Nuclear Half-Life Calculator

Radioactive decay is the process by which an unstable atomic nucleus loses energy by radiation. During this process, the nucleus transforms into a more stable configuration, emitting particles or electromagnetic radiation.

Half-life is the time required for exactly half of a radioactive substance to decay. It's a constant characteristic of each radioactive isotope and can range from fractions of a second to billions of years.

The decay constant (λ) is calculated using the formula λ = ln(2) / t₁/₂, where ln(2) ≈ 0.693 and t₁/₂ is the half-life. The decay constant represents the probability of decay per unit time.

Mean lifetime (τ) is the average time a nucleus will exist before decaying. It's related to half-life by τ = t₁/₂ / ln(2) ≈ 1.44 × t₁/₂. Mean lifetime is always longer than half-life.

Carbon-14 dating uses the known half-life of carbon-14 (5,730 years) to determine the age of organic materials. By measuring the remaining C-14 in a sample and applying decay formulas, scientists can calculate when the organism died.

Accuracy depends on precise measurements of initial and remaining quantities, accurate knowledge of the half-life constant, and ensuring no external contamination. Environmental factors generally don't affect nuclear decay rates.

Short half-lives indicate rapid energy release through radiation, creating higher radiation doses in shorter periods. Long half-lives release energy slowly over extended periods, resulting in lower immediate radiation exposure rates.