IB Physics SLTopic 5 — The Atomic & Nuclear WorldPaper 1 & 2iron is most stable~8 min read
Binding Energy per Nucleon
A big nucleus has a big binding energy — but that alone doesn’t tell you how stable it is, because it has more nucleons to share that energy between. Divide binding energy by the number of nucleons and you get the real measure of stability. Plot it against nucleon number and one curve explains why stars shine, why reactors work, and why iron sits at the bottom of it all.
📘 What you need to know
Binding energy per nucleon = total binding energy ÷ number of nucleons (A) — the fair measure of nuclear stability
A higher binding energy per nucleon means a more stable nucleus
The curve rises steeply for light nuclei, peaks around iron (A ≈ 56), then slowly falls for heavy nuclei
Iron-56 has the highest binding energy per nucleon, so it is the most stable nucleus
Fusion (joining light nuclei) climbs the steep left side, releasing energy — happens for A < 56
Fission (splitting heavy nuclei) moves up the gentle right side, releasing energy — happens for A > 56
Both fusion and fission move nuclei toward the peak, increasing binding energy per nucleon and releasing energy
Why Per Nucleon?
Total binding energy grows with size — a uranium nucleus has far more total binding energy than a helium one, simply because it has more nucleons holding together. That makes total binding energy useless for comparing stability. The fair comparison is binding energy per nucleon: how tightly, on average, each individual nucleon is held. The higher this is, the harder it is to pull any one nucleon out, so the more stable the nucleus.
Binding energy per nucleon
BE per nucleon = total binding energy ÷ A
The Curve
Plot binding energy per nucleon (up) against nucleon number A (across) and you get one of the most important graphs in physics. It rises steeply for the lightest nuclei, reaches a maximum around iron, then declines gently all the way to uranium.
Binding energy per nucleon peaks at iron-56, the most stable nucleus. Light nuclei gain stability by fusing (climbing the steep left side); heavy nuclei gain it by splitting (moving up the gentle right side). Both head toward the peak and release energy.
Iron: the Most Stable Nucleus
The top of the curve sits at iron-56. Because it has the highest binding energy per nucleon, its nucleons are the most tightly held of any element, making it the most stable nucleus. There’s nowhere “uphill” for iron to go — you can’t release energy by fusing it or splitting it, which is why fusion in stars stops at iron.
Fusion and Fission: Two Ways Uphill
Here’s the payoff. A reaction releases energy whenever it produces nuclei with a higher binding energy per nucleon than it started with — that is, whenever it moves up the curve toward iron. There are two ways to do this, depending on which side you start.
Fusion — join two light nuclei (A < 56) into a bigger one. On the steep left side, this climbs sharply toward the peak, releasing a lot of energy per nucleon. This is what powers the Sun.
Fission — split a heavy nucleus (A > 56) into two medium ones. On the gentle right side, the fragments sit higher up the curve than the original, releasing energy. This is what powers nuclear reactors.
The steep left side is why fusion releases more energy per nucleon than fission — the climb toward the peak is much sharper there.
light nuclei
→ FUSE →
toward iron peak
← SPLIT ←
heavy nuclei
Quick recap: binding energy per nucleon measures stability; the curve peaks at iron-56, the most stable nucleus; light nuclei fuse and heavy nuclei undergo fission, both moving up toward the peak and releasing energy.
🧭 Finding energy released in a nuclear reaction
Read the binding energy per nucleon of each nucleus from the curve
Multiply each by its nucleon number A to get each nucleus’s total binding energy
Add up the total binding energy of the products, and of the reactants
Energy released = total BE of products − total BE of reactants
A positive result confirms energy is released — the products are more tightly bound
WE 1
A uranium-235 nucleus undergoes fission: 23592U + 10n → 14156Ba + 9236Kr + 310n. Using binding energies per nucleon of 7.6 MeV (U-235), 8.3 MeV (Ba-141) and 8.6 MeV (Kr-92), calculate the energy released.
Step 1 — total binding energy of each nucleus (BE/nucleon × A)
U-235: 7.6 × 235 = 1786 MeV
Ba-141: 8.3 × 141 = 1170.3 MeV
Kr-92: 8.6 × 92 = 791.2 MeV
Step 2 — energy released = BE(products) − BE(reactant)= (1170.3 + 791.2) − 1786= 1961.5 − 1786energy released ≈ 176 MeVThe products sit higher on the curve than U-235, so energy is released — the sign comes out positive.
WE 2
(a) State which nucleus is the most stable and justify your answer using the curve. (b) Explain why fusion releases more energy per nucleon than fission.
Part (a) — most stable nucleus
iron-56 sits at the peak of the curve
it has the highest binding energy per nucleon
→ so its nucleons are the most tightly bound = most stablePart (b) — why fusion gives more per nucleon
the curve rises very steeply on the light (fusion) side
so fusing light nuclei gives a much bigger jump in binding energy per nucleon
→ more energy released per nucleon than the gentle fission side
💡 Top tips
Higher on the curve = more stable. The peak at iron-56 is the most tightly bound nucleus of all
Both fusion and fission move toward the peak — light nuclei climb from the left, heavy nuclei climb from the right
For energy released, work with total binding energy (BE/nucleon × A), then take products minus reactants
Drawing the curve? Don’t start it at A = 0 (that’s not a nucleus), label both axes with units, and mark the iron peak
⚠ Common mistakes
Confusing total binding energy with binding energy per nucleon — only the per-nucleon value measures stability
Thinking the heaviest nucleus is the most stable — it’s iron-56 at the peak, not uranium
Saying fission needs light nuclei or fusion needs heavy ones — it’s the reverse: fusion is light, fission is heavy
Starting the drawn curve at the origin (A = 0) — the lightest real nucleus is hydrogen (A = 1)
That completes Radioactive Decay — you can now go from an unstable nucleus all the way to why stars fuse and reactors split. This binding-energy curve is the single most useful diagram in the whole nuclear topic, so make sure you can sketch it from memory, iron peak and all.
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