Half-Life Calculator — Radioactive Decay Formula
Calculate remaining amount, decayed amount, or time elapsed using the radioactive decay formula N = N₀ × (½)^(t/t½). Enter initial amount, half-life, and time to get full decay analysis.
Common isotopes:
—
Remaining Amount
—
Decayed Amount
—
% Remaining
—
Number of Half-Lives
Step-by-Step Solution
Radioactive Decay Formula
- N = N₀ × (½)^(t/t½) — Amount remaining after time t
- λ = ln(2) / t½ ≈ 0.693 / t½ — Decay constant
- N = N₀ × e^(-λt) — Equivalent exponential form
- t = t½ × log₂(N₀/N) — Time to reach amount N
Frequently Asked Questions
What is radioactive decay?
Radioactive decay is the spontaneous process by which an unstable atomic nucleus loses energy by emitting radiation. The rate of decay is proportional to the amount of radioactive substance present, leading to exponential decay over time.
What is half-life?
Half-life (t½) is the time it takes for exactly half of a radioactive substance to decay. After one half-life, 50% remains. After two half-lives, 25% remains. After ten half-lives, about 0.1% remains. Half-life is constant for each radioactive isotope.
What is the half-life formula?
The decay formula is N = N₀ × (½)^(t/t½), where N is the remaining amount, N₀ is the initial amount, t is elapsed time, and t½ is the half-life. Equivalently: N = N₀ × e^(-λt) where λ = ln(2)/t½ is the decay constant.
What are some common half-lives?
Carbon-14: 5,730 years (used in radiocarbon dating). Uranium-238: 4.47 billion years. Iodine-131: 8.02 days (medical use). Polonium-210: 138 days. Radon-222: 3.82 days. Strontium-90: 28.8 years.
How is half-life used in carbon dating?
Carbon-14 (half-life 5,730 years) is absorbed by living organisms in a constant ratio with stable C-12. After death, C-14 decays without replenishment. By measuring the C-14/C-12 ratio and comparing to the original, scientists can calculate how long ago the organism died.