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Half-Life Nuclear & Particle Physics Seconds, Hours, or Years The time required for half the radioactive nuclei in a given sample to undergo spontaneous radioactive decay. t_½ = ln(2) / λ ≈ 0.693 / λ, N(t) = N₀ (½)^(t / t_½) Radiocarbon Dating Nuclear & Particle Physics Years Before Present (BP) A radiometric dating method that measures the residual decay activity of Carbon-14 in organic materials to determine their age up to ~50,000 years. t = -(t_½ / ln 2) ln(A(t) / A₀), t_½ = 5730 years Beta Decay Nuclear & Particle Physics MeV (Continuous Spectrum) A radioactive decay process mediated by the weak nuclear force in which a nucleus emits a beta particle (electron or positron) and a neutrino. β⁻: n → p + e⁻ + ν̄_e; β⁺: p → n + e⁺ + ν_e Decay Constant Nuclear & Particle Physics s⁻¹ or years⁻¹ The probability per unit time that an individual radioactive nucleus will undergo spontaneous nuclear decay. λ = -(1 / N) (dN / dt) = ln(2) / t_½ Radioactive Tracer Nuclear & Particle Physics MBq or mCi (Administered Activity) A chemical compound containing a radioisotope used to trace chemical or biological pathways through living organisms or industrial systems. A(t) = A₀ e^(-λ t) (Short half-life diagnostic radiopharmaceutical) Radon Gas Migration Geophysics & Environmental Physics Bq/m³ or pCi/L (Activity Concentration) The environmental migration of radioactive Radon-222 gas from decaying uranium in rocks and soil into indoor building spaces. Decay Chain: ²³⁸U → ²²⁶Ra → ²²²Rn (Half-life = 3.82 days)