The big idea: Inside a power-station reactor, one uranium nucleus splits in two — flinging out spare neutrons and a burst of energy. That splitting is nuclear fission.
From one fission to a chain
- Those spare neutrons hit other nuclei and split them too
- One fission triggers the next, and the next — a chain reaction
- Whether the chain dies out, stays steady, or grows is decided by how many neutrons are lost along the way
What goes IN
- One slow neutron hits a large nucleus (e.g. uranium-235)
- The nucleus absorbs it and becomes unstable
- This is induced fission — the splitting was triggered by a neutron
What comes OUT
- Two smaller daughter nuclei (the fission fragments) fly apart
- A few extra neutrons are released — typically 2 or 3
- A large amount of energy (the fragments fly off fast)
New words, plainly: Induced fission = fission that is triggered by a nucleus absorbing a neutron (not happening on its own).
Chain reaction = each fission releases neutrons that go on to cause more fissions.
Self-sustaining = the chain keeps itself going without any extra neutrons being added from outside.
Dies out (subcritical)
- On average fewer than one of the released neutrons causes the next fission
- Too many neutrons escape or get absorbed without splitting anything
- The reaction fades out and stops
Steady or growing
- Exactly one per fission → steady (critical) — runs at a constant rate
- More than one per fission → growing (supercritical) — rate climbs
- A reactor is kept critical; a bomb is deliberately supercritical
One fission, then a chain
Spontaneous fission too: Some very heavy nuclei (for example uranium-238 and plutonium isotopes) occasionally split on their own, with no neutron: spontaneous fission. Both kinds release energy, because the fragments are more tightly bound than the heavy nucleus.
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Each fission releases N neutrons (about 2 or 3). The chain only stays steady if, on average, exactly one of them causes the next fission.
Every other neutron is lost
- It escapes the fuel, or
- It is absorbed without causing a fission
The rule (a counting rule — not in the data booklet): For a steady (critical) chain reaction, exactly one neutron per fission must trigger the next one.
So if N neutrons are released per fission, the number that must be lost or absorbed is N − 1.
| Neutrons released per fission | Must cause next fission (steady) | Must be lost or absorbed |
|---|---|---|
| 2 | 1 | 1 |
| 3 | 1 | 2 |
| N | 1 | N − 1 |
Read the regime off the losses
- Lose exactly N − 1 → steady (critical) — runs at a constant rate
- Lose more than N − 1 → too few left → reaction dies out (subcritical)
- Lose fewer than N − 1 → too many left → reaction grows (supercritical)
- A reactor is held at critical; the lost neutrons are mostly mopped up by control rods
Each fission of a uranium-235 nucleus releases on average 3 neutrons. For a steady (self-sustaining) chain reaction, how many of those neutrons must be lost or absorbed per fission?
Model answer plan
See the answer broken into clear points, with guidance on how each point earns marks.
Worked example — energy released in one fission
In the reaction ²³⁵U + n → ¹⁴¹Ba + ⁹²Kr + 3n the masses are: U-235 = 235.043930 u, n = 1.008665 u, Ba-141 = 140.914411 u, Kr-92 = 91.926156 u. Find the energy released.
Solution
- Mass before and after:
- Mass defect and energy:
Final answer
About 173 MeV per fission (the neutron count matters: count every neutron on both sides).
The binding-energy route, and fuel mass: From the curve: the fragments have about 8.5 MeV per nucleon, uranium about 7.6 MeV, so 236 × 0.9 ≈ 200 MeV per fission.
To find the fuel a power station uses: energy needed ÷ energy per fission = number of fissions; ÷ NA × 0.235 kg mol⁻¹ = mass of uranium-235.
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How this is tested — neutron economy is a classic Paper 1A reasoning question, and the energy side turns up in Paper 2:
Paper 1A
- Choose the loss: given the neutrons released per fission, pick the loss value that keeps the chain steady (always N − 1).
- Name the regime: decide if a chain is dying out, steady or growing from how many neutrons continue.
Paper 2
- The energy per fission from the mass defect (E = mc²).
- Or describing the conditions for a self-sustaining reaction.
The classic trap: Thinking ALL the released neutrons must continue. Only one per fission keeps it steady — the rest are lost. Losing too few makes it grow, not steady.
Steady means break-even, not zero loss: A steady chain reaction is a balance: one neutron in, one neutron out, per fission.
You are NOT trying to keep all the neutrons. You want to lose all but one — that is what keeps the rate constant.
In a fission reactor each fission releases 2.5 neutrons on average. To run the reactor at a steady, self-sustaining rate, how many neutrons per fission (on average) must be lost or absorbed?
Model answer plan
See the answer broken into clear points, with guidance on how each point earns marks.