Fission and the Reactor

A nucleus that splits

The binding energy curve says that a uranium nucleus would release about 200 MeV if it split. It does not split by itself, or only very rarely. It needs a push: a neutron. A neutron has no charge, so it feels no Coulomb barrier and can drift into the nucleus even when it moves slowly.

Here is what happens. A slow neutron is captured by a uranium-235 nucleus, which becomes uranium-236 with some extra energy. The new nucleus quivers like a drop of liquid. If it stretches into a dumbbell, the electric repulsion between the two ends pushes them apart. The short-range nuclear force cannot pull them back. The nucleus splits.

The fragments are not the same every time. Fig 5.1 shows two of the splits: barium-141, krypton-92 and three neutrons, or xenon-140, strontium-94 and two neutrons. Equal halves are rare. The fragments pile up in two humps, one near \(A = 95\) and one near \(A = 139\). A split into two nuclei near \(A = 118\) is hundreds of times less likely. On average about 2.5 neutrons come out.

Most of the energy appears at once as the kinetic energy of the two fragments, about 170 MeV. They are pushed apart by their electric repulsion, then slowed by the surrounding atoms, which heats the fuel. The rest comes out as neutrons, gamma rays and, later, the decays of the fragments. The fragments carry too many neutrons for the line of stability of the last lesson, so they decay towards it.

The energy is enormous for its mass. One kilogram of uranium-235 holds \(\tfrac{1000}{235} \times 6.02 \times 10^{23} = 2.56 \times 10^{24}\) nuclei. At \(200\,\text{MeV} = 3.2 \times 10^{-11}\,\text{J}\) each, full fission gives \(8.2 \times 10^{13}\,\text{J}\). Burning a kilogram of coal gives about \(3 \times 10^{7}\,\text{J}\), nearly three million times less.

One fission leads to the next

Each fission takes one neutron and gives back two or three. If at least one of those causes another fission, the process keeps itself going. This is a chain reaction. Fissions come in generations: the neutrons of one generation cause the fissions of the next.

Not every neutron causes a fission. Some escape through the surface. Some are caught by nuclei that do not split. So \(k\) is less than the 2.5 neutrons born in each fission, and its value decides everything. With \(k < 1\) the chain dies out; the reactor is subcritical. With \(k = 1\) each generation equals the last; it is critical. With \(k > 1\) the chain grows without limit; it is supercritical.

Growth that looks small is not. With \(k = 1.01\), only one per cent above critical, the rate grows by \((1.01)^{100} = 2.7\) in 100 generations. It reaches a thousand times the starting rate after \(\ln 1000/\ln 1.01 \approx 690\) generations. In a bomb, with \(k\) near 2, ten generations multiply the rate by \(2^{10} = 1024\). A generation lasts only a small fraction of a second.

Critical mass

Neutrons are born throughout a lump of uranium, but they escape through its surface. In a small lump the surface is large compared with the volume, so most neutrons escape before they meet a uranium-235 nucleus, and \(k < 1\). A bigger lump has less surface for its volume, and \(k\) rises. The least mass for which \(k\) reaches 1 is the critical mass. A sphere needs the least, because it has the smallest surface for its volume; a thin sheet loses nearly every neutron through its faces.

Slowing the neutrons down

Fission neutrons leave with about 2 MeV. A uranium-235 nucleus catches slow neutrons hundreds of times more readily than fast ones. So a thermal neutron, slowed until its energy is about that of the surrounding atoms, \(0.025\,\text{eV}\), is the best trigger. Natural uranium is only 0.7 per cent uranium-235. The rest is uranium-238, which fast neutrons rarely split.

A moderator slows neutrons by elastic collisions. The chapter on Collisions found that a body striking an equal body head-on hands over all its energy. One striking a much heavier body bounces back with nearly all of it. A neutron striking a nucleus of mass number \(A\) head-on loses the fraction \(4A/(1 + A)^2\) of its kinetic energy.

For hydrogen, \(A = 1\), the fraction is 1: a proton can stop a neutron in one hit. For deuterium it is 0.89, for carbon 0.28, and for uranium-238 only 0.017. So a good moderator is made of light nuclei: ordinary water, heavy water or graphite. Even in carbon, a neutron needs more than a hundred collisions to become thermal.

The parts of a reactor

A reactor is a chain reaction held at \(k = 1\) while its heat is carried away. Fig 5.3 shows the parts of a thermal reactor, and each part has one job.

1. Fuel rods hold the uranium, usually as uranium oxide pellets sealed in metal tubes.
2. The moderator slows the fission neutrons to thermal speeds: ordinary water, heavy water or graphite.
3. Control rods of cadmium or boron soak up spare neutrons. Pushed in, they lower \(k\); pulled out, they raise it. Dropped fully in, they stop the reactor.
4. The coolant carries the heat from the core to a heat exchanger, which boils water into steam for the turbine. It is water, heavy water or liquid sodium.
5. The shield, thick concrete and steel, stops the neutrons and gamma rays from reaching people.

Boron works in a control rod through the reaction of the last lesson: \(n + {}^{10}\text{B} \to {}^{7}\text{Li} + \alpha\). It needs no threshold and no energy to start, so boron-10 swallows slow neutrons very readily. India's pressurised heavy water reactors, such as those at Rawatbhata and Kaiga, use heavy water as the moderator. Heavy water absorbs far fewer neutrons than ordinary water, so they can run on natural uranium.