Decay Law

N(t) = N₀ e^(−λt) λ = decay constant = ln2/t½ A = activity = λN (Bq) 1 Ci = 3.7×10¹⁰ Bq

Half-life Formulas

N = N₀(½)^n (n = # half-lives) N = N₀ e^(−0.693t/t½) t = (t½/ln2) × ln(N₀/N) For % remaining: (t½ × log(N/N₀))/log(½)

Carbon Dating

C-14: t½ = 5730 y Atmospheric ¹⁴C constant in living organisms Death → ¹⁴C/¹²C decreases t = −8267 ln(A/A₀) years Usable range: ~100–50,000 years

Binding Energy

BE = (Zmp + Nmn − M)c² Peak at Fe-56 (~8.8 MeV/A) Fusion (H→He): gain BE Fission (U→smaller): gain BE Mass defect: Δm = BE/c²

Radioactive Series

Uranium series: U-238 → Pb-206 Thorium series: Th-232 → Pb-208 Actinium series: U-235 → Pb-207 Neptunium series: Np-237 → Bi-209 (Artificial — no natural Np)

Geiger-Nuttall Law

log(λ) = A − B/√E Higher α energy → shorter t½ Po-212: t½ = 0.3 μs, E = 8.78 MeV Th-232: t½ = 14 Gy, E = 4.08 MeV