Nuclear Fusion & Fission
Revise Nuclear Fusion & Fission for Physics (IAL) — revision notes and instant AI marking. Free to start.
Nuclear Fusion & Fission
📋 Summary — What This Chapter Covers
- Mass defect (Δm): a nucleus always weighs LESS than its individual protons and neutrons added up separately.
- Binding energy (ΔE): the energy you'd need to put IN to rip a nucleus apart into free nucleons — calculated from the missing mass via E = mc².
- Mass–energy equivalence: Einstein's idea that mass and energy are two forms of the same thing, linked by ΔE = Δmc².
- Atomic mass unit (u): a handy mass unit for tiny particles, where 1 u = 1.66 × 10⁻²⁷ kg = 931.5 MeV.
- Binding energy per nucleon graph: the single most important graph in nuclear physics — it tells you which nuclei are stable, and predicts fusion (light elements) vs fission (heavy elements).
- Iron-56 sits at the peak of the graph — the most stable nucleus that exists.
- Nuclear fusion: small nuclei joining to form a bigger, more stable nucleus, releasing energy — powers stars and is the goal of D-T fusion reactors on Earth.
- Conditions for fusion: nuclei need huge kinetic energy (extreme heat/density) to overcome electrostatic repulsion and get close enough for the strong nuclear force to bind them.
- The proton–proton chain: the 5-stage process by which stars fuse 4 hydrogen nuclei into 1 helium nucleus.
1. Nuclear Binding Energy & Mass Deficit
Here's something that sounds impossible at first: if you carefully weigh a nucleus, and then separately weigh all the protons and neutrons that make it up, the nucleus weighs less than the sum of its parts. Not a rounding error — a real, measurable difference. This missing mass is called the mass defect (symbol Δm).
Why does this happen? Nucleons are held together by the strong nuclear force. Pulling them together into a bound nucleus is like a ball rolling down into a valley — it releases energy as it settles into that lower-energy, more stable state. Since mass and energy are equivalent (thanks, Einstein), releasing energy means losing a tiny bit of mass too. That lost mass IS the mass defect.
Z = proton number · A = nucleon (mass) number · mp = proton mass (kg) · mn = neutron mass (kg) · mtotal = measured nucleus mass (kg)
Binding Energy
Binding energy is defined as: the energy required to break a nucleus into its constituent protons and neutrons. It's essentially the mass defect converted into energy units using mass–energy equivalence.
Students constantly describe binding energy as "the energy stored inside the nucleus." This is WRONG. Binding energy is the energy you'd have to PUT IN to tear the nucleus apart — it's an input needed to pull nucleons apart, not something released or stored inside. Think of it like the energy needed to pull two magnets apart, not energy "stored" in the fact they're stuck together.
Formation of a nucleus from separate protons and neutrons releases energy (exothermic) — and separating a nucleus back into individual nucleons requires that same amount of energy back in.
The binding energy per nucleon for Oxygen-16 (¹⁶O) is 7.98 MeV. Find the total energy needed to completely separate all its nucleons.
2. The Atomic Mass Unit (u)
Kilograms are a clunky unit for particles this tiny — you end up writing 10⁻²⁷ everywhere. So physicists invented a friendlier unit: the unified atomic mass unit (u), defined as exactly one-twelfth of the mass of a carbon-12 atom.
| Particle | Mass / u |
|---|---|
| Proton | 1 |
| Neutron | 1 |
| Electron | 0.0005 |
| Alpha particle (α) | 4 |
Handy shortcut: the mass of an atom in u is roughly equal to its nucleon number A (e.g. Uranium-235 ≈ 235 u). But it's never exactly that number — the actual mass is always slightly less, because of the mass defect we just learned about!
Estimate the mass of the nucleus of copernicium-285 in kg, to 2 d.p. (in the form a × 10⁻²⁵ kg).
3. Binding Energy per Nucleon Graph
This is arguably the single most important graph in the whole of nuclear physics — it explains fusion, fission, star formation, nuclear power, and why iron is special, all in one picture.
Reading the Graph — Key Features
- At low A (light nuclei): binding energy per nucleon is low → these nuclei are less stable → they have weaker electrostatic forces holding them back → they're the ones most likely to undergo fusion (climbing up the steep left side of the curve releases energy).
- Helium-4, Carbon-12, and Oxygen-16 are anomalies that spike above the general trend. Helium-4 is unusually stable on its own; carbon-12 and oxygen-16 can be thought of as 3 and 4 helium nuclei bolted together, inheriting some of that extra stability.
- Iron-56 sits at the very peak — the most stable nucleus in existence. Nothing gains energy by fusing into iron or splitting out of it.
- At high A (heavy nuclei): the curve slowly decreases — these nuclei are less tightly bound and are the ones prone to fission (splitting apart to move back up toward the peak releases energy).
It seems weird that opposite processes (joining vs splitting) both release energy — but it makes total sense once you see the graph as a "stability hill" with iron at the summit. Any nuclear reaction that moves nuclei closer to iron-56 — whether by fusing light ones together or splitting heavy ones apart — moves them UP the binding-energy-per-nucleon curve, and releases energy in the process.
If asked to sketch this graph: (1) draw a best-fit curve, PLUS a separate cross to mark the He-4 anomaly. (2) Never start the curve at A = 0 — there's no such thing as a zero-nucleon nucleus! (3) Label both axes with correct units (MeV for binding energy per nucleon). (4) Mark numbers on the axes, especially near the peak, to show the position of iron-56.
4. Nuclear Fusion
Fusion is defined as: small nuclides combining together to make larger nuclei, releasing energy. This is the process that powers every star in the sky — including our Sun.
Deuterium–Tritium (D–T) Fusion
On Earth, fusion research (like in tokamak reactors) focuses on the deuterium-tritium reaction, because it has the lowest activation "barrier" of the practical fusion reactions:
Conditions Needed for Fusion
Getting two nuclei to fuse is genuinely difficult, and it comes down to a tug-of-war between two forces:
- Electrostatic repulsion: protons are positively charged, so nuclei repel each other electrostatically as they approach — like trying to push two north poles of a magnet together.
- Strong nuclear force: this is the force that actually binds nucleons together, but it only acts over extremely short ranges — nuclei have to get unbelievably close (femtometre distances) before it can "grab hold" and pull them into a fused nucleus.
To get close enough, nuclei need very high kinetic energy to punch through the electrostatic repulsion — which is exactly why fusion only happens naturally in environments as extreme as the core of a star (millions of degrees, immense pressure/density).
Picture electrostatic repulsion as a hill the two nuclei have to climb before they can "fall" into the strong-force valley on the other side. If they don't have enough kinetic energy (speed), they'll never make it over the hill and will just bounce apart. That's why fusion needs extreme heat — heat is just kinetic energy on a huge scale, giving nuclei enough speed to clear that hill.
Fusion Products & the Proton–Proton Chain
When two ordinary hydrogen nuclei (i.e. two lone protons) fuse, one of the protons converts into a neutron via beta-plus decay, producing a deuterium nucleus plus a positron and an electron neutrino:
In the core of stars, this is just the first step of a longer chain reaction — the proton–proton chain — where four hydrogen nuclei are ultimately fused into one helium nucleus, releasing energy that keeps the star burning:
The final helium-4 nucleus has less total mass than the four separate protons that went into making it — some mass was converted directly into energy (via ΔE = Δmc²) at each stage. Not all of that energy goes into the new nucleus's binding energy, so the excess is released outward. This is also why the binding energy per nucleon of the product (helium-4) ends up higher than that of the reactants (hydrogen-1) — the system has moved up the binding-energy curve.
In the reaction ²₁H + ³₁H → ⁴₂He + ¹₀n, the total mass of the reactants is 5.0303 × 10⁻²⁷ kg and the total mass of the products is 5.0113 × 10⁻²⁷ kg. Calculate the energy released.
🧠 What to Memorise
| Term / Formula | Meaning |
|---|---|
| Mass defect, Δm | Δm = Zmp + (A−Z)mn − mtotal — the "missing mass" compared to separated nucleons |
| Binding energy, ΔE | ΔE = Δmc² — energy needed to fully separate a nucleus into individual nucleons |
| Binding energy per nucleon | ΔE ÷ A — the best measure of nuclear stability; higher = more stable |
| Atomic mass unit | 1 u = 1.66 × 10⁻²⁷ kg = 931.5 MeV; defined as 1/12 the mass of a carbon-12 atom |
| Most stable nucleus | Iron-56 — sits at the peak of the binding energy per nucleon graph |
| Fusion | Small nuclei combine to form a larger nucleus, releasing energy — happens on the left/steep side of the graph |
| Fission | A large nucleus splits into smaller nuclei, releasing energy — happens on the right/heavy side of the graph |
| D-T fusion equation | ²₁H + ³₁H → ⁴₂He + ¹₀n |
| p-p chain net result | 4 × ¹₁H → ⁴₂He + energy (via 5 stages, releasing 2 positrons + 2 neutrinos) |
| Conditions for fusion | High kinetic energy needed to overcome electrostatic repulsion so the short-range strong force can act |
✅ Concepts Checklist
Tick these off as you become confident with each idea. Be honest with yourself!
🎯 Exam Tips & Common Mistakes
Don't call binding energy "stored energy"
Examiners specifically penalise this. Binding energy is energy that must be supplied to break the nucleus apart — always phrase it as "the energy required to separate..." not "the energy stored in..."
Watch your units religiously
Mass in kg with c in m s⁻¹ gives you energy in Joules. If you want MeV, either convert your mass to u first (and use 931.5 MeV/u), or convert your final Joules answer by dividing by 1.6 × 10⁻¹⁹ then by 10⁶. Mixing units mid-calculation is the #1 cause of lost marks here.
Graph sketches need the anomaly AND the peak
A "perfect" smooth curve without marking the He-4 spike, or without starting from a low A value (never A=0), will lose marks. Always label the axes with units, and mark Fe-56 near the peak with actual numbers.
"Higher binding energy per nucleon" = more stable, always
Don't confuse this with total binding energy — a huge nucleus like uranium has a large TOTAL binding energy simply because it has more nucleons, but a low binding energy PER nucleon, which is why it's actually less stable than iron.
Fusion needs BOTH high temperature AND high density
Students often only mention temperature. High density matters too — it increases the collision rate between nuclei, making fusion events more frequent. Mention both for full marks on "conditions for fusion" questions.
Always balance nuclide equations
Check that both the top numbers (nucleon number, A) and bottom numbers (proton number, Z) balance on both sides of any nuclear equation — including for beta-plus decay steps in the proton-proton chain, where a positron carries charge +1 and mass number 0.
- 1. Nuclear Binding Energy & Mass Deficit
- 🎯 Exam Tips & Common Mistakes
- Fusion Products & the Proton–Proton Chain
Read the full Nuclear Fusion & Fission notes free
That's the preview — create a free account to read the rest, plus flashcards and practice questions with instant AI marking. No credit card.
Unlock the full notes free →