Radioactive Decay
Stochastic decay of atoms vs theoretical N(t) = N₀e^(−λt) with λ = ln2/T½.
Key Notes
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.
Formulas
Decay law (exponential)
N₀ = initial number; λ = decay constant (s⁻¹).
Decay rate (activity)
Units: becquerel (Bq) = 1 disintegration/s. Curie (Ci) = 3.7 × 10¹⁰ Bq.
Half-life
Time for half the nuclei to decay.
Mean life
Average lifetime of a nucleus before decaying.
Important Points
Radioactive decay is a NUCLEAR property — not affected by chemistry, temperature, or pressure.
α-particles are highly ionising but short range (~few cm in air; stopped by paper). β-particles penetrate further (~mm of aluminum). γ-rays are most penetrating.
Health hazard: α inside the body (inhaled/ingested) is dangerous; outside skin, paper stops it. γ from outside is the main external hazard.
Decay constants vary over many orders of magnitude: U-238 T₁/₂ ≈ 4.5 × 10⁹ years; carbon-14 ≈ 5730 years; iodine-131 ≈ 8 days.
Activity (Bq) does NOT equal mass — a tiny amount of short-lived isotope can have HUGE activity.
Common pitfall: confusing 'decay constant' (s⁻¹) with 'half-life' (s). They're related by ln 2.
Radioactive Decay notes from sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs, Physics Lab). Class 12 physics revision for JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT, and CUET-UG.