IB Physics HLTopic 7 — Atomic, Nuclear & Particle PhysicsPaper 1 & 2iron sits at the peak~17 min read
Binding Energy per Nucleon
Total binding energy tells you how tightly a whole nucleus is held — but a big nucleus naturally has more of it just because it has more nucleons. To fairly compare stability across elements, we divide by the number of nucleons to get binding energy per nucleon. Plot that against nucleon number and you get one of the most powerful graphs in all of physics: a curve that peaks at iron and explains, in a single shape, both fusion and fission.
📚 What you need to know
Binding energy per nucleon = total binding energy ÷ number of nucleons
A higher binding energy per nucleon means a more stable nucleus
The curve rises steeply for light nuclei, peaks at iron (A ≈ 56), then slowly falls
Iron-56 has the highest binding energy per nucleon, so it’s the most stable nucleus
Light nuclei (left of the peak) release energy by fusion; heavy nuclei (right of the peak) release energy by fission
Both fusion and fission move nuclei towards the peak, releasing energy
Fusion releases more energy per kg than fission, but needs a large energy input to start
Why “per nucleon”?
Total binding energy isn’t a fair measure of stability on its own — a uranium nucleus has a huge total simply because it has 238 nucleons to hold together. To compare nuclei fairly, we ask how tightly each individual nucleon is held, by dividing:
Binding energy per nucleonbinding energy per nucleon = total binding energy ÷ number of nucleons
The bigger this value, the more energy it takes to remove a nucleon, so the more stable the nucleus. This single number lets us rank every element on the same scale.
The curve
Plotting binding energy per nucleon against nucleon number A gives a curve with a very distinctive shape:
The curve rises steeply, peaks at iron-56, then falls slowly. Fusion (light nuclei) and fission (heavy nuclei) both move nuclei up towards the peak, releasing energy.
Key features of the graph
Light nuclei (low A): low binding energy per nucleon, and the curve is very steep. These nuclei can gain stability by fusing together.
Iron (A ≈ 56): the peak — the highest binding energy per nucleon, so the most stable nucleus of all.
Heavy nuclei (high A): binding energy per nucleon slowly decreases, and the curve is less steep. These can gain stability by splitting (fission).
A few light nuclei (helium-4, carbon-12, oxygen-16) sit above the trend — they’re especially stable.
Here’s the mental model that makes the whole graph click: nuclei always want to climb towards the peak, because higher up means more stable. Light nuclei climb by fusing (moving right and up); heavy nuclei climb by splitting (moving left and up). Iron is at the very top, so it can’t release energy either way — it’s the end of the road. That single “climb to the peak” idea explains fusion, fission, and why stars eventually stop fusing at iron.
Fusion vs fission
Both processes release energy by moving nuclei towards the peak, and both work the same way underneath — the products have slightly less mass than the reactants, and that mass defect appears as released energy. But they happen at opposite ends of the curve:
Fusion
Fission
What happens
Two small nuclei combine
One large nucleus splits
Where on curve
Light nuclei (A < 56)
Heavy nuclei (A > 56)
Energy per kg
More
Less
Starting it
Needs a large energy input
Easier to trigger
In light nuclei, attractive nuclear forces dominate, so combining increases stability. In heavy nuclei, repulsive electrostatic forces between the many protons start to win, making them unstable and prone to splitting.
WE 1
A uranium-235 nucleus undergoes fission: 23592U + n → 9138Sr + 14254Xe + 3n. Using binding energies per nucleon of 7.5 MeV (U-235), 8.2 MeV (Sr-91) and 8.7 MeV (Xe-142), calculate the energy released.
Step 1 — total binding energy of each nucleusU-235: 235 × 7.5 = 1763 MeVSr-91: 91 × 8.2 = 746 MeVXe-142: 142 × 8.7 = 1235 MeVStep 2 — energy released = BE(after) − BE(before)= (746 + 1235) − 1763energy released = 218 MeVThe products sit higher on the curve (more stable), so the extra binding energy is released. Total binding energy after minus before gives the energy out. Multiply each BE-per-nucleon by that nucleus’s nucleon number first.
WE 2
Explain, using the binding energy per nucleon curve, why energy is released when two light nuclei fuse together.
Step 1 — where do light nuclei sit?
Light nuclei have a low binding energy per nucleon (low on the curve).
Step 2 — what fusion does
Fusing them makes a heavier nucleus higher up the curve, with more binding energy per nucleon.
The product is more stable, so the extra binding energy is releasedAlways frame these as “moving towards the peak”. Higher binding energy per nucleon = more stable = energy released as the nucleus climbs the curve.
⚛ Working a binding energy per nucleon question
Per nucleon? Divide total binding energy by A.
Most stable? Highest point on the curve (iron-56).
Fusion or fission? Light nuclei fuse; heavy nuclei split — both move towards the peak.
Energy released? Total binding energy of products − reactants.
Total BE from the graph? Read BE-per-nucleon, then multiply by A.
💡 Top tips
Higher binding energy per nucleon = more stable.
Iron-56 is at the peak — the most stable nucleus.
Both fusion and fission move nuclei towards the peak, releasing energy.
To get total BE from the graph: read per-nucleon value, multiply by A.
Energy released = BE(products) − BE(reactants).
⚠ Common mistakes
Reading total binding energy off the graph — it shows per nucleon
Forgetting to multiply by A to get total binding energy
Thinking heavy nuclei fuse — they fission (and vice versa for light)
Starting the curve at A = 0 — that’s not a nucleus
Saying a lower binding energy per nucleon is more stable — it’s the opposite
Quick recap:Binding energy per nucleon = total binding energy ÷ nucleons, and a higher value means a more stable nucleus. The curve rises steeply, peaks at iron-56 (most stable), then falls slowly. Light nuclei release energy by fusion and heavy nuclei by fission — both climbing towards the peak. Energy released = binding energy of products minus reactants.
The curve shows which nuclei are stable, but not why some combinations of protons and neutrons hold together and others don’t. That comes down to the balance between the attractive strong force and the repulsive electrostatic force — and it produces a clear “band of stability”. Next page: Nuclear Stability.
The binding energy curve not making sense yet?
Book a free meeting and we’ll drill the “climb to the peak” idea, fusion vs fission, and reading energy released off the graph.
