7.3 Nuclear Fission, Chain Reactions & Critical Mass
Key Takeaways
- Nuclear fission splits a heavy nucleus (typically Uranium-235) into two lighter fragments plus 2 to 3 free neutrons and a large release of energy
- A chain reaction becomes self-sustaining when neutrons released by one fission event go on to trigger further fission events in subsequent generations
- The neutron multiplication factor (k) determines the reaction's state: subcritical (k < 1, dies out), critical (k = 1, steady rate), or supercritical (k > 1, growing rate)
- Critical mass is the minimum amount of fissile material needed, under a given geometry, density, and purity, to sustain k = 1 without an external neutron source
- Compact geometry, higher fissile enrichment, and neutron reflectors all reduce the critical mass required by minimizing neutron leakage
Nuclear fission, chain reactions, and criticality are presented only at a public introductory-textbook level. This local enrichment is not based on a Navy-issued NAPT syllabus and does not describe operational reactor engineering.
The Fission Process
Nuclear fission is the splitting of a heavy, unstable nucleus into two smaller daughter nuclei, releasing additional free neutrons and a large amount of energy in the process. The isotope most associated with sustained fission is Uranium-235, introduced in section 7.1.
The basic sequence:
- A relatively slow, low-energy (called thermal) free neutron is absorbed by a U-235 nucleus.
- This creates a highly unstable intermediate nucleus (effectively U-236) that almost immediately splits apart.
- The nucleus splits into two medium-mass fission fragments (the specific pair of resulting elements varies from event to event), plus 2 to 3 new free neutrons, plus a large release of energy.
- That energy appears mostly as kinetic energy of the fast-moving fission fragments — consistent with the mass-defect/E = mc² logic from section 7.1: the fragments' combined mass is slightly less than the original nucleus plus the absorbed neutron, and that missing mass converts to energy.
In simplified conceptual form: neutron + U-235 → fission fragments + (2 to 3) neutrons + energy.
Neutron Multiplication and the Chain Reaction
The fact that each fission event releases more than one new neutron is what makes a chain reaction possible: if at least one of those newly released neutrons goes on to strike another fissile nucleus and cause a further fission, the process can sustain itself without any additional neutron source.
The key quantity describing this is the neutron multiplication factor (k) — essentially the average number of neutrons from one fission that go on to cause another fission in the next generation:
| Multiplication Factor | State | What Happens |
|---|---|---|
| k < 1 | Subcritical | Fewer neutrons cause new fissions than the last generation produced; the reaction rate declines and eventually dies out |
| k = 1 | Critical | Exactly as many neutrons cause new fissions as the last generation produced; the reaction rate holds steady — the target condition for a controlled, steady-power reactor |
| k > 1 | Supercritical | More neutrons cause new fissions than the last generation produced; the reaction rate grows generation to generation |
A chain reaction becomes self-sustaining the moment k reaches 1, because the population of neutrons — and therefore the rate of fission events — neither grows nor shrinks; each generation simply reproduces the last one.
Critical Mass
Critical mass is the minimum amount of fissile material — under a given set of conditions — needed to sustain a chain reaction at k = 1 without relying on an external neutron source. Below critical mass, too many neutrons escape from the material's surface (or are absorbed by non-fissile impurities) before they can cause another fission, so k stays below 1 and the reaction cannot sustain itself.
Several general, publicly documented factors affect how much material is needed to reach critical mass:
- Amount of fissile material — more material means more atoms available to absorb neutrons before they can escape, raising k toward 1.
- Geometry and density — compact shapes (a sphere is most efficient) minimize the surface area relative to volume, which minimizes the fraction of neutrons that leak out before causing fission.
- Enrichment/purity — a higher concentration of the fissile isotope (U-235) relative to non-fissile material (like U-238 or structural impurities) increases the odds that a free neutron encounters a fissile nucleus rather than being absorbed harmlessly or passing through.
- Neutron reflectors — a surrounding material that scatters escaping neutrons back into the fissile material lowers the mass needed to reach criticality, because fewer neutrons are lost to leakage.
None of these factors describe a specific weapon or reactor design — they are the same general physics concepts published in any introductory nuclear physics course or encyclopedia reference on fission.
Controlling the Chain Reaction
A reactor is engineered to hold the chain reaction as close to k = 1 as possible — steady, controlled power output — rather than letting it run supercritical. The tool used to do this, control rods, is covered in the next section, 7.4, along with the rest of a reactor's basic components.
Putting the Pieces Together
A useful way to connect sections 7.1 through 7.3: an unstable heavy nucleus (7.1's isotope concept) can be split by fission (7.3), releasing neutrons that can trigger more fission events — also 7.3 — at a rate controlled by the multiplication factor k, and everything releases energy because the fragments are more tightly bound, on average, than the original nucleus, exactly as the binding-energy curve from section 7.1 predicts.
A reactor's neutron multiplication factor (k) is measured at 1.00. What does this indicate?
Which factor, by itself, would tend to reduce the critical mass needed to sustain a chain reaction?