Nuclear Physics, Reactor Theory and Radiation Protection
Nuclear Physics, Reactor Theory and Radiation Protection tests the physics chain from a fission event to heat, the neutron balance that determines criticality, and the dose arguments that protect workers and the public.
Neutronics
- Fission of U-235 releases about 200 MeV; roughly 1.05 g of U-235 is consumed per MWd of thermal energy.
- k∞ = ε p f η; leakage is added through non-leakage probabilities, so k_eff = k∞ P_NL P_..., and criticality is k_eff = 1.
- Reactivity ρ = (k_eff − 1)/k_eff, in pcm or mk; β for U-235 is about 650 pcm, so prompt criticality needs ρ > β.
- Six delayed-neutron groups slow the power rise and make reactors controllable; the inhour equation converts reactivity to period.
- Feedback: the Doppler coefficient is prompt and negative in oxide fuel; moderator and void coefficients must be negative in the operating range of a power reactor.
- Xenon-135 has a huge absorption cross-section and builds after shutdown, delaying restart; samarium-149 is slower and effectively permanent.
Radiation protection
- Activity in becquerel, absorbed dose in gray, equivalent and effective dose in sievert with w_R and w_T.
- ICRP 103 limits: occupational 20 mSv/y averaged over 5 years with 50 mSv in any single year; public 1 mSv/y; lens 20 mSv/y; extremities 500 mSv/y.
- ALARA: time, distance (inverse square), shielding. Attenuation I = I0 e^(−μx), HVL = 0.693/μ, with a buildup factor for broad beams.
Worked example - shielding
A source gives 1.6 Sv/h at 1 m. At 4 m the inverse-square law gives 100 mSv/h. To reach 20 µSv/h needs a factor of 5000: n = ln(5000)/ln 2 = 12.3 half-value layers. With HVL = 1.2 cm of lead, the wall is about 14.7 cm, plus a buildup allowance.
Traps
- Confusing k_eff with k∞ and forgetting leakage.
- Reporting gray where the limit is stated in sievert.
- Applying the 1 mSv public limit to a classified radiation worker.
- Using the unshielded inverse-square result without a buildup correction in a broad-beam design.