Nuclear Fission: Chain Reactions and Criticality Explained

simulator advanced ~12 min
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k_eff ≈ 0.96 — subcritical (safe shutdown)

With 3.5% enriched uranium, k∞=1.1, and 50% control rod insertion, the effective multiplication factor is about 0.96 — subcritical. The chain reaction will gradually die out. Withdraw control rods to approach criticality.

Formula

k_eff = k∞ · P_NL (effective multiplication factor)
N(t) = N₀ · k^(t/τ) (neutron population over generations)
E = Δm·c² ≈ 200 MeV per fission event

Splitting the Atom

In December 1938, Otto Hahn and Fritz Strassmann discovered that bombarding uranium with neutrons produced barium — the uranium nucleus had split in two. Lise Meitner and Otto Frisch quickly explained the physics: the nucleus, like an overstretched liquid drop, could be destabilized by a neutron impact and split into two fragments, releasing the enormous binding energy difference. Each fission of U-235 releases about 200 MeV — roughly 50 million times the energy of burning one carbon atom.

The Chain Reaction

The key to nuclear energy is that each fission releases 2-3 free neutrons. If at least one of these neutrons causes another fission, the reaction is self-sustaining — a chain reaction. The multiplication factor k describes this: k=1 means each generation produces exactly one new fission (critical), k>1 means exponential growth (supercritical), and k<1 means the reaction dies (subcritical). Nuclear reactors operate at k=1.000; nuclear weapons require k≈1.1 or higher with fast neutrons.

Controlling the Beast

This simulation visualizes uranium atoms as cyan circles with neutrons bouncing between them. When a neutron hits a U-235 atom, it splits with a flash animation, releasing daughter fragments and new neutrons. Control rods (gray bars descending from above) absorb neutrons. Watch how adjusting rod insertion changes the neutron population — pull them out and the population grows exponentially; push them in and it decays. The generation counter shows how quickly the reaction multiplies.

Enrichment and Critical Mass

Natural uranium is only 0.7% U-235 (the fissile isotope); the rest is U-238, which absorbs neutrons without fissioning. Reactor fuel is enriched to 3-5% U-235. Weapons-grade uranium is enriched to >90%. The critical mass — the minimum amount needed for a self-sustaining chain reaction — depends on enrichment, geometry, and whether neutron reflectors are present. For weapons-grade uranium, it is about 52 kg as a bare sphere; with a good reflector, as little as 15 kg.

FAQ

What is nuclear fission?

Nuclear fission is the splitting of a heavy atomic nucleus (like uranium-235) into two lighter nuclei, releasing enormous energy (~200 MeV per fission) and 2-3 free neutrons. These neutrons can trigger further fissions, creating a chain reaction.

What does 'criticality' mean?

Criticality describes the state of a fission chain reaction. Subcritical (k<1): reaction dies out. Critical (k=1): reaction is self-sustaining at constant power. Supercritical (k>1): reaction grows exponentially. Reactors operate at k=1; bombs require k>>1.

How do control rods work?

Control rods are made of neutron-absorbing materials (boron, cadmium, hafnium). Inserting them absorbs neutrons, reducing k_eff and slowing the reaction. Withdrawing them allows more neutrons to cause fissions. They are the primary means of controlling reactor power.

What went wrong at Chernobyl?

During a safety test, operators disabled safety systems and withdrew too many control rods. A power surge caused a steam explosion. The reactor's positive void coefficient meant the reaction accelerated as coolant boiled away. k_eff went far supercritical in milliseconds.

Sources

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