Nuclear Fission & Reactors

Split one uranium nucleus and you release about 200 MeV, some fifty million times more than burning one carbon atom. Make each split trigger exactly one more, and you have a nuclear reactor.

Energy from the binding curve#

Coal, oil and gas are limited, and harnessing sunlight on a large scale is still a challenge. Nuclei offer another source. Middle-weight nuclei are more tightly bound per nucleon than heavy ones. If the nucleons of a heavy nucleus regroup into two middle-weight fragments, the total binding energy rises, the rest mass falls, and the difference is released, mostly as kinetic energy of the fragments. This is nuclear fission.

Why heavy nuclei don’t all split at once#

Before splitting, the nucleus must stretch into a dumbbell shape, and that intermediate state has more energy than the original nucleus. Classically, without an energy kick to get over this hump, the nucleus would never split.

Quantum mechanics allows barrier penetration (tunnelling): if the final state has lower energy, the system can occasionally pass through the hump without the energy to climb it. Energy conservation seems violated, but only for a time Δt allowed by the uncertainty relation ΔE·Δt ≈ h/2π. The higher and wider the barrier, the less likely this is. For ²³⁸U the half-life for spontaneous fission is about 10¹⁶ years.

Fission of uranium-235#

Natural uranium is 99.3 % ²³⁸U and only 0.7 % ²³⁵U. A slow (thermal, about 0.04 eV) neutron is readily absorbed by ²³⁵U, forming ²³⁶U, which is very likely to split. Many pairs of fragments are possible, for example:

• On average about 2.5 neutrons are released per fission.
• Unequal fragments are most likely, with mass numbers around 95 and 140; equal halves are rare.
• Fragments inherit uranium’s high N/Z, too high for their size, so they emit neutrons and then β⁻-decay, with γ rays. Some neutrons come out only after a fragment’s β decay: these delayed neutrons are vital for controlling reactors.
• About 200 MeV is released per fission, mostly as the fragments’ kinetic energy; neutrons carry about 5 MeV, and the later decays release another 15–20 MeV. The fragments stop within the fuel, heating it.

Chain reactions#

Each fission’s neutrons can cause more fissions, which release more neutrons: a chain reaction. If, on average, more than one neutron from each fission causes another, the rate grows in geometric progression and the energy is released almost at once: an explosion. Neutrons are lost by escaping through the surface (more so for small pieces) and by absorption without fission.

Fission neutrons are fast (about 2 MeV), and ²³⁵U absorbs fast neutrons poorly. While slowing down they pass through 1–100 eV, where ²³⁸U absorbs them very strongly (forming ²³⁹U, which does not fission). Those neutrons are lost to the chain.

The nuclear reactor#

Over time the ²³⁵U is used up and the rods must be replaced.

Breeder reactors

²³⁹Pu also fissions easily but doesn’t occur naturally. It can be made from ²³⁸U: ²³⁸U + n → ²³⁹U → (β⁻) ²³⁹Np → (β⁻) ²³⁹Pu. If spent rods of ²³⁸U surround the core and at least one neutron per fission is captured in them, the reactor makes as much fuel as it burns, or more. Such a breeder reactor stretches limited uranium supplies.