Lab 14 — Nuclear Physics
The Fission Chain Reaction
A neutron striking a heavy nucleus (²³⁵U or ²³⁹Pu) can trigger fission: the nucleus splits into two fragments and releases an enormous amount of energy along with two or three fresh neutrons — their average is ν̄. For example, ²³⁵U + n → ¹⁴¹Ba + ⁹²Kr + 3n + about 200 MeV. If those neutrons strike more nuclei, more fissions follow: a chain reaction. How many next-generation fissions each fission causes on average is the effective multiplication factor k — ν̄ times the probability that any one neutron goes on to cause a fission. Below 1, the population decays away (subcritical). At exactly 1, it holds steady (critical — the state a reactor runs in). Above 1, it multiplies by k every generation, growing exponentially (supercritical — bomb territory). Fire a neutron, tune k, and watch the chain reaction play out inside the box.
Push k above 1 and the neutron count runs away exponentially
The critical mass — an unreflected sphere — is roughly 52 kg for ²³⁵U and 10 kg for ²³⁹Pu; wrap it in a neutron reflector and both figures shrink. ²³⁸U is "fertile," not fissile: it mostly just captures neutrons instead of splitting, transmuting toward ²³⁹Pu — which is why natural uranium has to be enriched. Most neutrons appear at the instant of fission (prompt), but about 0.65% arrive seconds to tens of seconds late (delayed neutrons); that lag is exactly what lets a reactor be steered with slow-moving control rods instead of running away. The energy itself is a mass defect: the fragments weigh about 0.1% less than the original nucleus, and the missing mass reappears as energy via E=mc². One fission releases about 200 MeV (about 3.2×10⁻¹¹ J); fully fissioning 1 g of ²³⁵U yields about 8×10¹⁰ J — the heat of roughly 2.5 tonnes of coal, or about 17 tonnes of TNT. Hiroshima used a uranium gun-type weapon; Nagasaki a plutonium implosion device. The very same physics, tamed, powers nuclear plants today. One honest note about the box: stray neutrons occasionally appear on their own (the ambient background of spontaneous fission and cosmic rays), spent nuclei restock from the surrounding fuel after a moment, and the display caps at 220 neutrons — so a supercritical run saturates at the chart's dashed ceiling rather than growing forever.