Explain why a minimum mass of fissile material, known as the critical mass, is required to sustain a fission chain reaction.
Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).
In a nuclear fission chain reaction, each fission event releases neutrons that may go on to induce further fission events. Whether the reaction is self-sustaining depends critically on the quantity of fissile material present.
Model answer (4 marks)
Each fission event releases fast neutrons that must be absorbed by other fissile nuclei to continue the chain reaction.
Neutrons can escape from the surface of the fissile material without causing further fission, and the proportion that escape depends on the surface‑area‑to‑volume ratio of the material.
As the mass increases, the surface‑area‑to‑volume ratio decreases, so a smaller fraction of neutrons escape and more are available to cause fission.
The critical mass is the minimum mass at which, on average, exactly one neutron per fission event causes a further fission, making the chain reaction self‑sustaining (multiplication factor k = 1).
Neutrons can escape from the surface of the fissile material without causing further fission, and the proportion that escape depends on the surface‑area‑to‑volume ratio of the material.
As the mass increases, the surface‑area‑to‑volume ratio decreases, so a smaller fraction of neutrons escape and more are available to cause fission.
The critical mass is the minimum mass at which, on average, exactly one neutron per fission event causes a further fission, making the chain reaction self‑sustaining (multiplication factor k = 1).
Examiner tips
- Use the word ‘critical mass’ and explain the role of the neutron multiplication factor k = 1.
- Show the link between surface‑area‑to‑volume ratio and neutron escape.
- Mention that a larger mass reduces escape, increasing k.
- Keep the answer concise – 4 points, one sentence per point.
Common mistakes
- Confusing critical mass with the total mass of the reactor core.
- Failing to mention the surface‑area‑to‑volume ratio or the neutron multiplication factor.
- Giving a long, unfocused explanation that mixes unrelated concepts.
Mark scheme (4 marks)
- Each fission event releases (fast) neutrons that must be absorbed by other fissile nuclei to continue the chain reaction.
- Neutrons can escape from the surface of the fissile material without causing further fission, and the proportion that escape depends on the surface-area-to-volume ratio of the material.
- As the mass increases, the surface-area-to-volume ratio decreases, so a smaller fraction of neutrons escape and more are available to cause fission.
- The critical mass is the minimum mass at which, on average, exactly one neutron per fission event causes a further fission, making the chain reaction self-sustaining (multiplication factor k = 1).
Key terms in this question
critical mass · chain reaction
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