Nuclear Fission

The fission reaction

Typical U-235 fission:

²³⁵U + n → ²³⁶U* → ¹⁴¹Ba + ⁹²Kr + 3n + ~200 MeV

Various other product pairs possible. Energy distributed:

• ~167 MeV — kinetic energy of fragments.
• ~5 MeV — kinetic energy of prompt neutrons.
• ~7 MeV — prompt gamma rays.
• ~6 MeV — beta decays of fragments.
• ~7 MeV — gamma decays of fragments.
• ~10 MeV — neutrinos (escape).
• Total recoverable: ~190 MeV per fission.

Chain reactions

Multiplication factor k	State	Description
k < 1	Subcritical	Reactions die out
k = 1	Critical	Steady chain reaction (reactor)
k > 1	Supercritical	Exponentially growing reactions (bomb)
k = 1.0001	Slightly super	Reactor power slowly increases
k = 1.05	Prompt-critical	Reactor uncontrollable; only delayed neutrons preventable

Reactor designs

Type	Coolant/Moderator	Fuel
Pressurized water (PWR)	Light water (both)	3-5% enriched U
Boiling water (BWR)	Light water (both, boiling in core)	3-5% enriched U
CANDU (Canadian)	Heavy water (both)	Natural uranium (no enrichment)
Graphite-moderated (e.g., Chernobyl RBMK)	Graphite (mod) + water (cool)	Slightly enriched U
Fast breeder	Liquid sodium	Pu-239; converts U-238 to more Pu

JavaScript — fission calculations

// Energy from 1 kg U-235 (complete fission)
function fissionEnergy_perKg(efficiency = 1) {
  // ~200 MeV per fission, ~6.022e23 atoms per mole, U-235 mass = 235 g/mol
  // Per kg: (1000 g / 235 g/mol) × 6.022e23 atoms/mol × 200 MeV
  const fissions_per_kg = (1000 / 235) * 6.022e23;
  const energy_eV = fissions_per_kg * 200e6;
  const energy_J = energy_eV * 1.602e-19;
  return energy_J * efficiency;
}

console.log(`1 kg U-235 fully fissioned: ${(fissionEnergy_perKg() / 1e13).toFixed(2)} × 10¹³ J`);
console.log(`Equivalent in TNT: ${(fissionEnergy_perKg() / 4.184e9 / 1000).toFixed(0)} kt TNT`);
// ~19 kt TNT — Hiroshima bomb yield (with ~1% efficiency)

// Power from a reactor
function reactorPower(fissions_per_second) {
  // Energy per fission ~200 MeV = 3.2e-11 J
  return fissions_per_second * 3.2e-11;
}

// Typical 1 GW reactor needs ~3.1 × 10¹⁹ fissions/s
console.log(`1 GW reactor fissions: ${(1e9 / 3.2e-11).toExponential(2)} per sec`);

// Critical mass scaling (very simplified)
function criticalMass(density_g_cm3, neutron_age_cm2 = 50) {
  // Highly approximate; depends on geometry, reflectors, etc.
  // For bare U-235 sphere: ~52 kg; with reflector ~15 kg
  return 'Depends on geometry, density, isotope, reflector';
}

// Half-life and uranium decay
function naturalUraniumComposition() {
  return {
    'U-238': '99.27%, half-life 4.5 Gyr',
    'U-235': '0.72%, half-life 700 Myr',
    'U-234': '0.005%, half-life 245 kyr'
  };
}
console.log(naturalUraniumComposition());

// Reactor enrichment requirement
function fuelEnrichment(reactor_type) {
  const enrichments = {
    'PWR': '3-5%',
    'BWR': '3-5%',
    'CANDU': '0.7% (natural)',
    'RBMK': '~2-3%',
    'Naval reactor': '~95%',
    'Weapons': '~90%+'
  };
  return enrichments[reactor_type];
}

// Fuel rod: how much U-235 in a 1 kg fuel rod (3.5% enriched)?
const u235_in_rod = 1000 * 0.035;  // 35 g
const usable_fissions = u235_in_rod / 235 * 6.022e23 * 0.6;  // ~60% burnup
console.log(`3.5% rod usable fissions: ${usable_fissions.toExponential(2)}`);
console.log(`Energy: ${(usable_fissions * 3.2e-11 / 3.6e6).toFixed(0)} kWh`);

Where fission matters

• Nuclear power. ~10% of world electricity from fission reactors. Low-carbon, high-density.
• Naval propulsion. Submarines, aircraft carriers run on small fission reactors (decades between refuelings).
• Medical isotopes. Tc-99m, Mo-99 produced by fission for medical imaging.
• Weapons. Atomic bombs use uncontrolled fission of highly enriched U-235 or Pu-239.
• Spacecraft. RTGs use isotope decay heat (related, not chain reaction); some advanced concepts use small reactors.
• Research reactors. Neutron sources for materials science, nuclear physics.
• Industrial. Radioisotope production for tracers, sterilization, detectors.

Common mistakes

• Confusing fission and fusion. Fission — heavy nuclei split. Fusion — light nuclei combine. Both release energy due to binding-energy curve.
• Believing reactors can explode like bombs. They can't. Reactor U is too low-enriched. Worst case: meltdown (severe but not nuclear explosion).
• Treating all radioactive products equally. Different isotopes have different half-lives, energies, biological effects. Some quickly safe; some dangerous for centuries.
• Forgetting moderator role. Most reactors need slow neutrons (thermal). Without moderator, U-235 chain doesn't sustain.
• Confusing critical with detonation mass. Critical for steady chain. Bomb needs supercritical assembly (much more material, fast assembly).
• Mixing power and energy. Reactor at 1 GW thermal output produces ~340 MW electric (efficiency ~33%). Power vs total energy generated over time differ.