Radioactive Decay Series & Activity Calculator
Calculate radioactive activity, number of atoms remaining, and mass of a sample after any elapsed time. Compare different decay modes and find equilibrium activities.
Radioactive Decay Guide
Decay Equations
N = N₀ × e^(−λt) = N₀ × (½)^(t/t½). Where N = atoms remaining, N₀ = initial atoms, λ = decay constant = ln2/t½, t = elapsed time, t½ = half-life. Activity A = λN (decays per second, measured in becquerels, Bq). 1 Bq = 1 decay per second. 1 Curie (Ci) = 3.7×10¹⁰ Bq (defined as the activity of 1g of radium-226). After 1 half-life: 50% remains. After 2: 25%. After 10: 0.098% — essentially negligible for practical purposes. After 20 half-lives: less than 1 part per million.
Carbon-14 Dating
Living organisms exchange carbon with the atmosphere (via food/photosynthesis), maintaining a constant ratio of ¹⁴C to ¹²C (approximately 1.2×10⁻¹² by mass). At death, ¹⁴C stops being replenished and decays (t½ = 5,730 years). Measuring the current ¹⁴C/¹²C ratio allows calculation of time since death. Range: up to approximately 50,000 years (beyond that, too little ¹⁴C remains). Calibration: atmospheric ¹⁴C has varied over time — calibration curves (dendrochronology etc.) convert raw radiocarbon
Medical Isotopes
Technetium-99m (6-hour half-life): most widely used medical isotope. Gamma emitter — photons detected by gamma camera for organ imaging. Short half-life minimises patient dose. Used for: bone scans, heart perfusion, kidney and thyroid imaging. Iodine-131 (8-day half-life): concentrates in thyroid tissue — used to treat hyperthyroidism and thyroid cancer. Beta and gamma emitter. Iodine-123 (13-hour half-life): gamma only — used for thyroid imaging (lower dose than I-131). Fluorine-18 (110-minute
Radiation Types and Penetration
Alpha (α) particles: helium-4 nuclei (+2 charge). Range in air: ~5cm. Stopped by paper or skin. High ionising power — very damaging if ingested or inhaled (radon gas in homes). External alpha source: essentially harmless. Beta (β) particles: high-energy electrons or positrons. Range: up to ~3m in air. Stopped by a few mm of aluminium. Moderate ionising power. Gamma (γ) rays: electromagnetic radiation (photons). Very penetrating — requires cm of lead or metres of concrete to attenuate significant
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