Each fission causes exactly one further fission. Neutron numbers stay level, so power is steady and can be held there for years. Fuel is only 3–5% U-235, delayed neutrons make the reaction slow enough to control mechanically, and a hotter core is automatically less reactive. A reactor physically cannot undergo a nuclear explosion — the fuel is far too dilute and the feedback works against it.
Each fission causes more than one further fission, so neutron numbers double again and again. Starting from a single neutron, about 2⁸¹ fissions are needed for a 15 kt yield — roughly 81 doublings. With about 10 ns between generations, the entire energy release takes under a millionth of a second, which is why there is no possibility of intervening once it begins.
In fission, a heavy nucleus splits and releases energy. Each fission also releases spare neutrons, which can cause further fissions — a chain reaction.
In a reactor the chain reaction is controlled, so energy is released steadily and can be used to generate electricity. In a weapon it is uncontrolled, so almost all the energy is released at once.
The energy comes from a loss of mass. The products of fission have slightly less total mass than the original nucleus, and this missing mass appears as energy according to E = mc².
The Hiroshima bomb released about 15 kilotonnes of TNT equivalent, or 6.28 × 10¹³ J. Rearranging E = mc² gives the mass converted: Δm = E/c² = 6.28 × 10¹³ / (3.00 × 10⁸)² ≈ 7 × 10⁻⁴ kg — less than one gram. This is the single most striking number in the topic: under a gram of matter, converted completely to energy, destroyed a city.
Working backwards from the energy also gives the number of fissions. At about 200 MeV (3.2 × 10⁻¹¹ J) per fission, roughly 2 × 10²⁴ fissions were needed — which corresponds to under a kilogram of uranium nuclei actually splitting.
Note the difference between these two masses: about 0.76 kg of uranium fissioned, but only about 0.7 g of mass disappeared. The fission products are still there; they are simply lighter than what they came from.
Gun-type (Little Boy). Two pieces of uranium-235, each individually too small to sustain a chain reaction, are brought rapidly together. Combined, the assembly is large enough that neutrons are more likely to strike another nucleus than to escape, so the chain reaction runs away. Simple in principle, and wasteful — barely 1% of the uranium fissioned.
Implosion (Trinity, then Fat Man). Trinity, tested in the New Mexico desert on 16 July 1945, was the first nuclear explosion and used plutonium-239. Rather than joining two pieces, a single subcritical sphere is compressed. Critical mass depends on density: squeeze the same material into a smaller volume and neutrons travel less distance between nuclei, so proportionally fewer escape from the surface. A mass that was subcritical becomes supercritical without adding any material. This is far more efficient, which is why Fat Man fissioned a much greater fraction of a much smaller core.
Thermonuclear (hydrogen bomb). A fission device is used as a first stage, and the enormous temperature it produces triggers fusion of light nuclei in a second stage. Fusion is not limited by critical mass — there is no upper size limit in the way there is for a fission device — which is why yields leapt from kilotonnes to megatonnes. The fusion reaction itself is the same deuterium–tritium physics students meet in the fusion simulator.
Chain reaction growth is exponential: after n generations the neutron population is kⁿ. This is why the timing is so extreme. Run the simulation and watch the counter — after 70 generations the released energy is still trivial, and essentially the entire yield appears in the final handful of doublings. Exponential processes deliver almost everything at the very end, which is a general and important idea well beyond nuclear physics.
Efficiency explains the contrast between the two 1945 devices. Little Boy contained roughly 64 kg of uranium but fissioned less than a kilogram of it — around 1% — because the assembly blew itself apart before the reaction could propagate further. Fat Man fissioned a far larger fraction of its much smaller plutonium core. The physical reason is that once the material is heated to millions of degrees it expands violently, dropping the density and ending the chain reaction. The reaction destroys the conditions it needs to continue.
Thermonuclear (hydrogen) weapons add a second stage in which light nuclei fuse, as in your fusion simulator. Fusion releases several times more energy per nucleon than fission, and the fuel is not limited by critical mass, which is why yields jumped from kilotonnes to megatonnes — Castle Bravo was roughly a thousand times Hiroshima. The physics of the fusion reaction itself is the same D–T physics you have already modelled.