The big idea: Every second, the Sun turns four million tonnes of itself into sunlight — by fusing light nuclei into heavier ones deep in its core.
The heavier nucleus is slightly lighter than the bits that made it, and that missing mass comes out as energy.
The catch: nuclei are positive, so they repel. Only a star's core is hot and dense enough to force them together.
Before fusion
- Several light nuclei (e.g. hydrogen) flying around
- They repel each other — both are positive
- Only a super-hot, super-dense core can slam them together
After fusion
- They join into one heavier nucleus (e.g. helium)
- The product is slightly lighter than the parts added up
- That missing mass is released as energy (E = mc²)
New words, plainly: Fusion = small nuclei joining into a bigger one (the opposite of fission, which splits them).
Coulomb repulsion = the electrical push between two positive charges. Two nuclei both repel because both are positive.
Proton-proton (p-p) chain = the step-by-step set of reactions that fuses hydrogen into helium in stars like the Sun.
| The obstacle | How a star beats it |
|---|---|
| Both nuclei are positive, so they repel (Coulomb repulsion) | — |
| To touch, they must collide very fast | A very high temperature → nuclei move fast |
| Fast collisions must happen often | A very high density / pressure → nuclei packed close |
Why it needs heat AND density: High temperature gives the nuclei enough speed to slam together hard enough to beat the repulsion.
High density / pressure packs them close so those fast collisions happen often.
A star's core has both (~10⁷ K) — your kitchen does not, which is why hydrogen here just sits there.
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The energy a fusion reaction gives out comes from the mass defect — how much lighter the product is than the nuclei that fused. Find that missing mass, then turn it into energy with E = mc².
- energy released by the fusion reaction (J, or MeV)
- mass defect Δm — the mass that disappears when the nuclei fuse (kg)
- speed of light, 3.00 × 10⁸ m s⁻¹ (given constant)
Two units, one idea: In joules: put Δm in kilograms (1 u = 1.661 × 10⁻²⁷ kg) and multiply by c².
In MeV (faster): keep Δm in u and multiply by 931.5 (because 1 u = 931.5 MeV c⁻²).
Both give the same energy — pick whichever the question asks for.
In a star's core, light nuclei fuse into a heavier one. The total mass of the fusing nuclei is greater than the product by a mass defect Δm = 0.026900 u. Find the energy released, in MeV. (1 u = 931.5 MeV c⁻².)
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A balance of two pushes: A star is held together by gravity, which pulls every layer inward.
The energy from fusion makes the core blazing hot. That heat creates an outward pressure — from the radiation streaming out and the hot gas — that pushes outward.
When these two balance, the star's radius stays steady. This is stellar (hydrostatic) equilibrium.
A main-sequence star's balance: gravity pulls every layer inward, while the outward pressure from fusion's radiation and hot gas pushes back. When the two are equal the radius stays steady — this is stellar (hydrostatic) equilibrium.
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It is self-correcting: The balance fixes itself:
- If the core shrinks a little → it gets hotter → fusion speeds up → more outward pressure → it pushes back out. - If it expands a little → it cools → fusion slows → less pressure → gravity pulls it back in.
So a main-sequence star keeps a stable size for billions of years.
Equilibrium — what to say in the exam
- Gravity pulls inward on every layer of the star
- Fusion heats the core → radiation + gas pressure push outward
- The two are equal and opposite → the net force is zero → the radius is stable
- It is self-correcting: shrink → hotter → more fusion → pushes back out
How this is tested — fusion + stellar equilibrium is a classic Paper 2 topic, with a quick Paper 1A version:
Paper 1A
- A quick multiple-choice — which condition allows fusion, or what balances gravity in a star.
Paper 2
- Calculate the energy released in MeV from a mass defect (Δm → E = mc² → × 931.5).
- Outline / explain the conditions for fusion (high temperature + density to beat Coulomb repulsion), or how the star stays in equilibrium (pressure out balances gravity in).
The classic trap: Writing that fusion 'holds the star up' directly. It is the pressure produced by fusion's heat — radiation and hot gas — that balances gravity, not the reactions themselves.
Deep in a star, several light nuclei fuse into a single heavier nucleus. The combined mass of the original nuclei exceeds the mass of the product by Δm = 0.025600 u. Calculate the energy released by this reaction, in MeV. (1 u = 931.5 MeV c⁻².)
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A main-sequence star keeps a roughly constant radius for billions of years. Outline how it maintains this equilibrium.
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