Nuclear Fission

Nuclear fission is the process by which a heavy atomic nucleus — typically uranium-235 or plutonium-239 — absorbs a neutron and splits into two smaller nuclei (called fission fragments), releasing a tremendous amount of energy along with two or three additional neutrons. This energy release dwarfs anything possible in ordinary chemical reactions: a single fission event releases roughly 200 MeV of energy, compared to just a few eV from burning a molecule of fuel. To put that in perspective, 1 kilogram of uranium-235 undergoing complete fission releases as much energy as burning about 3 million kilograms of coal. The energy released in fission comes directly from Einstein's mass-energy equivalence, E = mc². When the nucleus splits, the combined mass of the products is measurably less than the original nucleus plus the neutron that triggered it. This 'missing' mass — called the mass defect — is converted entirely into kinetic energy of the fragments, gamma-ray photons, and neutrinos. Because c² ≈ 9 × 10¹⁶ m²/s², even a tiny mass difference translates into an enormous energy release. Fission is the physical principle behind both nuclear reactors and nuclear weapons. In a controlled chain reaction (as in a power plant), the extra neutrons released by each fission event are moderated and carefully managed so that, on average, exactly one neutron triggers the next fission — maintaining a steady, self-sustaining reaction. In an uncontrolled chain reaction (as in a nuclear bomb), the number of fissions doubles with each generation, releasing catastrophic energy in microseconds. Understanding fission is therefore central not only to modern physics but to energy policy, international security, and humanity's technological future.

Key takeaways
  • Neutron Capture
  • Nuclear Deformation and Splitting
  • Neutron Emission
  • Energy Distribution
  • The Chain Reaction and Criticality

Neutron Capture

A slow (thermal) neutron travelling at roughly 2200 m/s approaches a uranium-235 nucleus. The neutron is absorbed, forming a highly unstable compound nucleus, uranium-236 (²³⁶U), in an excited state. Slow neutrons are far more effective at inducing fission than fast ones because they spend more time near the nucleus — like a ball rolling slowly past a hole versus one thrown at high speed.

Nuclear Deformation and Splitting

The ²³⁶U nucleus vibrates violently. The liquid-drop model of the nucleus helps explain what happens next: the nucleus behaves somewhat like a droplet of water. If the excitation energy is large enough to overcome the surface tension-like nuclear binding force, the nucleus elongates, forms a neck, and splits into two unequal fission fragments — most commonly barium-141 (¹⁴¹Ba) and krypton-92 (⁹²Kr) — though many different fragment pairs are possible.

Neutron Emission

Along with the two main fragments, 2–3 prompt neutrons are ejected almost instantaneously (within ~10⁻¹⁴ s). These neutrons are fast (energies of ~1–2 MeV) and can go on to trigger further fission events in nearby uranium nuclei. This possibility of a self-sustaining chain reaction is what makes fission so powerful — and so dangerous if uncontrolled.

Energy Distribution

The ~200 MeV released per fission is distributed roughly as follows: ~168 MeV goes into kinetic energy of the fission fragments (which heats the reactor fuel), ~5 MeV into prompt gamma rays, ~5 MeV into fast neutrons, and ~12 MeV into beta particles, gamma rays, and antineutrinos from the subsequent radioactive decay of the fission fragments. In a reactor, almost all of this energy (except the neutrino share) is eventually converted to heat, which drives steam turbines to generate electricity.

The Chain Reaction and Criticality

The multiplication factor k is defined as the average number of neutrons from one fission that go on to cause another fission. If k < 1 (subcritical), the reaction dies out. If k = 1 (critical), the reaction is self-sustaining at a constant rate — exactly what a reactor aims for. If k > 1 (supercritical), the reaction grows exponentially. In a reactor, control rods made of neutron-absorbing materials (such as boron or hafnium) are inserted or withdrawn to keep k precisely at 1. A moderator (often water or graphite) slows fast neutrons to thermal speeds so they are more likely to cause further fission rather than being captured unproductively.

The Key Equation

92235U+01n→56141Ba+3692Kr+3 01n+Q{}^{235}_{92}\text{U} + {}^{1}_{0}\text{n} \rightarrow {}^{141}_{56}\text{Ba} + {}^{92}_{36}\text{Kr} + 3\,{}^{1}_{0}\text{n} + Q
  • {}^{235}_{92}\text{U} — Uranium-235 (none): The fissile target nucleus — 92 protons and 143 neutrons.
  • {}^{1}_{0}\text{n} — Neutron (none): The incoming (and outgoing) neutrons that sustain the chain reaction.
  • {}^{141}_{56}\text{Ba},\; {}^{92}_{36}\text{Kr} — Fission Fragments (none): The two daughter nuclei produced; their exact identity varies, but atomic numbers and mass numbers must each sum to those of ²³⁶U.
  • Q — Q-value (energy released) (MeV): Energy released, equal to the mass defect Δm multiplied by c². For this reaction Q ≈ 173 MeV (excluding neutrinos).

Worked Example

Problem. The total mass of the reactants in a particular uranium-235 fission event is 236.052591 u, and the total mass of all products (fragments + neutrons) is 235.837784 u. Calculate the energy released in this event in MeV. (Use 1 u = 931.5 MeV/c².)

Q=Δm⋅c2=0.2148 u×931.5 MeVu≈200 MeVQ = \Delta m \cdot c^2 = 0.2148\,\text{u} \times 931.5\,\frac{\text{MeV}}{\text{u}} \approx 200\,\text{MeV}

Answer. Approximately 200 MeV of energy is released in this fission event.

Figure
Diagram
Nuclear Fission Chain Reactionn²³⁵U+nunstable²³⁶U*excitedSPLIT¹⁴¹Bafragment⁹²Krfragmentnnn3 neutrons(chainreaction)Energy released Q ≈ 200 MeV(kinetic energy of fragments + gamma rays + neutron KE)
Origins · 1 minLise Meitner and how this was discovered
LM
Lise Meitner
1878–1968 · Austrian-Swedish

Lise Meitner, working with Otto Hahn and Fritz Strassmann, provided the theoretical explanation for nuclear fission in 1938–1939. After Hahn and Strassmann's chemical experiments in Berlin showed that barium was produced from uranium irradiated with neutrons, Meitner and her nephew Otto Frisch correctly interpreted the result as the uranium nucleus splitting in two — a process Frisch named 'fission' by analogy with biological cell division. Meitner used the liquid-drop model to calculate that the energy released would be ~200 MeV, in agreement with Einstein's E = mc². Her insight was foundational to all subsequent nuclear science. Despite being nominated for the Nobel Prize multiple times and having element 109 (meitnerium, Mt) named in her honour, Meitner never received the Nobel Prize — an omission widely regarded as one of the greatest oversights in Nobel history.

  • Nuclear Fusion — Fusion is the opposite process — light nuclei combining — yet both fission and fusion release energy because of nuclear binding energy and mass defect, making comparison essential for understanding nuclear energy.
  • Nuclear Binding Energy — The energy released in fission directly reflects the difference in binding energies between the heavy parent nucleus and the lighter fragments; understanding the binding energy curve explains why fission of heavy nuclei releases energy.
  • Mass-Energy Equivalence (E = mc²) — The Q-value of fission is calculated directly from the mass defect using E = mc²; this concept is the quantitative foundation of all nuclear energy calculations.
  • Radioactive Decay — Fission fragments are themselves highly radioactive and undergo beta and gamma decay; radioactive decay is therefore an immediate consequence of every fission event.