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 is the physical process that makes naval nuclear propulsion possible, and the NAPT's own study materials specifically flag fission chain reactions and critical mass as core nuclear-science content. This section stays at the level of a public high-school or intro-college physics explanation — the same level of detail found in general encyclopedias and physics textbooks — and does not describe classified or 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?