Key Idea: This topic is where mass turns into energy. Weigh a nucleus and it is always a little lighter than its separate protons and neutrons — that missing mass defect, through E = mc², is the binding energy that holds the nucleus together. Plot the binding energy per nucleon against nucleon number and the curve peaks near iron: any reaction that moves toward that peak releases energy, which is why both fusion (joining light nuclei) and fission (splitting heavy ones) give out energy. From there the topic builds out to fission as a power source — induced fission, the chain reaction, the neutron economy that keeps it steady, and the four parts of a nuclear reactor. It is examined on both papers. Paper 1A is quick multiple-choice — read off the most stable nucleus, compare energy released per unit mass in fusion vs fission, pick the neutron loss that keeps a chain steady, or match a reactor component to its job. Paper 2 is longer structured work — find a mass defect, the binding energy and the binding energy per nucleon, calculate the energy released in a fission, or outline how a reactor works.
📋 Key formulas
Only one equation in this topic carries the data-booklet badge — E = mc² (look for it). The mass-defect, per-nucleon and neutron-economy relations below are bookkeeping rules, not printed equations, so you remember those.
- energy equivalent of the mass — the binding energy, or the energy released in a reaction (J, or MeV)
- mass converted — the mass defect Δm of the nucleus or reaction (kg, or u)
- speed of light, 3.00 × 10⁸ m s⁻¹ (given constant)
- mass defect — mass that goes missing when the nucleus forms (u or kg)
- number of protons (each of mass m_p)
- number of neutrons (each of mass m_n)
- actual mass of the bound nucleus (always the lighter total)
- total binding energy of the nucleus (MeV)
- nucleon number — the number of protons + neutrons
- number of neutrons released per fission (about 2–3)
- number that must be lost or absorbed so exactly ONE continues the chain (steady)
⚖️ Mass defect, binding energy & 'per nucleon'
| Quantity | What it means | How to get it |
|---|---|---|
| Mass defect (Δm) | The mass that goes missing when the nucleus forms — the nucleus is lighter than its loose nucleons | Δm = (Z·mₚ + N·mₙ) − nucleus mass |
| Binding energy (Eb) | Energy that mass is worth; the energy needed to pull the nucleus fully apart | E = mc²; in MeV, Δm(in u) × 931.5 |
| Binding energy per nucleon | A fair stability score for any nucleus — higher = more tightly bound = more stable | Eb ÷ A (nucleon number) |
☢️ Fusion vs fission on the curve
| Fusion | Fission | |
|---|---|---|
| What happens to the nuclei | Two light nuclei join into a larger one | One heavy nucleus splits into two smaller ones |
| Where on the curve | Climbs the steep left side toward iron | Climbs the gentle right side toward iron |
| Why energy is released | Products are more tightly bound (higher up the curve) | Products are more tightly bound (higher up the curve) |
| Energy per unit mass of fuel | More — several MeV per nucleon | Less — under 1 MeV per nucleon |
Higher on the binding-energy-per-nucleon curve = more tightly bound = more stable, and the peak sits near iron (A ≈ 56). Any reaction that moves a nucleus toward that peak ends up more tightly bound, so it releases energy — that is why BOTH fusion (from the light side) and fission (from the heavy side) give out energy. The classic trap is thinking only fission releases energy.
🔁 The chain reaction & the reactor
| Regime | Neutrons continuing per fission | What the chain does |
|---|---|---|
| Subcritical | Fewer than one (more than N − 1 are lost) | Dies out |
| Critical | Exactly one (N − 1 are lost or absorbed) | Steady — the reactor's working state |
| Supercritical | More than one (fewer than N − 1 are lost) | Grows — rate climbs each generation |
| Reactor part | Its one job | Typical material |
|---|---|---|
| Fuel | Fissions and releases the energy | Uranium-235 (or plutonium-239) |
| Moderator | Slows the fast neutrons so they cause more fissions | Water or graphite |
| Control rods | Absorb spare neutrons to keep the chain steady | Boron or cadmium |
| Heat exchanger | Removes the heat to make steam for the turbine | Coolant loop (water / CO₂) |
Important: Both the moderator and the control rods act on neutrons, but oppositely: - moderator → slows neutrons (helps fission) - control rods → absorb neutrons (limit fission) Swapping these two is the most common reactor mistake.
✏️ Worked exam-style questions
A boron-11 nucleus has 5 protons and 6 neutrons. Proton mass = 1.007276 u, neutron mass = 1.008665 u, and the boron-11 nucleus has mass 11.00931 u. (a) Find the mass defect. (b) Find the total binding energy in MeV. (c) Find the binding energy per nucleon. (1 u = 931.5 MeV c⁻².)
🔒 Model answer plan
See the mark-by-mark plan — for / against / judgement, with marking guidance — in study mode.
A fusion reaction releases 18 MeV from a total of 5 nucleons of light fuel. A fission reaction releases 195 MeV from a total of 235 nucleons of heavy fuel. Find the ratio of the energy released per unit mass of the fusion fuel to that of the fission fuel.
🔒 Model answer plan
See the mark-by-mark plan — for / against / judgement, with marking guidance — in study mode.
Each fission of a uranium-235 nucleus releases on average 3 neutrons. (a) For a steady, self-sustaining chain reaction, how many neutrons per fission must be lost or absorbed? (b) If instead only 0.9 neutrons per fission go on to cause the next fission, state whether the reaction grows, stays steady or dies out.
🔒 Model answer plan
See the mark-by-mark plan — for / against / judgement, with marking guidance — in study mode.
In one fission event the total mass of the products is 0.198 u less than the mass of the original nucleus plus the absorbed neutron. (a) Using 1 u ≡ 931.5 MeV, find the energy released in this fission, in MeV. (b) A reactor produces 8.0 × 10⁸ W of thermal power and each fission releases 3.2 × 10⁻¹¹ J. Find the number of fissions per second.
🔒 Model answer plan
See the mark-by-mark plan — for / against / judgement, with marking guidance — in study mode.
🧠 Quick self-check
Tap each card to reveal the answer.
What is the mass defect of a nucleus? (Mass of the separate protons + neutrons) − (mass of the bound nucleus). The nucleus is always the lighter one; that missing mass is the binding energy via E = mc².
How do you get the binding energy per nucleon, and what does 'higher' mean? Total binding energy ÷ nucleon number (A). Higher = more tightly bound = more stable. The curve peaks near iron (A ≈ 56).
Why do BOTH fusion and fission release energy? Both move nuclei toward the iron peak (more tightly bound), so both release energy. Fusion (light nuclei) gives more energy per unit mass of fuel.
What keeps a chain reaction STEADY, and how many neutrons are lost? On average exactly one neutron per fission triggers the next. So of the N released, N − 1 must be lost or absorbed (N = 3 → lose 2).
Subcritical, critical, supercritical — what decides which? The number of neutrons that continue per fission. Fewer than one → dies out (subcritical); exactly one → steady (critical); more than one → grows (supercritical).
Moderator vs control rods — what's the difference? Both act on neutrons but oppositely: the moderator slows them (water/graphite, helps fission); the control rods absorb them (boron/cadmium, limit fission).
🎯 Exam tips
Exam Tips
- Mass defect FIRST: add the separate protons and neutrons, then subtract the nucleus mass. Keep every decimal place — Δm is a tiny difference of two large numbers, so early rounding ruins it.
- Binding energy: E = mc². With Δm in u, just multiply by 931.5 to get MeV; for joules, put Δm in kilograms (×1.661 × 10⁻²⁷) first, then ×c². For 'per nucleon', divide by A.
- Higher binding energy per nucleon = more stable. The curve peaks near iron (A ≈ 56). 'Most stable' means the highest PER-NUCLEON value, never the highest total.
- BOTH fusion (light nuclei) and fission (heavy nuclei) release energy by moving toward iron. Fusion releases more energy per unit mass of fuel — energy per nucleon is the fair per-kilogram comparison.
- Steady (critical) chain reaction = exactly ONE neutron per fission causes the next, so N − 1 are lost or absorbed. Lose more → dies out (subcritical); lose fewer → grows (supercritical).
- Energy per fission from a mass defect in u: use the ×931.5 shortcut. Reactor power ÷ energy per fission gives the number of fissions per second — watch the negative power of ten.
- Reactor parts by their verb: fuel FISSIONS, moderator SLOWS neutrons (water/graphite), control rods ABSORB neutrons (boron/cadmium), heat exchanger REMOVES heat. Lower the rods to slow the reaction, raise them to speed it up.