Fission Chain Reaction

When a neutron strikes a uranium-235 nucleus, the atom splits into two smaller atoms and releases 2 to 3 additional neutrons. Each of those neutrons can strike another U-235 atom, releasing still more neutrons. Left unchecked, the number of fissions doubles every microsecond. That is a bomb. Controlled to exactly one new fission per fission, it is a power plant.

Nuclear fission is the splitting of a heavy nucleus into lighter nuclei, releasing energy because the products have slightly less total mass than the original. That "missing" mass converts to energy via E = mc². A single fission of U-235 releases about 200 million electron-volts (MeV), roughly 50 million times more energy than burning one carbon atom.

The chain reaction is what makes fission practical as an energy source. Each fission releases neutrons that can trigger further fissions. The key metric is the multiplication factor (k): the average number of fissions caused by each preceding fission. At k = 1, the reaction is critical: self-sustaining at a constant rate. At k > 1, it is supercritical: power increases. At k < 1, it is subcritical: the reaction dies out. Reactors operate at k = 1 during steady power generation and briefly above 1 to increase power.

Worked Example

A reactor starts with 1,000 fissions per microsecond. The operator adjusts control rods so k = 1.001 (just barely supercritical).

• After one generation. 1,000 x 1.001 = 1,001 fissions.
• After 1,000 generations. 1,000 x 1.001¹⁰⁰⁰ = about 2,718 fissions.

How does the reactor prevent k from drifting higher?

Control rods made of neutron-absorbing material (boron or hafnium) are inserted or withdrawn to absorb excess neutrons and hold k at exactly 1. This is the primary mechanism for controlling reactor power output.

The chain reaction is what distinguishes nuclear energy from chemical energy: it is self-sustaining, enormously energy-dense, and requires precise control rather than continuous fuel feed.

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