Nuclear Fission: Splitting the Atom

Nuclear fission is the process of splitting a heavy atomic nucleus into two lighter nuclei, releasing enormous energy. When a slow neutron is absorbed by a uranium-235 nucleus, it becomes unstable U-236, which splits into two "daughter" nuclei (e.g., barium-141 and krypton-92), 2–3 additional neutrons, and about 200 MeV of energy.

The key equation for our example:

$^{1}_{0}\text{n} + ^{235}_{92}\text{U} \to ^{141}_{56}\text{Ba} + ^{92}_{36}\text{Kr} + 3\,^{1}_{0}\text{n} + 200\text{ MeV}$

Where the energy comes from

The binding energy per nucleon is higher for medium-mass nuclei (~8.5 MeV for Ba, Kr) than for heavy nuclei (~7.6 MeV for U-235). When you split uranium into barium and krypton, the total binding energy increases — and that extra binding energy is released as kinetic energy of the fragments, gamma radiation, and kinetic energy of the neutrons.

$200$ MeV per fission seems small, but per kilogram: 1 kg of U-235 contains $\sim 2.56 \times 10^{24}$ atoms. Total energy: $\sim 8.2 \times 10^{13}$ J = 82 TJ ≈ 20 kilotons of TNT.

Chain reaction

The 2–3 neutrons released can each trigger another fission event. If each fission releases on average $k$ neutrons that cause further fissions (the multiplication factor):

• $k < 1$ (subcritical): reaction dies out
• $k = 1$ (critical): sustained, controlled reaction — nuclear reactor
• $k > 1$ (supercritical): exponentially growing reaction — nuclear weapon

Critical mass is the minimum mass of fissile material needed for $k \geq 1$. For U-235, it's about 52 kg as a bare sphere (less with a neutron reflector).

Applications

• Nuclear reactors: Controlled fission at $k = 1$. Control rods (boron, cadmium) absorb excess neutrons. Heat boils water → steam → turbine → electricity. ~450 reactors worldwide provide ~10% of global electricity.
• Nuclear weapons: Uncontrolled fission at $k \gg 1$. Two designs: gun-type (Hiroshima) and implosion (Nagasaki).
• Medical isotopes: Fission reactors produce Mo-99 (for Tc-99m, the most-used medical imaging isotope).

Common mistakes

• Thinking fission "destroys" matter. It doesn't — it rearranges nucleons. The mass of products is slightly less than reactants; the "missing" mass is the energy ($E = \Delta m \cdot c^{2}$).
• Confusing fission with radioactive decay. Decay is spontaneous; fission is induced by a neutron (though spontaneous fission exists for very heavy elements).

Try it in the visualization

Watch the neutron approach and be absorbed by the U-235 nucleus. The nucleus wobbles, elongates, and splits into two fragments that fly apart. The released neutrons shoot outward. Toggle "chain reaction" to see the exponential branching — each fission triggers more. Adjust the control rod slider to see the difference between subcritical, critical, and supercritical regimes.