The Physics of Nuclear Fission: How We Learned to Split the Atom — and Why It Changed Everything
In 1938, a uranium nucleus was split in a Berlin laboratory. Within seven years, that discovery had ended a world war and launched the nuclear age. Here's the physics of fission — from neutron capture to chain reactions to the reactors that generate 10% of the world's electricity.
Table of Contents
The Discovery That Split the Century
On the morning of 17 December 1938, in a basement laboratory at the Kaiser Wilhelm Institute in Berlin, Otto Hahn and Fritz Strassmann made a discovery that would reshape human history. They had been bombarding uranium with neutrons, expecting to create heavier elements. Instead, they found barium — an element with roughly half the mass of uranium.
Uranium had split in two.
Hahn, a chemist, was baffled. He wrote to his former colleague Lise Meitner, who had fled to Sweden months earlier to escape the Nazis. Meitner and her nephew Otto Frisch worked out the physics over Christmas, during a now-famous walk in the snow near Gothenburg. They realised that the uranium nucleus had become so unstable after absorbing a neutron that it had divided into two roughly equal fragments, releasing an enormous amount of energy — energy that could be calculated from Einstein’s equation E = mc².
Frisch coined the term “fission,” borrowing from biology (cell fission — division). Within weeks, laboratories around the world had confirmed the result. Within seven years, two fission bombs had been dropped on Japan, ending the Second World War. Within eighteen years, the first commercial nuclear power plant was operating in the UK.
No discovery in physics has ever been translated into both weapon and power source so quickly, or with such far-reaching consequences.
The Binding Energy Curve: Why Fission Releases Energy
To understand why splitting a heavy nucleus releases energy, you need the binding energy curve — one of the most important plots in nuclear physics.
Every nucleus is held together by the strong nuclear force, which binds protons and neutrons despite the electrostatic repulsion between the positively charged protons. The binding energy is the energy required to completely disassemble a nucleus into individual protons and neutrons. The higher the binding energy per nucleon (proton or neutron), the more tightly bound — and therefore more stable — the nucleus is.
The binding energy per nucleon peaks at iron-56 and nickel-62, at about 8.8 MeV per nucleon. Lighter nuclei have lower binding energy per nucleon, so fusing them into heavier nuclei (up to iron) releases energy — this is nuclear fusion, the process that powers stars. Heavier nuclei also have lower binding energy per nucleon than iron, so splitting them into lighter fragments also releases energy — this is fission.
When uranium-235 (binding energy about 7.6 MeV/nucleon) splits into two fragments near the peak of the curve (about 8.5 MeV/nucleon), the increase in binding energy — about 0.9 MeV per nucleon times 235 nucleons — is released as kinetic energy of the fragments, free neutrons, and gamma radiation. That’s about 200 MeV per fission event.
To put 200 MeV in perspective: a single chemical reaction (burning one carbon atom with oxygen) releases about 4 eV. Fission releases 50 million times more energy per atom. One kilogram of uranium-235, fully fissioned, releases as much energy as burning about 2,500 tonnes of coal.
The Chain Reaction: One Becomes Many
Fission wouldn’t be practically useful if it had to be triggered one nucleus at a time. What makes it revolutionary is the chain reaction.
When uranium-235 absorbs a neutron and fissions, it releases 2–3 free neutrons along with the two fragment nuclei. If those free neutrons are captured by other uranium-235 nuclei, they trigger additional fissions, releasing more neutrons, which trigger more fissions. The process is exponential: 1 fission → 2–3 fissions → 4–9 fissions → 8–27 fissions, and so on.
The key parameter is k, the multiplication factor — the average number of neutrons from each fission that go on to cause another fission.
k = 1 — critical. Each fission causes exactly one more. The reaction rate is constant. This is the operating condition of a nuclear reactor.
k > 1 — supercritical. The reaction rate increases exponentially. In a reactor, this is used briefly to increase power. In a bomb, k is made as large and fast as possible — a weapon-grade assembly might achieve k ≈ 2 with a neutron generation time of about 10 nanoseconds, meaning the power increases by a factor of 2¹⁰⁰ ≈ 10³⁰ in about one microsecond.
k < 1 — subcritical. The reaction dies out. This is the safe shutdown condition.
Enrico Fermi achieved the first controlled chain reaction on 2 December 1942, in Chicago Pile-1 — a stack of uranium and graphite blocks assembled beneath the stands of a disused football stadium. The graphite served as a moderator, slowing the fast neutrons emitted during fission to thermal speeds, which greatly increases their probability of being captured by uranium-235. Cadmium control rods were used to regulate the neutron population. The pile reached criticality at 3:25 PM. Fermi’s team celebrated with a bottle of Chianti.
How a Nuclear Reactor Works
A nuclear power reactor is, in its essence, a controlled chain reaction that produces heat, coupled to a conventional steam power plant.
The core contains fuel — typically uranium dioxide (UO₂) ceramic pellets, enriched to about 3–5% uranium-235 (natural uranium is 0.7% U-235, 99.3% U-238). The pellets are stacked in metal tubes (fuel rods), bundled into fuel assemblies, and submerged in a coolant.
Moderator material slows neutrons from the high energies at which they’re emitted (about 2 MeV) to thermal energies (about 0.025 eV). Slow neutrons are far more likely to cause fission in U-235. Most reactors use ordinary water as both moderator and coolant. Some use heavy water (deuterium oxide) or graphite.
Control rods of neutron-absorbing material (boron, cadmium, hafnium) are inserted into or withdrawn from the core to regulate the chain reaction. Fully inserted, they absorb enough neutrons to shut down the reaction. Partially withdrawn, they maintain k = 1.
Coolant (usually water under pressure) removes the heat from the core. In a pressurised water reactor (PWR), the most common type worldwide, water in the primary loop is pressurised to about 155 atmospheres (15.5 MPa) to prevent boiling at 315 °C. This hot water heats a secondary water loop through a steam generator. The secondary loop produces steam at lower pressure, which drives a turbine and generator.
The thermal efficiency of a nuclear plant is typically 33–37%, limited by the Carnot efficiency at the operating temperatures. A typical 1,000 MW electrical plant produces about 3,000 MW of thermal power — the remaining 2,000 MW is rejected as waste heat through cooling towers or water discharge.
Reactor Types: Many Designs, One Principle
The nuclear industry has developed several reactor types, each with different trade-offs:
Pressurised Water Reactors (PWRs) are the most common worldwide (~300 of ~440 operating reactors). Water serves as both coolant and moderator. The primary coolant remains liquid under high pressure. Safe and well-understood, but the high-pressure system requires robust containment.
Boiling Water Reactors (BWRs) allow the coolant to boil directly in the core, producing steam that drives the turbine without a secondary loop. Simpler design but the turbine handles slightly radioactive steam.
CANDU reactors (Canada) use heavy water as moderator and natural (unenriched) uranium as fuel. They can be refuelled while operating — no need to shut down for refuelling.
Generation IV designs under development include molten salt reactors (fuel dissolved in liquid salt — inherently safe because the salt expands and slows the reaction if temperature rises), high-temperature gas reactors (helium-cooled, can reach higher temperatures for better efficiency), and fast breeder reactors (which use fast neutrons and can convert uranium-238 into plutonium-239 fuel, potentially extending fuel supplies by a factor of 60).
Small modular reactors (SMRs) — factory-built units producing 50–300 MW — are attracting significant investment as of the mid-2020s. Their smaller size allows passive safety systems (the reactor shuts itself down by physics, not by engineered systems requiring power) and modular construction.
The Waste Problem
Fission produces radioactive waste. This is the technology’s most challenging consequence.
Spent fuel assemblies removed from a reactor contain hundreds of different radioactive isotopes. The fission products — fragments of split uranium nuclei — include isotopes with half-lives from fractions of a second to millions of years. The most concerning are caesium-137 (half-life 30 years), strontium-90 (29 years), and iodine-129 (15.7 million years).
The actinides — elements heavier than uranium, produced by successive neutron captures — include plutonium-239 (half-life 24,100 years), americium-241 (432 years), and neptunium-237 (2.14 million years). These dominate the long-term radiological hazard.
The total volume is surprisingly small. A 1,000 MW reactor produces about 20–30 tonnes of spent fuel per year — roughly enough to fill a few parking spaces. All the nuclear waste ever produced by all commercial reactors worldwide would fit in a single football field, stacked a few metres high.
But the radioactivity is intense and long-lived. After 1,000 years, the fission products have mostly decayed. After 10,000 years, the remaining hazard is dominated by plutonium and other actinides. After about 300,000 years, the waste is no more radioactive than the original uranium ore.
Deep geological disposal — burying waste in stable rock formations hundreds of metres underground — is the internationally agreed solution. Finland’s Onkalo facility, the world’s first deep geological repository, is designed to isolate spent fuel for at least 100,000 years in Precambrian bedrock that has been stable for nearly 2 billion years.
What Fission Teaches Us
Nuclear fission occupies a unique position in physics — it’s a discovery that revealed something fundamental about the nature of matter (that nuclei can be split, releasing energy predicted by E = mc²) and simultaneously created both the most destructive weapon and one of the most concentrated energy sources ever developed.
The physics is beautiful. The binding energy curve, the chain reaction, the interplay of neutron moderation and absorption — these are elegant examples of nuclear physics applied to engineering. A reactor is, at its heart, a precisely balanced system: too many neutrons and it overheats; too few and it shuts down. The balance is maintained by the physics itself (negative temperature coefficients, Doppler broadening) as much as by engineered controls.
The ethics are harder. Fission produces zero carbon emissions during operation but creates waste that remains hazardous for timescales that exceed all of recorded human civilisation. It provides about 10% of the world’s electricity — the largest source of low-carbon baseload power — but carries the risk, however small, of catastrophic accidents (Chernobyl, Fukushima).
The physics doesn’t resolve these tensions. It just tells you what’s possible and what it costs. The decisions — to build, to decommission, to store waste, to develop new designs — are human choices, made with imperfect information, under real constraints.
What physics can tell you is this: one kilogram of uranium contains as much energy as 2,500 tonnes of coal. Whether that fact is a gift or a burden depends on what we do with it.
Frequently Asked Questions
What is nuclear fission?
Nuclear fission is the splitting of a heavy atomic nucleus into two or more lighter nuclei, accompanied by the release of energy and free neutrons. When a uranium-235 nucleus absorbs a slow neutron, it becomes unstable uranium-236, which splits into two medium-mass fragments (such as barium-141 and krypton-92), releasing 2-3 additional neutrons and about 200 MeV of energy per fission event. That 200 MeV is roughly 50 million times more energy than a single chemical combustion reaction. The energy comes from the difference in nuclear binding energy: the two fragment nuclei are more tightly bound than the original uranium nucleus, and the 'missing' mass is converted to energy via E = mc². Fission was discovered in December 1938 by Otto Hahn and Fritz Strassmann in Berlin, and the physical explanation was provided by Lise Meitner and Otto Frisch within weeks.
What is a chain reaction?
A chain reaction occurs when the neutrons released by one fission event trigger additional fission events, which release more neutrons, triggering still more fissions. If each fission produces 2-3 neutrons and at least one of them causes another fission, the reaction is self-sustaining. In a nuclear reactor, the chain reaction is carefully controlled so that on average exactly one neutron from each fission causes another fission — this is called criticality (k = 1). If k > 1 (supercritical), the reaction rate increases exponentially — this is the principle of a nuclear weapon. If k < 1 (subcritical), the reaction dies out. Control is achieved using control rods made of neutron-absorbing materials (boron, cadmium, hafnium) that can be inserted or withdrawn to adjust the neutron population. The first controlled self-sustaining chain reaction was achieved by Enrico Fermi's team under the stands of the University of Chicago's football stadium on 2 December 1942.
How does a nuclear power plant generate electricity?
A nuclear power plant is essentially a very expensive way to boil water. The fission reactions in the reactor core produce heat — about 3,000 megawatts of thermal power in a typical large reactor. This heat is transferred to a coolant (usually water, sometimes gas or liquid metal), which either directly produces steam or heats a secondary water loop that produces steam. The high-pressure steam drives a turbine connected to an electrical generator, producing about 1,000 megawatts of electrical power (roughly 33% thermal efficiency, limited by the second law of thermodynamics). The spent steam is condensed back to water using a cooling system (cooling towers, river water, or seawater) and returned to the steam generator. The nuclear part is the heat source; everything downstream is conventional steam power engineering identical to coal or gas plants.
Why is nuclear waste so problematic?
Nuclear fission produces radioactive waste products with half-lives ranging from seconds to millions of years. The spent fuel removed from a reactor contains fission products (like caesium-137 with a 30-year half-life and strontium-90 with a 29-year half-life), actinides (like plutonium-239 with a 24,000-year half-life), and activated structural materials. The high-level waste is intensely radioactive and generates significant heat for decades. After about 300-500 years, the fission products decay to safe levels. But the long-lived actinides remain hazardous for tens of thousands of years — far longer than any human civilisation has existed. This creates a unique engineering and ethical challenge: designing storage that remains secure for geological timescales. Deep geological repositories (like Finland's Onkalo facility) are the current solution, placing waste in stable rock formations hundreds of metres underground.
How is fission different from fusion?
Fission splits heavy nuclei (like uranium or plutonium) into lighter fragments. Fusion combines light nuclei (like hydrogen isotopes) into heavier ones. Both release energy, but from opposite ends of the binding energy curve. Fission releases about 200 MeV per event from a uranium-235 nucleus (mass 235). Fusion releases about 17.6 MeV per event from deuterium-tritium fusion (combined mass about 5). Per unit mass, fusion releases roughly 4 times more energy than fission. Fusion produces no long-lived radioactive waste (the main product is helium) and the fuel (hydrogen isotopes) is virtually unlimited. But fusion requires temperatures of 100 million degrees to overcome electrostatic repulsion between nuclei, making it extraordinarily difficult to sustain. Fission has powered commercial reactors since 1956. Fusion remains a research challenge — though significant progress has been made, with the first net energy gain achieved at NIF in 2022.