Fission

Nuclear fission is a reaction in which a nucleus is split (or fissured). Controlled fission is used to generate electricity, whereas commercial electricity generation from fusion remains a goal. In 2024, more than 400 nuclear fission reactors were in operation around the world, and nuclear power supplied about 9% of the world’s electricity (see Figure 14.10.1). Its share was much higher in some countries: nuclear power generated about 67% of France’s electricity and 61% of Slovakia’s electricity that year.

Fission is the opposite of fusion and releases energy only when heavy nuclei are split. As noted in “Fusion”, energy is released if the products of a nuclear reaction have a greater binding energy per nucleon ($\text{BE}/A$) than the parent nuclei. Figure 14.10.2 shows that $\text{BE}/A$ is greater for medium-mass nuclei than heavy nuclei, implying that when a heavy nucleus is split, the products have less mass per nucleon, so that mass is destroyed and energy is released in the reaction. The amount of energy per fission reaction can be large, even by nuclear standards. The graph in Figure 14.10.2 shows $\text{BE}/A$ to be about 7.6 MeV/nucleon for the heaviest nuclei ($A$ about 240), while $\text{BE}/A$ is about 8.6 MeV/nucleon for nuclei having $A$ about 120. Thus, if a heavy nucleus splits in half, then about 1 MeV per nucleon, or approximately 240 MeV per fission, is released. This is about 10 times the energy per fusion reaction, and about 100 times the energy of the average $\alpha$, $\beta$, or $\gamma$ decay.

Spontaneous fission can occur, but this is usually not the most common decay mode for a given nuclide. For example, ${}^{\text{238}}\text{U}$ can spontaneously fission, but it decays mostly by $\alpha$ emission. Neutron-induced fission is crucial as seen in Figure 14.10.2. Being chargeless, even low-energy neutrons can strike a nucleus and be absorbed once they feel the attractive nuclear force. Large nuclei are described by a liquid drop model with surface tension and oscillation modes, because the large number of nucleons act like atoms in a drop. The neutron is attracted and thus, deposits energy, causing the nucleus to deform as a liquid drop. If stretched enough, the nucleus narrows in the middle. The number of nucleons in contact and the strength of the nuclear force binding the nucleus together are reduced. Coulomb repulsion between the two ends then succeeds in fissioning the nucleus, which pops like a water drop into two large pieces and a few neutrons. Neutron-induced fission can be written as

where ${\text{FF}}_1$ and ${\text{FF}}_2$ are the two daughter nuclei, called fission fragments, and $x$ is the number of neutrons produced. Most often, the masses of the fission fragments are not the same. Most of the released energy goes into the kinetic energy of the fission fragments, with the remainder going into the neutrons and excited states of the fragments. Since neutrons can induce fission, a self-sustaining chain reaction is possible, provided more than one neutron is produced on average — that is, if $x>1$ in $n+{}^A\text{X}\to {\text{FF}}_1+{\text{FF}}_2+xn$. This can also be seen in Figure 14.10.3.

An example of a typical neutron-induced fission reaction is

Note that in this equation, the total charge remains the same (is conserved): $92+0=56+36$. Also, as far as whole numbers are concerned, the mass is constant: $1+235=142+91+3$. This is not true when we consider the masses out to 6 or 7 significant places, as in the previous example.

Not every neutron produced by fission induces fission. Some neutrons escape the fissionable material, while others interact with a nucleus without making it fission. We can enhance the number of fissions produced by neutrons by having a large amount of fissionable material. For a specified composition, shape, density, and surroundings, the minimum mass needed for a self-sustaining chain reaction is called the critical mass. Some nuclides, such as ${}^{\text{239}}\text{Pu}$, produce more neutrons per fission than others, such as ${}^{\text{235}}\text{U}$. Additionally, some nuclides are easier to make fission than others. In particular, ${}^{\text{235}}\text{U}$ and ${}^{\text{239}}\text{Pu}$ are easier to fission than the much more abundant ${}^{\text{238}}\text{U}$. Both factors affect critical mass, which is smallest for ${}^{\text{239}}\text{Pu}$.

The reason ${}^{\text{235}}\text{U}$ and ${}^{\text{239}}\text{Pu}$ are easier to fission than ${}^{\text{238}}\text{U}$ is that the nuclear force is more attractive for an even number of neutrons in a nucleus than for an odd number. Consider that ${}_{\text{92}}{}^{\text{235}}\text{U}_{\text{143}}$ has 143 neutrons, and ${}_{\text{94}}{}^{\text{239}}\text{P}_{\text{145}}$ has 145 neutrons, whereas ${}_{\text{92}}{}^{\text{238}}\text{U}_{\text{146}}$ has 146. When a neutron encounters a nucleus with an odd number of neutrons, the nuclear force is more attractive, because the additional neutron will make the number even. About 2-MeV more energy is deposited in the resulting nucleus than would be the case if the number of neutrons was already even. This extra energy produces greater deformation, making fission more likely. Thus, ${}^{\text{235}}\text{U}$ and ${}^{\text{239}}\text{Pu}$ are superior fission fuels. The isotope ${}^{\text{235}}\text{U}$ is only 0.72% of natural uranium, while ${}^{\text{238}}\text{U}$ is 99.27%, and ${}^{\text{239}}\text{Pu}$ does not exist in nature. Australia has the largest deposits of uranium in the world, standing at 28% of the total. This is followed by Kazakhstan and Canada. The US has only 3% of global reserves.

Most fission reactors utilize ${}^{\text{235}}\text{U}$, which is separated from ${}^{\text{238}}\text{U}$ at some expense. This is called enrichment. The most common separation method is gaseous diffusion of uranium hexafluoride (${\text{UF}}_6$) through membranes. Since ${}^{\text{235}}\text{U}$ has less mass than ${}^{\text{238}}\text{U}$, its ${\text{UF}}_6$ molecules have higher average velocity at the same temperature and diffuse faster. Another interesting characteristic of ${}^{\text{235}}\text{U}$ is that it preferentially absorbs very slow moving neutrons (with energies a fraction of an eV), whereas fission reactions produce fast neutrons with energies in the order of an MeV. To make a self-sustained fission reactor with ${}^{\text{235}}\text{U}$, it is thus necessary to slow down (“thermalize”) the neutrons. Water is very effective, since neutrons collide with protons in water molecules and lose energy. Figure 14.10.4 shows a schematic of a reactor design, called the pressurized water reactor.

Control rods containing nuclides that very strongly absorb neutrons are used to adjust neutron flux. A chain reaction is critical when, on average, each fission leads to one further fission. Its average rate then remains steady; this condition is called criticality. It is subcritical when the rate decreases and supercritical when the rate increases. Supercriticality means that each generation produces more fissions in the next. Whether a sample sustains a chain reaction depends on neutron production, absorption, and escape. Critical mass therefore depends on composition, shape, density, and surroundings, including neutron moderators and reflectors. Control rods help prevent overheating, perhaps even a meltdown or explosive disassembly. The water that is used to thermalize neutrons, necessary to get them to induce fission in ${}^{\text{235}}\text{U}$, and achieve criticality, provides a negative feedback for temperature increases. In case the reactor overheats and boils the water to steam or is breached, the absence of water kills the chain reaction. Considerable heat, however, can still be generated by the reactor’s radioactive fission products. Other safety features, thus, need to be incorporated in the event of a loss of coolant accident, including auxiliary cooling water and pumps.

Neutron capture can convert fertile material, such as uranium-238, into fissile material, such as plutonium-239. This production of new fissile material is called breeding. The following reaction sequence shows how uranium-238 can be converted into plutonium-239 in a reactor.

Uranium-239 then ${\beta }^{-}$ decays:

Neptunium-239 also ${\beta }^{-}$ decays:

As in other ${\beta }^{-}$ decays, an electron and an electron antineutrino (${\overline{\nu }}_e$) are emitted.

Some plutonium-239 is produced when uranium-238 in reactor fuel captures neutrons. A breeder reactor is designed to produce more fissile material than it consumes.

Plutonium-239 has advantages over ${}^{\text{235}}\text{U}$ as a reactor fuel — it produces more neutrons per fission on average, and it is easier for a thermal neutron to cause it to fission. It is also chemically different from uranium, so it is inherently easier to separate from uranium ore. This means ${}^{\text{239}}\text{Pu}$ has a particularly small critical mass, an advantage for nuclear weapons.