Nuclear Physics and Reactor Theory
Core concepts
A candidate must be fluent in binding energy per nucleon and the mass defect, the four-factor formula and the six-factor formula (k-effective with fast fission, resonance escape, thermal utilization, reproduction factor, and leakage terms), and the distinction between delayed and prompt neutrons. Know the delayed neutron fraction (β ≈ 0.0065 for U-235), prompt neutron lifetime, and reactor period relationships including the inhour equation concept. Understand reactivity in dollars and pcm, subcritical multiplication (1/(1−k)), and the role of temperature coefficients (Doppler, moderator, void).
Common traps
Watch for confusion between k-effective and reactivity (ρ = (k−1)/k), between the prompt critical threshold (ρ = β) and delayed critical, and between the signs of coefficients. Questions often swap "moderator temperature coefficient" with "fuel temperature coefficient" or test whether a negative void coefficient is always desirable. Another trap: mixing thermal vs fast cross-section behavior, or treating delayed neutrons as negligible when they are the basis of controllability. Also beware of asking for "binding energy released" in fission vs fusion - both release energy, but only up to iron-56.
Worked example / rule of thumb
Rule of thumb: one dollar of reactivity equals β. If k = 1.005 and β = 0.0065, then ρ = (1.005−1)/1.005 ≈ 0.00498, or about 0.77 dollars - sub-prompt-critical and controllable. If someone claims 1.5 dollars is safe, that is prompt supercritical and must be rejected.
Study tip
Practice converting between k, ρ, dollars, and pcm (1 dollar = 100 cents; 1 pcm = 10⁻⁵). Draw the neutron life cycle and label each factor; many exam items are just one factor moved around.