Nuclear Fission and Nuclear Reactors
Nuclear fission is the splitting of a heavy nucleus, such as uranium-235 after absorbing a neutron, into two lighter nuclei plus two or three neutrons, releasing about 200 MeV of energy per fission; if on average one neutron from each fission goes on to cause another fission, a controlled chain reaction is sustained in a nuclear reactor. In brief: the energy comes from the increase in binding energy per nucleon (from 7.6 MeV for uranium to about 8.5 MeV for the fragments). One kilogram of uranium-235 fissioning completely releases about 8 × 1013 J, roughly 2.7 million times the energy of 1 kg of coal. A reactor has fuel, a moderator to slow neutrons, control rods that absorb neutrons, a coolant to carry away the heat, and shielding. The multiplication factor k = 1 for steady operation.
About 10 percent of the world’s electricity comes from nuclear fission. This guide describes the fission process and chain reaction, the components and operation of a nuclear reactor, the issues of waste and safety, compares fission reactors with fossil fuel plants in a table, works through energy calculations and corrects common mistakes.
What is nuclear fission?
When a slow (thermal) neutron is absorbed by a uranium-235 nucleus, the compound nucleus 236U is formed in a highly excited state and deforms like a liquid drop, then splits. A typical reaction: 10n + 23592U → 14156Ba + 9236Kr + 3 10n + energy. There are many possible pairs of fragments, in general of unequal mass, with a mean of 2.4 neutrons released per fission. The energy released, about 200 MeV, appears mainly as kinetic energy of the fragments (about 168 MeV, which turns into heat), kinetic energy of the neutrons (5 MeV), gamma rays, and the decay of the radioactive fragments (beta particles, antineutrinos and gamma rays). Only uranium-235 (0.72 percent of natural uranium), plutonium-239 and uranium-233 are fissile with slow neutrons; uranium-238 undergoes fission only with fast neutrons, but can absorb neutrons and be converted into plutonium-239.
What is a chain reaction?
The neutrons emitted in a fission can cause further fissions. The multiplication factor k is the average number of neutrons from one fission that cause another fission. If k < 1 the reaction dies out (subcritical); if k = 1, it proceeds at a steady rate (critical); if k > 1, the rate increases exponentially (supercritical), as in a nuclear weapon. In a reactor, k is held very close to 1. Control is possible because a small fraction (about 0.65 percent) of the neutrons are “delayed neutrons”, emitted seconds to minutes after the fission by the decay of fission products, which slows the response of the reactor to a time scale of seconds rather than microseconds. A critical mass of fissile material is needed so that not too many neutrons escape through the surface.
How does a nuclear reactor work?
- Fuel: uranium dioxide pellets enriched to 3 to 5 percent uranium-235 (natural uranium is 0.72 percent), in zirconium alloy tubes.
- Moderator: fast neutrons from fission (about 2 MeV) are slowed to thermal energies (0.025 eV) by collisions with the nuclei of a light material (water, heavy water, or graphite), because slow neutrons are much more likely to cause fission in uranium-235.
- Control rods: made of neutron-absorbing materials (boron, cadmium, hafnium). Inserting them reduces k; withdrawing them increases k. Rods can be inserted quickly to shut down the reactor (scram).
- Coolant: water, heavy water, gas or liquid metal flows through the core, removing the heat. In a pressurized water reactor (PWR), the water at about 155 bar and 300 °C transfers the heat to a secondary circuit, producing steam for turbines and generators. The thermal efficiency is about 33 percent.
- Shielding and containment: thick concrete and steel absorb the radiation and contain accidents.
What about waste and safety?
Spent fuel contains fission products (strontium-90, cesium-137, iodine-131) and actinides (plutonium, americium) that are highly radioactive, and some stay hazardous for thousands of years; it is stored in cooling pools and dry casks, and long-term plans include deep geological repositories (such as Onkalo in Finland). The decay heat of the fission products continues after shutdown (about 6 percent of full power immediately after shutdown, falling quickly), so cooling must be maintained; the failures of cooling caused the accidents at Three Mile Island (1979), Chernobyl (1986, with a different design and a power excursion) and Fukushima (2011). Advantages of nuclear power: very low emissions of carbon dioxide during operation, high energy density, steady output; disadvantages: waste, accident risk, high construction costs, and proliferation concerns.
Fission and fossil fuel compared
| Feature | Nuclear fission | Coal |
|---|---|---|
| Energy per kg of fuel | about 8 × 1013 J (U-235, complete fission) | about 3 × 107 J |
| Fuel for a 1,000 MW(e) plant per year | about 25 to 30 tonnes of enriched fuel | about 3 to 4 million tonnes |
| CO2 in operation | None | About 1 kg per kWh |
| Main concern | Radioactive waste, accidents | Emissions, air pollution |
Worked example: energy and fuel use
- Energy per kilogram. The number of nuclei in 1.0 kg of uranium-235: N = (1,000 g ÷ 235 g/mol) × 6.022 × 1023 = 2.56 × 1024. Energy = 2.56 × 1024 × 200 MeV × 1.602 × 10−13 J/MeV = 8.2 × 1013 J. Compared with coal (3 × 107 J/kg), the ratio is 2.7 × 106.
- Energy released from the mass defect. 200 MeV per fission corresponds to a mass of 200 ÷ 931.5 = 0.215 u, about 0.09 percent of the 236 u of the compound nucleus; 1.0 kg of uranium converts about 0.9 g to energy.
- Fuel consumption of a power plant. A plant of 1,000 MW electrical output with an efficiency of 33 percent has a thermal power of 3,030 MW. Per day: 3.03 × 109 W × 86,400 s = 2.62 × 1014 J, which needs 2.62 × 1014 ÷ 8.2 × 1013 = 3.2 kg of U-235 fissioned per day (about 1.2 tonnes a year of U-235 fissioned, with the total loading of enriched fuel at about 25 to 30 tonnes per year, as only part of the fuel is used before it is removed).
- Coal equivalent. The same plant burning coal would burn 2.62 × 1014 ÷ 2.4 × 107 = 1.1 × 107 kg = 11,000 tonnes of coal per day (with 24 MJ/kg).
- Neutron balance. If each fission releases 2.4 neutrons and one is needed to continue the chain, the other 1.4 neutrons must be absorbed by control rods, absorbed by non-fission reactions (including in uranium-238), or lost from the core, so that k = 1.
How was fission discovered?
Otto Hahn and Fritz Strassmann found barium in uranium bombarded with neutrons in December 1938. Lise Meitner and Otto Frisch explained it as fission in early 1939, and calculated the energy of about 200 MeV from the mass defect. Enrico Fermi’s team achieved the first self-sustaining chain reaction in the Chicago Pile-1 on 2 December 1942. The first nuclear power plant to supply electricity to a grid was Obninsk in the Soviet Union (1954), followed by Calder Hall in the UK (1956) and Shippingport in the US (1957).
Which mistakes are common?
Mistake 1: Confusing a reactor with a bomb
A reactor operates with k = 1 at low enrichment, and cannot explode like a weapon, which needs highly enriched material and a rapid assembly.
Mistake 2: Thinking that the moderator is the same as the control rods
The moderator slows neutrons so that fission is more probable; the control rods absorb neutrons to reduce the reaction rate.
Mistake 3: Saying that fission converts matter entirely to energy
Only about 0.1 percent of the mass is converted. The rest remains as the mass of the fragments.
Mistake 4: Forgetting the decay heat after shutdown
The fission products continue to produce heat, so cooling is needed for days after shutdown.