IB Physics HLTopic 7 — Atomic, Nuclear & Particle PhysicsPaper 1 & 2the band of stability~16 min read
Nuclear Stability
Why do some nuclei sit unchanged forever while others fall apart? It comes down to a tug-of-war inside the nucleus: the strong nuclear force pulling nucleons together against the electrostatic force pushing protons apart. When those forces balance, the nucleus is stable. Plot neutron number against proton number and the stable nuclei trace out a clear band of stability — and whether a nucleus sits above, below, or beyond that band tells you exactly how it will decay.
📚 What you need to know
Stability depends on the balance between the strong nuclear force (attractive) and the electrostatic force (repulsive)
The strong force is very short range (~0.5 to 3.0 fm), attractive over most of that range and repulsive below ~0.5 fm
Stable nuclei form a band of stability on a graph of neutron number N against proton number Z
Light stable nuclei follow N = Z; heavier stable nuclei need more neutrons than protons
Above the band (too many neutrons) → beta-minus decay
Below the band (too many protons) → beta-plus decay
Beyond the band (too heavy) → alpha decay
The tug-of-war inside the nucleus
Two forces compete inside every nucleus:
The electrostatic force pushes protons apart (they’re all positive). It’s long range, so it acts across the whole nucleus.
The strong nuclear force pulls nucleons together. It’s far stronger, but only over a tiny range — each nucleon only feels its immediate neighbours.
Gravity also acts (mass attracts mass), but it’s so weak compared to the other two that we ignore it. If electrostatic repulsion were the only force, no nucleus could hold together — so there must be a stronger attractive force: the strong nuclear force.
The strong force is repulsive below ~0.5 fm (stopping the nucleus collapsing), attractive up to ~3 fm (max around 1 fm), then negligible. Its short range is why big nuclei struggle to stay stable.
The strong force’s tiny range is the whole story of why big nuclei are unstable. Because it only reaches neighbouring nucleons, adding more protons far apart doesn’t add more binding — but their electrostatic repulsion reaches right across the nucleus. So in heavy nuclei, repulsion starts to win, and extra neutrons are needed to space the protons out and add more strong-force “glue” without adding charge.
The band of stability
Plot every stable nucleus on a graph of neutron number N against proton number Z and they cluster into a curved band. The shape of that band reveals a key pattern:
Light stable nuclei sit on N = Z; heavier ones curve above it (more neutrons). Where a nucleus sits relative to the band predicts its decay: above → β−, below → β+, beyond → α.
Reading the band
Light nuclei (Z < 20): most stable when N = Z — equal protons and neutrons.
Heavy nuclei (Z > 20): need more neutrons than protons to stay stable, so the band curves upward, above the N = Z line.
The most common, stable elements in the universe have N and Z below about 20 (plus iron).
How position predicts decay
An unstable nucleus decays in whatever way moves it towards the band. Its position tells you exactly which decay:
Above band (too many n)
β− decay
Below band (too many p)
β+ decay
Beyond band (too heavy)
(and very heavy nuclei → alpha decay)
WE 1
A nucleus lies above the band of stability, meaning it has too many neutrons relative to its protons. Predict its decay mode and explain how it moves towards the band.
Step 1 — identify the imbalance
Above the band means too many neutrons.
Step 2 — which decay reduces neutrons?
Beta-minus turns a neutron into a proton (N −1, Z +1).
Beta-minus decay — moves it down and right, onto the bandToo many neutrons → convert one to a proton via β−. On the N–Z graph this steps the nucleus down-right, straight towards the stable band.
WE 2
Explain why heavy stable nuclei need more neutrons than protons, whereas light stable nuclei have roughly equal numbers.
Step 1 — the forces at play
The strong force is short range; electrostatic repulsion is long range.
Step 2 — why extra neutrons help
In heavy nuclei, proton repulsion reaches across the whole nucleus. Extra neutrons add strong-force attraction and space the protons out, without adding charge.
Extra neutrons offset the growing electrostatic repulsion in large nucleiLight nuclei are small enough that N = Z works. As nuclei grow, repulsion builds faster than the short-range strong force can counter, so more neutrons are needed — the band curves above N = Z.
⚛ Predicting decay from position
Above the band (too many neutrons) → beta-minus.
Below the band (too many protons) → beta-plus.
Beyond the band (too heavy) → alpha.
Light nucleus stable? Expect N ≈ Z.
Heavy nucleus stable? Expect N > Z.
💡 Top tips
The strong force is short range (~0.5–3.0 fm); repulsion is long range.
Light stable nuclei: N = Z; heavy stable nuclei: N > Z.
Above → β−, below → β+, beyond → α.
Nuclei decay in whatever direction moves them towards the band.
Below ~0.5 fm the strong force is repulsive, stopping collapse.
⚠ Common mistakes
Mixing up above/below the band — above = too many neutrons = β−
Thinking heavy stable nuclei have N = Z — they need more neutrons
Forgetting the strong force is repulsive at very short range
Claiming gravity holds the nucleus together — it’s far too weak
Assuming the strong force is long range — it only reaches neighbours
Quick recap: Stability is a balance between the short-range attractive strong force and the long-range repulsive electrostatic force. Stable nuclei form a band of stability: light ones follow N = Z, heavy ones need N > Z. Position predicts decay — above → β−, below → β+, beyond → α — always moving the nucleus towards the band.
A nucleus can be stable in its overall make-up but still be holding excess energy — sitting in an “excited state” after a decay. Just like electrons, nuclei have discrete energy levels, and they drop between them by emitting gamma photons of precise energies. Next page: Nuclear Energy Levels.
The band of stability still confusing?
Book a free meeting and we’ll drill the strong-vs-electrostatic balance and how a nucleus’s position predicts α, β− or β+ decay.
