Radioactive Decay & Half-Life Calculator
Calculate radioactive decay, remaining activity, and time elapsed using the half-life equation. Covers all decay modes with activity in becquerels.
Radioactive Decay Guide
The Decay Equations
N(t) = N₀ × e^(−λt). Where N₀ = initial number of nuclei, λ = decay constant (s⁻¹), t = time (s). Relationship between half-life and λ: T½ = ln2 / λ = 0.693 / λ. Activity: A = λN (in Becquerels, Bq). 1 Bq = 1 decay per second. A(t) = A₀ × e^(−λt) — activity falls at the same rate as the number of nuclei. After n half-lives: N = N₀ × (1/2)ⁿ. Example: C-14 (T½ = 5730 years). After 11,460 years (2 half-lives): N = N₀ × (1/2)² = N₀/4 = 25% remaining.
Carbon Dating
Radiocarbon dating uses C-14 to date organic material up to approximately 50,000 years old. C-14 is produced in the upper atmosphere by cosmic ray bombardment of N-14. Living organisms continually exchange carbon with the atmosphere — maintaining a constant C-14/C-12 ratio (approximately 1 in 10¹²). After death: no more C-14 intake. C-14 decays with T½ = 5,730 years. By measuring the C-14 activity relative to living organisms, the time since death can be calculated. Calibration curve (IntCal20):
Medical Applications
Technetium-99m (T½ = 6.01 hours): the most widely used medical radioisotope. Used in over 30 million diagnostic scans per year worldwide. Very short half-life means it decays rapidly, minimising patient radiation dose. Iodine-131 (T½ = 8.02 days): thyroid cancer treatment and hyperthyroidism diagnosis. The thyroid specifically absorbs iodine — so I-131 delivers targeted radiation to thyroid tissue. PET scanning: uses short-lived positron emitters (F-18, T½ = 110 minutes). Tracer in glucose analo
Nuclear Waste and Long-Term Storage
Half-life determines how long radioactive waste must be stored. Short-lived waste (T½ < 30 years): Cs-137 (30.17 yr), Sr-90 (28.8 yr). After 300 years (10 half-lives): activity reduced to less than 0.1% of original. Intermediate storage for decades. Long-lived waste: I-129 (T½ = 15.7 million years), Tc-99 (T½ = 211,000 years). Must be stored for geological timescales (>100,000 years). Deep geological disposal (DGD) is the internationally agreed solution — stable rock formations at 300-1000m dept
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