Fission, fusion and radiation dose

Burning 1 kg of methane releases 5.55 × 10⁷ J; fissioning all of 1 kg of uranium-235 releases 8.2 × 10¹³ J — about one and a half million times as much. The difference goes back to the binding-energy curve of the first lesson: a chemical reaction rearranges a few outer electrons, a few electronvolts per atom; a nuclear reaction rearranges the nucleus itself, about 1 MeV per nucleon. And where does the energy come from? From mass: the products are lighter than the reactants, and the missing mass has become energy through $E = mc^2$.

When ²³⁵U absorbs a slow neutron it becomes an excited ²³⁶U, which stretches like a squeezed droplet and snaps into two medium-sized fragments, releasing about 2.4 neutrons on average. If more than one of those neutrons, on average, triggers another fission, the reaction sustains itself — a chain reaction.

• In a small lump of uranium most neutrons escape through the surface and the reaction dies out; above the critical mass each generation has more fissions than the last. The critical mass depends on shape, density, enrichment and whether a neutron reflector surrounds the fuel.
• Only 0.72 % of natural uranium is fissile ²³⁵U; the rest is ²³⁸U, which does not fission with slow neutrons. Power-reactor fuel is enriched to 3–5 % ²³⁵U, a moderator (water or graphite) slows the neutrons down, and neutron-absorbing control rods hold the number of neutrons per generation at exactly one.
• Fission fragments are neutron-rich and intensely radioactive, which is why spent fuel is hard to deal with; ²³⁸U that captures a neutron becomes, via ²³⁹U and ²³⁹Np, fissile ²³⁹Pu.

Fusing light nuclei climbs the binding-energy curve: $\ce{^{2}_{1}H} + \ce{^{3}_{1}H} \mathrel{\ce{->}} \ce{^{4}_{2}He} + \ce{^{1}_{0}n}$ releases 17.6 MeV. The difficulty is that both nuclei are positively charged; to come close enough for the strong force to act they must overcome their Coulomb repulsion, so a fusion plasma needs temperatures above a hundred million kelvin — and must be confined long enough. The Sun’s core is only about 15 million kelvin; with its enormous mass and quantum tunnelling, the proton–proton chain slowly turns four ¹H into one ⁴He, releasing 26.7 MeV net. The Sun loses about 4.3 million tonnes of mass every second this way.

Three units answer three different questions:

• Becquerel (Bq): how active a source is — one decay per second. It says nothing about who the radiation reaches.
• Gray (Gy): absorbed dose — 1 J of energy absorbed per kilogram of matter.
• Sievert (Sv): equivalent and effective dose — the absorbed dose multiplied by a radiation weighting factor $w_R$ (1 for γ and β, 20 for α, 2.5–21 for neutrons depending on energy) and then weighted by how sensitive each organ is, so that different exposures can be compared.

Medicine is the largest artificial source of radiation dose. ⁹⁹ᵐTc (half-life 6.0 hours) emits γ rays of about 140 keV, just right for a γ camera; it is made continuously from ⁹⁹Mo (66 hours) in a hospital “technetium generator”, where the ⁹⁹ᵐTc activity peaks again about 23 hours after each elution — so the generator is milked once a day. The PET isotope ¹⁸F is made in a cyclotron by the ¹⁸O(p,n)¹⁸F reaction; with a half-life of only 110 minutes it must be delivered and used within hours.