Nuclear Reactor Physics
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Direct answer
One slow neutron splits a U-235 nucleus into two fragments, about 200 MeV of energy and on average two to three fresh neutrons — and whether those neutrons each trigger further fissions decides everything. The multiplication factor k (neutrons in one generation over the previous) classifies the system: k < 1 subcritical and dying, k = 1 critical and self-sustaining (the reactor's operating condition), k > 1 supercritical and escalating (the bomb's condition). A reactor tames the chain with four components: a moderator (heavy water, graphite, ordinary water) to slow neutrons to thermal speeds where U-235 fission is most probable; control rods (boron carbide, cadmium) that swallow neutrons to hold k at 1; a coolant to carry heat away; and shielding. Delayed neutrons — a small fraction emitted seconds after fission by the decaying fragments — are what make control mechanically possible at all.
What you must remember
- Energy scale: each U-235 fission releases about 200 MeV (≈ 3.2 × 10⁻¹¹ J), split roughly 80-10-10 between fragment kinetic energy, prompt neutrons and gamma, plus later beta decay of fragments.
- Multiplication factor: k = 1 critical for steady power, k > 1 supercritical (weapons, reactor startup), k < 1 subcritical; control rods trim k by absorbing neutrons.
- Thermal neutrons: slowed to about 0.025 eV (speed near 2200 m/s) at room temperature, where the U-235 fission cross-section is large; moderation works because light nuclei soak up momentum in elastic collisions.
- Moderators: heavy water D2O, graphite, light water; heavy water is prized because it absorbs almost no neutrons, which is why Indian PHWRs can run on natural uranium with its 0.7 per cent U-235 content.
- Control rods and coolant: boron carbide and cadium for neutron absorption; pressurised heavy water carries the heat in PHWRs, light water in LWRs — light-water reactors need uranium enriched to about 3-5 per cent.
- Delayed neutrons: about 0.6 per cent arrive seconds late from fragment decay, stretching response time from milliseconds to seconds.
- Breeding: fast reactors convert fertile U-238 into fissile Pu-239, and Th-232 into fissile U-233 — creating fuel while burning it.
How a PHWR tames the chain
Do the energy arithmetic first, because JEE asks it. One kilogram of U-235 contains 1000/235 × 6.02 × 10²³ ≈ 2.56 × 10²⁴ nuclei; at 3.2 × 10⁻¹¹ J each, full fission yields 8.2 × 10¹³ J — equal to burning roughly 2,700 tonnes of coal, the ratio every textbook quotes.
Now the control physics. Fresh fission neutrons are fast, around 2 MeV, and at that energy U-238 gobbles many of them non-fissilely; slow them to 0.025 eV through moderator collisions and they fission U-235 with high probability. The Indian PHWR design exploits heavy water's low absorption: natural uranium works, no enrichment plant needed. Operators hold k at 1 by partial rod insertion — pull slightly and power rises, push in and it falls — feasible because delayed neutrons stretch the chain's millisecond timescale to seconds, something rods and humans can follow. The breeder logic completes the arc: a U-238 blanket breeds Pu-239, stage two of the Bhabha plan; stage three repeats it with India's vast thorium reserves into U-233.
Reactor physics in JEE
The moderator-versus-control-rod confusion is the most reliable one-mark loser: moderators slow neutrons, control rods absorb them, and swapping the two functions in a statement is exactly how assertion-reason items are built. Second, numbers are asked straight: 200 MeV per fission, 0.025 eV thermal neutron energy, 0.7 per cent natural enrichment; the 200 MeV-to-joule-to-kWh conversion is a standard numerical. Third, the Indian framing: the three-stage programme (natural-uranium PHWRs, plutonium fast breeders, thorium into U-233) is a national-policy fact Indian question-writers enjoy, and it attaches neatly to the fertile-versus-fissile distinction. Fourth, fission fragments are neutron-rich and beta-active — the origin of reactor waste's radioactivity and of the delayed neutrons. Advanced couples reactor physics with binding-energy curves: fission of heavy nuclei and fusion of light nuclei both roll nuclei downhill toward iron's peak binding energy per nucleon.
Frequently asked questions
What does the multiplication factor k mean in a reactor?
The ratio of neutrons in one generation to those in the previous one: k = 1 sustains steady power, k > 1 grows the chain, and k < 1 lets it die out; control rods hold k at unity.
Why does a reactor need a moderator?
Fast fission neutrons are likely to be captured by U-238 without fission; a moderator slows them to thermal energies where U-235 fissions readily, using light nuclei that carry away momentum in elastic collisions.
What is the difference between fissile and fertile nuclei?
Fissile nuclei like U-235 and Pu-239 fission with thermal neutrons directly; fertile nuclei like U-238 and Th-232 convert into fissile ones (Pu-239, U-233) after neutron capture.
Why are delayed neutrons essential for reactor control?
They stretch the neutron generation time from milliseconds to seconds, letting mechanical control rods respond; a chain sustained only by prompt neutrons would outrun any machinery.
How much energy comes from one kilogram of fully fissioned U-235?
About 8 × 10¹³ J — the energy of a few thousand tonnes of coal — from 200 MeV per fission across roughly 2.5 × 10²⁴ nuclei.