What fission is

Nuclear fission is a nuclear process in which a heavy nucleus splits into two or more lighter nuclei, usually releasing neutrons and energy. It matters most for very heavy nuclei: with so many protons packed in, electrostatic repulsion makes the nucleus easier to deform and split.

In nuclear notation, a nuclide is written as

In a balanced nuclear equation, total nucleon number and total proton number are conserved. Do that bookkeeping first, before any energy calculation.

Spontaneous fission is a radioactive decay process in which a heavy nucleus splits without being struck by an incoming neutron. Naturally occurring very heavy nuclei such as uranium and thorium can do this, but for these nuclei it is rare compared with alpha decay.

Neutron-induced fission is a nuclear reaction in which an incoming neutron is absorbed by a heavy nucleus, producing an excited unstable nucleus that then splits. This is the version used in reactors, since the emitted neutrons can trigger further fissions.

A typical induced fission of uranium-235 may be represented as

The asterisk on $^{236}_{92}\text{U}^{*}$ shows that the nucleus is in an excited, unstable state. There is not just one possible pair of fission fragments; many pairs can occur, provided the nucleon and proton numbers balance.

Where the energy comes from

Binding energy is the energy required to separate a nucleus completely into its individual protons and neutrons. Equivalently, it is the energy released when those nucleons bind together to form the nucleus. Fission releases energy because the medium-mass product nuclei have a greater binding energy per nucleon than the original heavy nucleus.

Binding energy per nucleon is the binding energy divided by the number of nucleons,

Heavy nuclei such as uranium-235 have lower binding energy per nucleon than nuclei nearer the middle of the graph, so when a heavy nucleus splits, the products move towards a more tightly bound region.

Do not picture the energy as being “inside the uranium” like fuel in a tank. The energy is released because the total rest mass of the system decreases as the products become more tightly bound. That lost mass appears as kinetic energy of the fragments and neutrons, gamma-ray photons, and later radiation from radioactive fission products.

For calculations, use

Then

If $\Delta m$ is measured in unified atomic mass units, it is often quicker to use $1\,\text{u}=931.5\,\text{MeV}\,c^{-2}$, so the energy released in MeV is $\Delta m$ in u multiplied by 931.5.

When atomic masses are used in fission calculations, the electron masses usually cancel as long as the total proton number is the same on both sides. This is why IB questions often give atomic masses rather than nuclear masses.

A uranium-235 fission typically releases about 200 MeV, which is about $3.2\times10^{-11}$ J. For one nucleus, that is tiny. Per kilogram, it is enormous, because a macroscopic sample contains so many nuclei.

The same result can be estimated from binding energies: calculate the total binding energy of the final nuclei, subtract the total binding energy of the initial heavy nucleus, and the increase is the energy released. For example, if the final stable products have larger total binding energy by about 200 MeV, that is the energy available from the fission and subsequent decays.

Forms of the released energy

Most of the immediately recoverable energy is the kinetic energy of the two heavy fission fragments. Both fragments are positively charged, so just after the split they strongly repel each other. This electrostatic repulsion accelerates them apart; as they slow down in the reactor material, their kinetic energy becomes internal energy.

Other energy appears as kinetic energy of emitted neutrons, gamma photons produced during nuclear transitions, beta particles and gamma photons from later decays of fission products, and antineutrinos. An antineutrino is a neutral lepton emitted in beta-minus decay that carries energy, momentum and lepton number away from the nucleus. The antineutrino energy is not usefully recovered in a reactor.

This is a useful point to connect atomic and nuclear photons. A photon is a quantum of electromagnetic radiation that carries energy and momentum. Photons from atomic transitions usually have energies of order eV, because electron energy levels are separated by eV-scale gaps. Gamma photons from nuclear transitions often have keV to MeV energies, because nuclear energy level separations are much larger.

The neutrino family also comes from a conservation problem. In beta decay, the observed beta-particle energies form a continuous range; energy and momentum did not appear to balance if only the daughter nucleus and beta particle were included. Introducing the neutrino or antineutrino restored conservation of energy, momentum and angular momentum, and later experiments confirmed it.

A nucleus could not be stable if only gravity and electric forces were considered. Gravity between nucleons is negligible on nuclear scales, while the electric force between protons is repulsive. The strong nuclear force is the short-range attractive interaction between nucleons that binds nuclei; fission becomes favourable in very heavy nuclei because the long-range electrostatic repulsion between protons increasingly competes with this short-range attraction.

Stability in a nucleus is therefore not the same sort of balance as equilibrium in a star. A star can remain in macroscopic equilibrium when outward thermal or radiation pressure balances inward gravitational effects. A nucleus is a quantum system whose stability depends on binding energy, the strong force, electrostatic repulsion and possible decay routes.

From one fission to many

A chain reaction is a sequence of reactions where particles made in one reaction trigger further reactions of the same type. In fission, the key particles are neutrons. A single uranium-235 fission may release two or three neutrons; if at least one of them causes another fission, sustained energy production becomes possible.

A fissile nucleus is a nucleus that can undergo fission after absorbing a slow neutron. Uranium-235 and plutonium-239 are important fissile nuclei. Uranium-238 does not work in the same way in a thermal reactor, because with slow neutrons it tends to absorb the neutron rather than undergo fission.

A reactor is not designed for an uncontrolled multiplication of fissions. What’s useful is a steady chain reaction: on average, one neutron from each fission causes one more fission. If the average is less than one, the reaction dies away. If it is greater than one, the rate rises.

The fission rate is directly linked to power. For a reactor-generator system,

This answers the question “How is binding energy used to determine the rate of energy production?”: binding energy gives $\Delta E$ per fission, and the required power tells you how many fissions per second are needed.

For example, with a fixed electrical output, a lower efficiency requires a larger fission rate. Nuclear power stations are heat engines, so they cannot convert all fission energy into electrical energy. In practice, the efficiency is much less than 100%, commonly around a few tens of percent.

Why neutrons matter

Neutrons are useful because they are uncharged. A positively charged particle approaching a uranium nucleus would be repelled by the positive nuclear charge. A neutron can approach the nucleus without electrostatic repulsion and may be absorbed.

The neutrons emitted in fission are fast at first, with MeV-scale kinetic energies. In many reactor designs, slow neutrons are much more effective at inducing fission in uranium-235. So a chain reaction depends on having enough neutrons, controlling their speeds, and preventing too many from being absorbed by non-fissile material.

Natural uranium is mostly uranium-238, with only a small fraction of uranium-235. Reactor fuel is usually enriched uranium, meaning uranium in which the proportion of uranium-235 has been increased. Enrichment makes it more likely that a neutron meets a uranium-235 nucleus, helping the chain reaction remain self-sustaining.

The reactor as an energy-transfer device

A nuclear power plant is not just a “nuclear boiler”, though that is a good first model to keep in mind. Fission raises the internal energy of the reactor core. A coolant carries energy away from the core, then a heat exchanger produces steam. That steam turns turbines, and the turbines drive generators.

A reactor core is the central region of a nuclear reactor that contains the fuel and the components needed to sustain and control fission. In a typical thermal reactor, the core holds fuel rods, moderator and control rods inside a strong reactor vessel, with shielding and containment around it.

Fuel rods

Fuel rods are sealed metal tubes containing nuclear fuel pellets. They keep the fissile material in a form with a large surface area for heat transfer, while also containing the radioactive material. The rods are arranged so neutrons can move between the fuel and the moderator.

Uranium fuel contains uranium-235 for fission and uranium-238 as the more abundant isotope. If there is too much uranium-238, it absorbs too many neutrons, so in many reactors the uranium-235 fraction is increased before the fuel is used.

Moderators

A moderator is a material in a reactor core that slows fast neutrons by elastic collisions without absorbing too many of them. Slow neutrons that are in thermal equilibrium with their surroundings are called thermal neutrons, which are neutrons with kinetic energies comparable to particles at ordinary temperatures.

Moderation is needed because uranium-235 is much more likely to undergo fission when hit by slow neutrons than by very fast ones. Fast neutrons released in fission collide with moderator nuclei and transfer kinetic energy to them. Common moderator materials include water, heavy water and graphite.

A good moderator transfers energy efficiently, survives the reactor environment and has a low probability of absorbing neutrons. Hydrogen nuclei take kinetic energy from neutrons very effectively because their masses are similar, but ordinary hydrogen can also absorb neutrons. So the material choice is a compromise, not just a matter of “slow it down as much as possible”.

Control rods

Control rods are movable rods made from neutron-absorbing material that regulate the neutron population in a reactor core. Boron is one example, because it absorbs neutrons readily.

When the control rods are lowered deeper into the core, they remove more neutrons from the chain reaction, so the fission rate falls. Raising the rods leaves more neutrons available, so the fission rate can rise. During an emergency shutdown, the rods are inserted rapidly to reduce the chain reaction.

Heat exchangers

A heat exchanger is a device that transfers internal energy from one fluid circuit to another without mixing the fluids. In a nuclear plant, that separation matters because the fluid passing through or near the reactor core may become radioactive or contaminated.

In a pressurized-water reactor, water in the primary circuit is kept under high pressure so it can carry energy away from the core without boiling. It then passes through a heat exchanger and transfers energy to a secondary water circuit, which produces steam for the turbine. The turbine circuit is therefore kept separate from the reactor vessel.

Shielding and containment

Shielding is material placed around a radiation source to absorb or reduce ionizing radiation before it reaches people or the environment. Reactors need shielding because fission produces penetrating neutron radiation and gamma radiation, along with radioactive materials inside the core.

Thick steel in the reactor vessel helps contain pressure and absorb some radiation. Reinforced concrete around the vessel absorbs more neutrons and gamma photons. The containment building adds another engineered barrier, designed to keep radioactive material inside even during serious faults.

Remote handling also acts as part of shielding in real reactor work. Spent fuel rods are intensely radioactive, so robots and shielded equipment are used to move them. Reactor safety is layered: control the chain reaction, remove heat, contain radioactive material, and keep distance and shielding between radiation and people.

What fission products are like

Fission products are the nuclei formed when a heavy nucleus splits during fission. Compared with stable nuclei of similar mass, they usually contain too many neutrons, so many of them are radioactive. They often decay by beta-minus decay, followed by gamma emission.

The products do not appear as one tidy pair of nuclei. In uranium-235 fission, the fragments come in a distribution, commonly with one lighter fragment and one heavier fragment rather than two equal halves. That matters in a reactor core, because the core slowly builds up a mixture of radioactive isotopes with different chemical properties and half-lives.

Products with short half-lives have high activity and give out significant heat soon after they are removed from the reactor. Products with longer half-lives may be less active, but they can remain a storage problem for many generations. Exponential change comes in here: radioactive nuclei decay exponentially, so activity drops by repeated half-lives, not by the same amount each year.

Some fission energy is delayed, since radioactive fission products keep decaying after the chain reaction has been reduced or stopped. This decay heat is heat produced by radioactive decay after fission has occurred, and it is one reason spent fuel needs careful cooling.

Changes inside fuel rods

Several processes take place in the fuel rods during reactor operation:

• Some uranium-235 nuclei fission into pairs of lighter nuclei.
• Some uranium-235 absorbs a neutron but does not fission, producing uranium-236, which has a long half-life.
• Some uranium-238 absorbs a neutron and can eventually lead to plutonium-239.

Plutonium-239 is a fissile isotope produced in reactors when uranium-238 absorbs neutrons and undergoes subsequent nuclear changes. It can be used as reactor fuel, but it also brings security and proliferation concerns. For that reason, fission technology is never just a technical issue.

The solid fuel changes physically as well. When one uranium nucleus is replaced by two fission product nuclei, the fuel structure is disrupted and the fuel rod can become distorted. Operators therefore remove fuel before all possible uranium-235 has fissioned.

Managing waste

Radioactive waste is material containing unstable nuclei at activity levels that require controlled handling, storage or disposal. It ranges from low-level items such as contaminated gloves to high-level spent fuel containing intense beta, gamma and neutron sources.

Spent fuel first goes into cooling ponds under water. The water carries away decay heat and acts as shielding. Recently removed fuel has dangerous radiation levels nearby, so remote handling is essential.

After this initial cooling period, some fuel may be reprocessed. Reprocessing is a chemical treatment of spent nuclear fuel that separates reusable uranium and plutonium from fission products and other waste. It can reduce the amount of unused fuel thrown away, but it adds cost, chemical hazards and security concerns.

Long-term waste management has to deal with both radioactivity and chemical toxicity. Some waste is sealed in containers for surface storage; some is immobilized in stable solids and put into engineered underground repositories. The main requirement is isolation from groundwater, living organisms and future accidental disturbance for times comparable with many half-lives of the dangerous isotopes.

At the end of a plant’s life, decommissioning is the process of safely shutting down, dismantling or enclosing a nuclear facility and managing its radioactive materials. It can take decades, and the cost has to be counted honestly as part of the cost of nuclear electricity.

Fission and climate change

Fission has a serious place in the climate discussion because it can produce large amounts of continuous electrical power with low carbon dioxide emissions during operation. Unlike wind and solar generation, it is not weather-dependent, so it can provide reliable baseload or firm low-carbon power.

The case is not one-sided, though. Mining, construction, decommissioning, accident risk, waste storage, high capital cost and public trust all matter. Long-term storage is especially important: the waste problem is not just “where do we put it next year?”, but “how do we keep it isolated beyond the lifetime of present institutions?”

A balanced answer is that fission can help reduce fossil-fuel use, but it is not a complete solution by itself. The scientific responsibility is to set out the energy benefits, radiation risks, waste timescales and uncertainties clearly, so society can decide what level of risk and cost it is willing to accept.