In December 1938 the chemists Otto Hahn and Fritz Strassmann reported a baffling result from bombarding uranium with neutrons. Weeks later Lise Meitner and her nephew Otto Frisch explained what had happened: the uranium nucleus had split in two. Frisch borrowed a word from biology, where cells divide, and called it fission.
When a uranium-235 nucleus absorbs a slow neutron and splits, it releases about 200 million electron-volts of energy, mostly as the two fragments flying apart. That is a tiny amount in everyday terms, but there are a lot of atoms in a kilogram. Fully fissioning one kilogram of uranium-235 would release about 8 × 1013 joules, roughly 2.5 million times more than burning a kilogram of pure carbon. One fission releases about fifty million times more energy than burning one carbon atom.
Each fission also throws out new neutrons, on average about 2.5. If at least one of them goes on to split another nucleus, the reaction sustains itself. Physicists track this with one number, k: how many fissions, on average, each fission causes in the next generation.
| k | Name | What happens |
|---|---|---|
| below 1 | subcritical | the reaction dies away |
| exactly 1 | critical | steady power: what a running reactor aims for |
| above 1 | supercritical | power grows, generation after generation |
"Critical" sounds alarming but means "steady". The difficulty is that a neutron generation in a typical power reactor lasts only about a ten-thousandth of a second. If k were 1.001, just 0.1% too high, you'd get 10,000 generations a second, and the power would multiply by e10, about 22,000 times, every second. No mechanical control rod could ever keep up.
Here is the fact that saves the day. About 0.65% of the neutrons from uranium-235 fission are not released at once. They come out of certain fission fragments as those decay, with delays from a fraction of a second up to nearly a minute, averaging about 13 seconds. Reactors are designed so that the chain reaction can't sustain itself without these delayed neutrons. That stretches the effective generation time from a ten-thousandth of a second to about a tenth of a second, and turns a runaway into something operators and control rods can comfortably steer. See it for yourself:
A standard textbook model ("point kinetics" with one averaged group of delayed neutrons): generation time 10−4 s, delayed fraction 0.65%, average delay 13 s. It shows how power responds before any temperature feedback or control action kicks in. Real reactors differ in detail.
Push k up to about 1.0065 and something sinister happens: the reactor becomes prompt critical. It can now sustain and grow its chain reaction on the instant neutrons alone, and the delayed ones no longer set the pace. Above that line, power can rise many times over in a fraction of a second. Keeping reactors far from that line, and designing them so they naturally push themselves back from it, is the heart of reactor safety.
Less than one neutron in a hundred arrives late. That small fraction is what makes nuclear power controllable.
Many power reactors use ordinary water, and it does three jobs at once:
Moderator. Neutrons from fission are fast, and fast neutrons are poor at splitting uranium-235. Colliding with the light hydrogen nuclei in water slows them down to the speeds at which they split U-235 most readily.
Coolant. The water carries the heat away from the fuel.
Steam. The heat ultimately makes steam that drives a turbine and generator, exactly as in a coal or gas plant (see How Electricity Actually Reaches Your Wall).
The fuel is uranium enriched to a few percent uranium-235; natural uranium is only about 0.7%. Control rods made of neutron-absorbing materials slide in and out to trim k. In an emergency they all drop in at once, a "scram", which shuts the chain reaction off. (Even then, as the interactive shows, the delayed neutrons make the fission rate fade over the following minute or so rather than instantly.)
The water-cooled design has a built-in safety feature. If the water overheats and turns to steam bubbles, there is less water to slow the neutrons, so fewer fissions happen and the power drops. The physics pushes back against a power surge.
Chernobyl, 26 April 1986. The Soviet RBMK design, moderated by graphite rather than water, had the opposite property: more steam bubbles meant more reactivity, a "positive void coefficient". During a safety test at unit 4, with the reactor in an unstable state, power surged. When the emergency shutdown button was pressed, the graphite tips on the control rods briefly added reactivity as they entered. The reactor exploded. Two workers died that night, and 28 more died of acute radiation sickness within months. Longer-term health effects are still debated.
Fukushima Daiichi, 11 March 2011. The three operating reactors shut down automatically when the earthquake struck, as designed. But a shut-down reactor keeps producing heat from the decay of its radioactive fragments: about 6.5% of full power at the moment of shutdown, about 1.5% after an hour and 0.4% after a day. The tsunami about 50 minutes later flooded the emergency diesel generators that powered the cooling. Without cooling, that leftover heat damaged the fuel in three reactors, and hydrogen explosions wrecked several buildings. The lesson was not about the chain reaction at all. It was about the heat that outlasts it.
In May 1972, routine analysis at a French uranium-enrichment plant at Pierrelatte found ore from Oklo, in Gabon, with too little uranium-235 in it. The missing uranium had already been "burned". About 1.7 to 2 billion years ago, when natural uranium was about 3% uranium-235 (it decays faster than uranium-238), groundwater seeping into the ore slowed the neutrons enough to start chain reactions. They ran on and off for a few hundred thousand years: roughly 30 minutes of fission until the water boiled away, then about 2½ hours of cooling while it seeped back. The output probably never exceeded 100 kilowatts. Long before there was anyone to build one, the Earth was running its own reactors, regulated by the very same moderator feedback engineers use today.
The first human-made reactor, Chicago Pile-1, a stack of graphite and uranium built under the stands of a sports field at the University of Chicago, went critical on the afternoon of 2 December 1942. Fermi let the chain reaction run for about four and a half minutes, at roughly half a watt, before it was shut down. (A "28 minutes" figure also circulates; it is the span of the final approach that afternoon, not how long the pile ran critical.)
Nuclear power produces large amounts of steady electricity with very low carbon emissions, from a tiny amount of fuel. Against that: its waste stays dangerous for a very long time and needs secure long-term storage; accidents, though rare, can contaminate large areas and displace communities; and new plants are expensive and slow to build. Reasonable people weigh these differently. The physics doesn't settle the argument, but it does make clear what the argument is about.
A reactor boils water using heat from a chain reaction of splitting uranium-235 nuclei, each fission releasing about 200 MeV and about 2.5 neutrons. The multiplication factor k is held at exactly 1. A neutron generation lasts only about 10−4 s, but the 0.65% of neutrons that arrive seconds late slow the chain's response enough for control. Above k ≈ 1.0065 (prompt critical) that protection vanishes. Good designs push back against power surges; Chernobyl's didn't. Even a shut-down reactor needs cooling for its decay heat, the lesson of Fukushima.
Try this: in the interactive, compare k = 1.0010 and k = 1.0070. One gives operators about a minute to react. The other gives them nothing. Then picture an engineer whose job is to make sure the second can never happen.
Sources. Discovery of fission (Hahn and Strassmann, Dec 1938; Meitner and Frisch, Jan 1939), ~200 MeV per U-235 fission (mean 202.8 MeV), ~2.5 neutrons per fission, : Wikipedia, "Nuclear fission". The per-atom comparison is computed: 200 MeV ÷ about 4.1 eV released per carbon atom burned ≈ 50 million. Delayed-neutron fraction 0.0065 for U-235, generation time of order 10−4 s, and the six-group half-lives and yields: Wikipedia, "Delayed neutron". Decay heat 6.5% / 1.5% / 0.4%: Wikipedia, "Decay heat". Chernobyl (date, RBMK, positive void coefficient, graphite-tipped rods, 2 + 28 deaths) and Fukushima (automatic shutdown, tsunami ~50 min later, generators flooded, hydrogen explosions): Wikipedia articles on each accident. Oklo (1972 discovery at Pierrelatte, ~1.7–2 billion years ago, ~3% U-235, 30 min on / 2.5 h off, under 100 kW): Wikipedia, "Natural nuclear fission reactor". Chicago Pile-1 (2 Dec 1942, Stagg Field): Argonne National Laboratory and Atomic Heritage Foundation; run of about 4.5 minutes at about 0.5 W: Physics Today, "First self-sustaining nuclear reactor" (AIP, 2 Dec 2015, doi:10.1063/PT.5.031103) and Richard Rhodes, The Making of the Atomic Bomb (1986), p. 440; the 28 minutes as the time taken that afternoon: University of Chicago News, "The first nuclear reactor, explained". Computed in Python and node: 200 MeV × NA ÷ 0.235 kg = 8.2 × 1013 J/kg; carbon combustion 393.5 kJ/mol ÷ 12.011 g/mol = 32.8 MJ/kg; ratio 2.5 million; average delay from the six-group data = 13.0 s; e0.001/10−4 = e10 ≈ 22,026. The interactive solves the one-group point-kinetics equations exactly; it was checked against a separate step-by-step numerical integration in node.