Radioactive Decay

Radioactive decay: unstable nuclei spontaneously emit α, β, or γ radiation and transform into another nucleus.

α-decay: emits ⁴₂He nucleus. (A, Z) → (A−4, Z−2) + α. Common in heavy nuclei (Z ≥ 83).

β⁻-decay: a neutron converts to proton + electron + antineutrino. (A, Z) → (A, Z+1) + e⁻ + ν̄. Occurs in neutron-rich nuclei.

β⁺-decay (positron emission): proton → neutron + e⁺ + ν. Occurs in proton-rich nuclei.

γ-decay: nucleus de-excites by emitting a γ-ray photon (no change in A or Z) — analogous to atomic transitions.

Decay is RANDOM: any single nucleus may decay at any time. Only the STATISTICAL behaviour is predictable.

Decay law: dN/dt = −λN ⇒ N(t) = N₀ e^(−λt). λ = decay constant. τ = 1/λ = mean life.

Half-life T_½ = (ln 2)/λ — time for half the nuclei to decay.