Nuclear Physics

Nuclear structure

A nucleus is described by Z (proton number), N (neutron number), and A = Z+N (mass number). Notation: ^A_ZX. Isotopes share Z but differ in N (¹²C and ¹⁴C). Nuclear radius R = R₀A^1/3, with R₀ ≈ 1.2 fm. Nuclear density is essentially constant at ~2.3×10¹⁷ kg/m³, independent of A — a hallmark of the strong force's short range and saturation.

Mass defect and binding energy

The actual nuclear mass is less than the sum of constituent nucleons; the deficit Δm is the mass defect. Binding energy BE = Δm·c² = Δm(amu)·931.5 MeV. Binding energy per nucleon peaks around ⁵⁶Fe at about 8.8 MeV/nucleon — this is why both fission of heavy nuclei and fusion of light ones release energy. The ⁴He nucleus has BE/A ≈ 7.07 MeV (especially stable due to closed-shell structure).

Radioactive decay

Three modes: alpha (α = ⁴₂He, A decreases by 4, Z by 2), beta-minus (β⁻: neutron → proton + e⁻ + ν̄, Z increases by 1), and gamma (γ: photon, no change in A or Z). Decay law N(t) = N₀e^−λt; half-life t_½ = ln 2/λ ≈ 0.693/λ. After n half-lives, fraction remaining = (½)ⁿ. Activity A = λN, in becquerels (1 Bq = 1 decay/s) or curies (1 Ci = 3.7×10¹⁰ Bq). Carbon-14 dating uses t_½ = 5730 years; ¹³¹I (medical) has t_½ = 8 days.

Fission and fusion

Fission: ²³⁵U + n → ¹⁴¹Ba + ⁹²Kr + 3n + ~200 MeV. The chain reaction sustains itself if at least one neutron causes another fission (criticality). Reactor moderators (graphite, heavy water) slow neutrons to thermal energies for higher fission cross-section. Fusion: ²H + ³H → ⁴He + n + 17.6 MeV, the basis of stars and H-bombs. The Sun fuses ~6×10¹¹ kg of hydrogen per second.

Detection and biological effects

Geiger-Müller counter detects ionising radiation via avalanche multiplication; scintillators and semiconductor detectors offer better energy resolution. Absorbed dose: gray (1 Gy = 1 J/kg). Equivalent dose multiplies by quality factor Q (alpha Q ≈ 20, beta/gamma Q ≈ 1) to give sieverts. Deterministic effects appear above thresholds; stochastic (cancer) increase linearly with dose. References: HRW Chapters 42-43, Serway Modern Physics Chapters 29-31, FSc Chapter 21.