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, where the electrostatic repulsion between so many protons makes the nucleus easier to deform and split.

In nuclear notation, a nuclide is written as (^{A}_{Z}X), where (A) is the nucleon number (dimensionless), (Z) is the proton number (dimensionless), and (X) is the chemical symbol of the element. For any balanced nuclear equation, the total nucleon number and total proton number must be conserved. Check that bookkeeping first, before you start 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 version is useful in reactors, since the emitted neutrons can go on to trigger further fissions.

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

[ ^{235}{92} ext{U}+^{1}{0} ext{n}\rightarrow ^{236}{92} ext{U}^{*}\rightarrow ^{144}{56} ext{Ba}+^{89}{36} ext{Kr}+3,^{1}{0} ext{n}+\Delta E, ]

where (\Delta E) is the energy released by the reaction (J or MeV). The asterisk on (^{236}_{92} ext{U}^{*}) shows that the nucleus is in an excited, unstable state. This is only one possible pair of fission fragments; many pairs can form, 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, (B/A), where (B) is total binding energy (MeV) and (A) is nucleon number (dimensionless). Heavy nuclei such as uranium-235 have lower binding energy per nucleon than nuclei nearer the middle of the graph, so splitting a heavy nucleus moves the products towards a more tightly bound region.

Don’t imagine the energy as being “inside the uranium” like fuel sitting in a tank. The release comes from a decrease in the total rest mass of the system 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

[ \Delta m=m_i-m_f, ]

where (\Delta m) is the mass decrease in the reaction (kg or u), (m_i) is the total initial mass (kg or u), and (m_f) is the total final mass (kg or u). Then

[ \Delta E=\Delta m c^2, ]

where (c) is the speed of light in a vacuum (m s(^{-1})). If (\Delta m) is measured in unified atomic mass units, it is often quicker to use (1, ext{u}=931.5, ext{MeV},c^{-2}), so the energy released in MeV is (\Delta m) in u multiplied by 931.5.

When fission calculations use atomic masses, the electron masses usually cancel, as long as the total proton number is the same on both sides. That’s 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 imes10^{-11}) J. For one nucleus, that is tiny. Per kilogram, it is enormous, because a macroscopic sample contains so many nuclei.

You can estimate the same result 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 and, just after the split, they strongly repel each other. This electrostatic repulsion accelerates them apart; when the reactor material slows them down, their kinetic energy becomes internal energy.

Some energy also 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. A reactor does not usefully recover the antineutrino energy.

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 argument. 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. Adding 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.

Nuclear stability is therefore not the same kind 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 in which particles produced by one reaction trigger further reactions of the same type. In fission, the particles that matter are neutrons. One uranium-235 fission may release two or three neutrons; if at least one of them causes another fission, sustained energy production can happen.

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 them rather than fission.

In a reactor, the goal is not to let fissions multiply without control. What’s useful is a steady chain reaction: on average, one neutron from each fission causes one more fission. If fewer than one does this, the reaction dies away. If more than one does this, the rate rises.

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

[ P_e=\eta R\Delta E, ]

where (P_e) is the electrical power output (W), (\eta) is the overall efficiency of converting fission energy to electrical energy (dimensionless), and (R) is the fission rate (s(^{-1})). This gives the clean answer to “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, if the electrical output is fixed, 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 especially useful because they have no charge. 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 emitted neutrons are fast at first, with MeV-scale kinetic energies. In many reactor designs, slow neutrons induce fission in uranium-235 much more effectively. 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 contains mostly uranium-238 and 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 improves the chance that a neutron meets a uranium-235 nucleus and keeps the chain reaction self-sustaining.

The reactor as an energy-transfer device

A nuclear power plant is more than a “nuclear boiler”, although that picture is a good place to start. Fission raises the internal energy of the reactor core. Coolant carries energy away from the core, then a heat exchanger makes steam. That steam drives turbines connected to 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 has 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 hold the fissile material in a form with a large surface area for heat transfer, while keeping the radioactive material contained. The rods are arranged so that neutrons can pass 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 use.

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 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 produced 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 choice of material is a compromise, not just a simple “slow it down as much as possible” decision.

Control rods

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

When the control rods are lowered deeper into the core, they remove more neutrons from the chain reaction, and the fission rate falls. Raising them 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, this separation is vital 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 passes through a heat exchanger and transfers energy to a secondary water circuit, which produces steam for the turbine. The turbine circuit therefore stays 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 is also part of shielding in practice. 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.