Nuclear fission.

Step 1 of 6

A nucleus that tears

Uranium is the heaviest element found in quantity in nature, and its nuclei are barely holding together: their 92 protons push on each other, held in only by the short-range strong force. In 1938 Otto Hahn and Fritz Strassmann found barium, a much lighter element, in uranium they had bombarded with neutrons. Lise Meitner and Otto Frisch worked out what had happened: the nucleus had split in two. They called it fission.

The Scene has a reactor core: the orange nuclei are fissile, like uranium-235, and the grey ones swallow a neutron without splitting, like uranium-238.

Step 2 of 6

Where the energy comes from

The fragments after a split weigh about a tenth of a per cent less than the uranium nucleus and neutron that went in. The missing mass has become energy, by Einstein’s formula:

$E = mc^2$⁠

The speed of light squared is an enormous number, so a little mass is a great deal of energy: about 200 MeV a split, millions of times more than any chemical reaction between two atoms.

Step 3 of 6

The multiplication factor

The new neutrons can split more nuclei, and those release more neutrons. What matters is how many of the new neutrons, on average, cause another split: the multiplication factor $k$⁠. Here each split frees 2.5 neutrons on average, and each must miss the Control rods and meet a fissile nucleus:

$k = 2.5 \times (\text{fissile share}) \times (1 - \text{absorbed share})$$k =$$2.5 \times (\text{fissile share}) \times (1 - \text{absorbed share})$⁠

If $k < 1$⁠, every chain dies out. If $k = 1$⁠, each split leads to exactly one more, and the reaction holds steady. If $k > 1$⁠, the number of splits grows with every generation. Fissile fuel and Control rods are fixed now.

Step 4 of 6

A steady chain

Natural uranium is only about 0.7% uranium-235, so fuel is enriched, to a few per cent in most reactors. Control rods, of boron or cadmium, soak up neutrons: pushing them in lowers $k$⁠, pulling them out raises it. Count the neutrons is On: the graph shows how many neutrons are in flight, on a log scale. The Fissile fuel is fixed at 90%.

Step 5 of 6

Pulling the rods out

Fissile fuel at 50% and Control rods at 20% absorbed: $k = 2.5 \times 0.5 \times 0.8 = 1$$k =$$2.5 \times 0.5 \times 0.8 =$$1$⁠. After you predict, Count the neutrons will switch On.

Try it: after answering, push Control rods in to 60% absorbed, and watch the chains die out.

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Step 6 of 6

Ten generations

A generation in a reactor lasts much less than a thousandth of a second. A real reactor can be controlled at human speed only because a small share of the neutrons, under one in a hundred, arrive seconds late from decaying fragments. Fissile fuel and Control rods are fixed: $k = 2.5 \times 0.5 \times 0.88 = 1.1$$k =$$2.5 \times 0.5 \times 0.88 =$$1.1$⁠.