Radioactive Decay Calculator
Calculate remaining radioactive substance using N = N₀ × (1/2)^(t/t½) from initial quantity and half-life.
Returns remaining mass and activity in becquerels.
Radioactive decay is the spontaneous process by which an unstable atomic nucleus loses energy by emitting radiation. The rate of decay follows a precise mathematical law.
The radioactive decay formula: N(t) = N₀ × e^(−λt)
Where:
- N(t) = number of atoms remaining at time t
- N₀ = initial number of atoms
- λ (lambda) = decay constant (unique to each isotope)
- t = elapsed time
- e = Euler’s number (≈ 2.71828)
Half-life formula: t½ = ln(2) ÷ λ ≈ 0.693 ÷ λ
This gives the half-life — the time required for exactly half the atoms to decay.
Remaining fraction after n half-lives: Remaining = (1/2)^n = N₀ ÷ 2^n
Worked example: Carbon-14 has a half-life of 5,730 years. A sample originally contained 100 g. After 3 half-lives (17,190 years): Remaining = 100 × (1/2)³ = 100 ÷ 8 = 12.5 g
Common isotope half-lives:
| Isotope | Half-Life | Use |
|---|---|---|
| Carbon-14 | 5,730 years | Archaeological dating |
| Uranium-238 | 4.47 billion years | Geological dating |
| Iodine-131 | 8 days | Medical treatment |
| Polonium-210 | 138 days | Industrial sources |
| Radon-222 | 3.8 days | Home radon concerns |
Activity: Activity (decays/second) = λ × N(t). Measured in Becquerels (Bq) — 1 Bq = 1 decay per second. 1 Curie = 3.7 × 10¹⁰ Bq.