Radioactive decay calculator

Radioactive decay is the spontaneous transformation of unstable atomic nuclei emitting particles (alpha, beta) or gamma radiation. For large ensembles it follows N(t) = N0 * (1/2)^(t/T½) statistically.

Half-life T½ is the time after which half of the original nuclei have transformed. It is isotope-specific: polonium-210 T½ = 138 days, uranium-238 T½ = 4.5 billion years.

Each nucleus has a constant probability of decay per unit time. For a large population this gives exponential decrease. After each T½ the count halves, regardless of how many remain.

Activity A = lambda * N(t), where lambda = ln2/T½ is the decay constant. Measured in becquerel (Bq): 1 Bq = 1 decay per second. The older unit curie (Ci) = 3.7 * 10^10 Bq.

By measuring activity over time and fitting an exponential curve. For very long-lived isotopes, atom counting by mass spectrometry is used: T½ = N * ln2 / A.

Radiometric dating (C-14 archaeology, U-Pb geology), nuclear medicine (short T½ isotopes for PET/SPECT), nuclear waste management and radiation therapy.

Yes. Enter time and T½ in the same units and the formula works unchanged. Example: T½ = 5730 years (C-14), t = 11 460 years gives N(t) = N0/4.

Alpha: helium nuclei (2p+2n) from heavy nuclides (uranium, radium). Beta: electrons or positrons from neutron/proton conversion (C-14). Gamma: high-energy photons accompanying alpha/beta transitions, no change in nuclear composition.

C-14 (T½ = 5730 years) is absorbed by living organisms. After death the C-14/C-12 ratio decreases. Measuring this ratio gives the age of organic samples (effective range: up to about 50 000 years).

The formula gives the statistical mean for a large ensemble. For small counts (below a few thousand) actual decay fluctuates randomly around the mean following Poisson statistics.