How Nuclear Fission Generates Energy: The Physics Inside a Reactor

The Energy Inside the Nucleus

A single kilogram of uranium-235, when fully fissioned, releases approximately 82 terajoules of energy — equivalent to burning 3,000 metric tons of coal. This extraordinary energy density is why 440 nuclear reactors generate about 10% of global electricity while occupying a fraction of the land and consuming a fraction of the fuel that fossil plants require. The source of this energy is not chemical but nuclear: the conversion of mass into energy according to Einstein's mass-energy equivalence, E = mc², where the speed of light squared makes even tiny mass differences produce enormous energy releases.

Nuclear fission was discovered in December 1938 when German chemists Otto Hahn and Fritz Strassmann, working with physicist Lise Meitner's theoretical framework, bombarded uranium with neutrons and found barium among the products — proof that the uranium nucleus had split. Meitner and her nephew Otto Frisch provided the physical explanation and coined the term fission, borrowed from cell biology. Within seven years, the process had been developed into both weapons and the first commercial power reactors.

The Physics of Fission

Atomic nuclei are held together by the strong nuclear force, which overcomes electrostatic repulsion between protons at very short ranges. Heavy nuclei like uranium-235 (92 protons, 143 neutrons) are in a metastable state — they contain more binding energy per nucleon in total, but their large proton count creates significant internal instability.

When a uranium-235 nucleus absorbs a slow (thermal) neutron, the combined uranium-236 nucleus enters an excited state that rapidly deforms and splits — typically into two medium-mass fission fragments, two to three free neutrons, and several gamma ray photons. A typical fission reaction might produce barium-141 and krypton-92:

²³⁵U + ¹n → ²³⁶U* → ¹⁴¹Ba + ⁹²Kr + 3¹n + energy (200 MeV)

The 200 megaelectronvolts per fission event may sound modest, but consider scale: one gram of U-235 contains approximately 2.56 × 10²¹ atoms. Fissioning all of them releases approximately 82 terajoules. The energy emerges as kinetic energy of the fission fragments (hitting surrounding matter and producing heat), kinetic energy of neutrons (moderated to heat), gamma radiation (absorbed as heat), and beta particles and neutrinos from subsequent radioactive decay of fission fragments.

The Chain Reaction

The key to sustained power generation is the chain reaction. Each fission event releases 2–3 neutrons on average. If at least one of these neutrons causes another fission event, the chain sustains itself. If fewer than one does, it dies out. If more than one does, it grows exponentially.

The multiplication factor k (or k-effective, k_eff) quantifies this. k_eff = 1 is criticality — the self-sustaining chain reaction required for steady power production. k_eff < 1 is subcritical (chain dies). k_eff > 1 is supercritical (power level rises). A nuclear weapon achieves very rapid supercriticality (prompt criticality) where the chain multiplies in microseconds without waiting for delayed neutrons. A reactor operates in a controlled region where prompt neutrons alone would not sustain criticality — it depends on delayed neutrons emitted by fission fragments over seconds to minutes. This ~0.65% delayed neutron fraction gives operators time to adjust control systems.

Reactor Core Design: Fuel, Moderator, Coolant

Natural uranium is 99.3% uranium-238, which doesn't fission easily, and only 0.7% uranium-235, which does. Most commercial reactors use uranium enriched to 3–5% U-235. The fuel is formed into ceramic pellets of uranium dioxide (UO₂), stacked inside metal tubes (fuel rods) typically made of zirconium alloy (Zircaloy), which has low neutron absorption and high corrosion resistance.

Fast neutrons released by fission are too energetic to efficiently cause further fissions in U-235 — they need to be slowed to thermal energies (~0.025 eV). A moderator material slows neutrons through elastic collisions. The most effective moderators have nuclei close to neutron mass (so more energy transfers per collision) and absorb few neutrons.

In a PWR, the reactor operates at ~155 atmospheres pressure to keep water liquid at ~325°C. This hot pressurized water flows through a steam generator, heating a secondary water loop that flashes to steam and drives turbines. The separation of radioactive primary coolant from the steam turbines simplifies maintenance. BWRs allow the coolant to boil directly in the reactor vessel, producing steam that drives turbines — a simpler design but one that makes the turbines mildly radioactive.

Control Systems

Reactor power is controlled by inserting or withdrawing control rods made of neutron-absorbing materials — typically boron carbide (B₄C), hafnium, or cadmium. Inserting control rods absorbs more neutrons, reducing k_eff and lowering power; withdrawing them raises k_eff. In a fully scrammed (emergency shutdown) reactor, all control rods insert fully, dropping k_eff well below 1 and halting the chain reaction within seconds.

• After shutdown, the reactor still produces decay heat from fission product radioactive decay — initially about 7% of operating power, falling to ~1% after an hour and ~0.1% after a day. Decay heat requires continuous cooling even after shutdown; the 2011 Fukushima Daiichi accident occurred because the tsunami disabled the cooling systems needed to remove decay heat from three shutdown reactors.
• PWRs have an important intrinsic safety feature: negative temperature coefficient of reactivity. As fuel temperature rises, Doppler broadening of uranium-238 absorption resonances captures more neutrons, automatically reducing the chain reaction. This self-correcting behavior means PWRs tend to moderate themselves without operator action.

From Fission Heat to Electric Grid

The thermal efficiency of nuclear plants — typically 33–37% — is similar to coal plants, because both ultimately run steam turbines. A 1,000 MW(e) nuclear plant therefore produces roughly 3,000 MW of thermal power. The chain: fission heats coolant → coolant produces steam → steam spins turbine → turbine drives generator → electricity goes to grid. The heat not converted to electricity is rejected to cooling towers or a river or ocean.

Waste and the Long-Term Challenge

The fission fragments produced in a reactor are highly radioactive, decaying over timescales from seconds to millions of years. High-level waste includes spent fuel assemblies and, in reprocessing programs, concentrated liquid waste. Spent fuel consists predominantly of:

• ~95% residual uranium (mostly U-238)
• ~1% plutonium (some isotopes are fissile, usable as fuel)
• ~4% fission products, including short-lived highly radioactive isotopes and long-lived actinides

After 40–50 years of wet storage in cooling pools (to remove decay heat), spent fuel can be transferred to dry cask storage — inert gas-filled steel and concrete containers that require no active cooling. All nuclear fuel ever used in the US would, if consolidated, fill a two-meter-deep area roughly the size of a football field. The challenge is not volume but toxicity: isotopes like iodine-129 (half-life 15.7 million years) require geological isolation. Finland's Onkalo repository, being excavated in stable granite 400 meters underground, is the world's first permanent high-level nuclear waste repository and is expected to receive waste by the mid-2020s.