Nuclear Energy: Fission, Reactors & Safety

Low-carbon firm power from the atom. Learn nuclear binding energy and fission, chain reactions, criticality and the multiplication factor, moderators and coolants, reactor types (PWR, BWR, PHWR, fast breeders, SMRs), fuel, enrichment and burnup, energy density, India's three-stage programme and thorium, decay heat and safety (defence in depth, passive safety), radiation protection, waste management and fusion basics — with Python for fission energy and fuel consumption.

Nuclear power produces about 10% of the world's electricity with very low lifecycle CO₂ and high capacity factors (~90%). A single kilogram of U-235 fission releases as much energy as thousands of tonnes of coal.

Nuclear engineering balances this extraordinary energy density with rigorous safety, radiation protection and long-term waste management. India operates PHWRs, is building fast breeders and plans to use its large thorium reserves.

An analogy

A reactor is like a carefully managed campfire where each burning log (fissioning nucleus) must light exactly one more: fewer and the fire dies (subcritical), more and it flares up (supercritical). Control rods and moderators keep it exactly steady.

Fission and chain reactions

A neutron splits U-235 (or Pu-239, U-233) into two fission products, releasing ~200 MeV and 2–3 new neutrons. Slowed ('moderated') neutrons are more likely to cause further fissions. Control rods (boron, cadmium, hafnium) absorb neutrons to keep k_eff = 1. Delayed neutrons (≈ 0.65% for U-235) make reactors controllable.

Reactor types

Main designs:

• PWR — light water moderator/coolant at ~155 bar, steam generators (most common worldwide)
• BWR — water boils in the core, direct steam cycle
• PHWR (CANDU, Indian 220/700 MWe) — heavy water, natural uranium, on-power refuelling
• Fast breeder (PFBR Kalpakkam) — sodium-cooled, breeds Pu from U-238
• SMRs and advanced reactors — factory-built, passive safety (molten salt, high-temperature gas)

Safety

Defence in depth: fuel pellet, cladding, pressure boundary, containment, emergency planning. Reactors must shut down, cool the fuel (decay heat starts at ~6–7% of full power and persists for days — the lesson of Fukushima) and confine radioactivity. Passive systems use gravity and natural circulation. Negative temperature/void coefficients provide inherent stability.

Fuel cycle, waste and fusion

Front end: mining, conversion, enrichment (3–5% U-235 for LWRs), fabrication. Back end: spent-fuel pools, dry casks, reprocessing (India's closed cycle), and deep geological disposal of high-level waste. India's three-stage programme: PHWRs → fast breeders → thorium (U-233) reactors. Fusion (ITER, tokamaks, stellarators, inertial confinement) promises abundant fuel but remains experimental.

Formulas

• Mass–energy: E = Δm·c²
• Energy per kg U-235: ≈ 200 MeV × N_A/0.235 ≈ 8.2 × 10¹³ J ≈ 1 MWd/g
• Criticality: k_eff = 1 critical, < 1 subcritical, > 1 supercritical
• Fuel use: mass = thermal energy / burnup
• Decay heat (Way–Wigner): P/P₀ ≈ 0.066·t^(−0.2) (t in s after shutdown)
• Radioactive decay: N = N₀·e^(−λt), t½ = ln2/λ

Worked example: Energy per gram

Given: 1 g U-235 fissioned

Find: Energy.

• 8.2e13 J/kg × 0.001

Answer: 8.2e10 J ≈ 0.95 MWd

Worked example: Decay heat

Given: 3000 MWth reactor, 1 hour after shutdown

Find: Decay heat.

• 0.066 × 3600^(−0.2) = 1.29%

Answer: ≈ 39 MW — pumps must keep running

Worked example: Reactivity

Given: k_eff = 1.002

Find: ρ.

• 0.002/1.002

Answer: ≈ 200 pcm (below β ≈ 650 pcm, controllable)

Fission energy and annual fuel needs of a 1000 MWe reactor

# Nuclear energy: fission energy density and fuel use of a 1000 MWe PWR
MeV = 1.602e-13          # J
E_fission = 200 * MeV
N_A = 6.022e23
E_per_kg_U235 = E_fission * N_A / 0.235      # J per kg U-235 fissioned
print(f"energy per kg U-235 fissioned: {E_per_kg_U235/3.6e9:.2e} MWh ({E_per_kg_U235/3.6e12:.0f} GWh)")
coal_J_per_kg = 20e6
print(f"= {E_per_kg_U235/coal_J_per_kg/1000:.0f} tonnes of coal")
P_e, eta, CF = 1000e6, 0.33, 0.9
thermal_J = P_e / eta * CF * 365 * 24 * 3600
print(f"U-235 fissioned per year: {thermal_J/E_per_kg_U235:.0f} kg")
# Burnup: 45 GWd/tU -> fuel loaded per year
burnup = 45e3 * 24 * 3600 * 1e6      # J per tonne (MWd/t -> J/t)
print(f"enriched fuel needed per year at 45 GWd/t: {thermal_J/burnup:.0f} t")
# energy per kg U-235 fissioned: 2.28e+04 MWh (23 GWh)
# = 4105 tonnes of coal
# U-235 fissioned per year: 1048 kg
# enriched fuel needed per year at 45 GWd/t: 22 t

About one tonne of U-235 fissions per year in a 1000 MWe plant, loaded as ~22 tonnes of low-enriched fuel — versus ~3 million tonnes of coal for the same output. Spent fuel is small in volume but highly radioactive, requiring cooling, shielding and long-term management.

Common mistakes

• Wrong: Thinking shutdown ends heat generation. — Right: Decay heat requires cooling for days.
• Wrong: Confusing radiation dose units. — Right: Gray = absorbed dose; Sievert = effective dose.
• Wrong: Comparing waste by mass only. — Right: Consider radiotoxicity, heat and half-lives.

Applications

• Base-load electricity: Firm low-carbon supply.
• Industrial heat & hydrogen: High-temperature reactors.
• Medical isotopes: Research reactors (Mo-99, Co-60).
• Naval propulsion: Submarines and carriers.

Key takeaways

• Fission: ~200 MeV, ~1 MWd per gram.
• Control k_eff = 1 with rods and moderators.
• Decay heat demands continuous cooling.
• India: PHWR → FBR → thorium.

Going further

• Neutron transport: Diffusion theory and Monte Carlo (MCNP, OpenMC).
• Thorium fuel cycle: U-233 breeding in India's stage 3.
• Fusion engineering: Tritium breeding blankets and plasma confinement.