temperature

• Nuclei repel, so they must approach within about 10⁻¹⁵ m, where the strong nuclear force acts.
• High kinetic energy means high temperature (mean energy (3/2)kT), so the fuel is a plasma at millions of kelvin.
• Product binding energy per nucleon is higher, so energy is released.
• Hard to achieve on Earth because the plasma must be heated and contained.

Worked reminder. Deuterium has a total binding energy of 2.22 MeV, so 2.22 ÷ 2 = 1.11 MeV per nucleon. Helium-4 has 28.3 MeV, so 28.3 ÷ 4 ≈ 7.1 MeV per nucleon. Fusing light nuclei into helium moves them far up the curve, which is why the energy released per kilogram of fuel is so large.

Must-know distinctions

• Mass defect is a mass; binding energy is an energy; binding energy per nucleon is energy per particle.
• Moderator slows neutrons; control rods absorb them.
• Fission splits one heavy nucleus; fusion joins two light ones. Both move towards the peak of the curve.
• Pair creation needs a photon; annihilation produces photons.

Quick self-test

1. Write ΔE = Δmc² with the SI unit of each quantity.
2. A mass of 2.0 × 10⁻³⁰ kg is converted completely to energy. Find the energy in joules.
3. An electron and a positron annihilate at rest. Find the wavelength of each photon. (Electron mass 9.11 × 10⁻³¹ kg, h = 6.63 × 10⁻³⁴ J s.)
4. A nucleus has a binding energy of 1.6 × 10⁻¹¹ J. Find its mass defect in kg.
5. A calcium-40 nucleus has a binding energy of 342 MeV. Find the binding energy per nucleon.
6. Why does fusion of light nuclei release energy?
7. State the job of the moderator.
8. State what happens to the reaction rate if control rods are withdrawn, and why.
9. A small research reactor has a thermal power of 1.0 × 10⁶ W. Each fission releases 3.2 × 10⁻¹¹ J. Find the fissions per second.
10. ²³⁵₉₂U + ¹₀n → ¹⁴¹₅₆Ba + ⁹²₃₆Kr + x ¹₀n. Find x.
11. Explain why fusion needs a very high temperature.
12. Give one problem of storing high-level nuclear waste.

Answers

1. Energy change in J = mass change in kg × (speed of light in m s⁻¹)².
2. E = 2.0 × 10⁻³⁰ × (3.00 × 10⁸)² = 1.8 × 10⁻¹³ J.
3. Each photon carries one rest energy: 9.11 × 10⁻³¹ × (3.00 × 10⁸)² = 8.20 × 10⁻¹⁴ J. λ = hc/E = 6.63 × 10⁻³⁴ × 3.00 × 10⁸ / 8.20 × 10⁻¹⁴ = 2.43 × 10⁻¹² m.
4. Δm = 1.6 × 10⁻¹¹ / (3.00 × 10⁸)² = 1.8 × 10⁻²⁸ kg.
5. 342 ÷ 40 = 8.55 MeV per nucleon.
6. The product has a higher binding energy per nucleon, so some mass is converted to energy.
7. It slows fast neutrons by collisions, so they are more likely to cause fission.
8. The rate rises, because fewer neutrons are absorbed and more fissions are caused.
9. 1.0 × 10⁶ / 3.2 × 10⁻¹¹ = 3.1 × 10¹⁶ per second.
10. Nucleon number: 236 = 141 + 92 + x, so x = 3 (charge: 92 = 56 + 36 balances).
11. Nuclei repel, so they must be given large kinetic energy to reach the range of the strong nuclear force, and kinetic energy rises with temperature.
12. It stays radioactive and hot for a very long time, so it needs secure storage for thousands of years.

Where marks are usually lost

• Using mass in u or g in ΔE = Δmc² and forgetting to convert to kilograms.
• Giving the energy of one annihilation photon as the total, or writing one photon instead of two.
• Dividing the binding energy by the proton number rather than the nucleon number.
• Mixing atomic and nuclear masses in the same mass-defect sum.
• Saying the control rods slow the neutrons, or that the moderator absorbs them.
• Reading the curve backwards: fission is on the right, fusion on the left.
• Writing a waste answer with no reason or with only advantages.
• Forgetting to check proton number as well as nucleon number in equations.

Official syllabus

OCR Level 3 Advanced GCE in Physics A (H556), Version 3.0 (March 2026), first assessment 2017, published by OCR. Section 6.4.4, outcomes (a) to (k).