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Calculate remaining quantity after radioactive decay or find elapsed time using the half-life formula.
Half-Life Formula:
N = N0 x (1/2)^(t / t_half)
Solving for time:
t = t_half x ln(N0 / N) / ln(2)
N0 = initial quantity, N = remaining, t = elapsed time, t_half = half-life period
Half-life is the time required for half of a radioactive substance to decay. After one half-life, 50% remains; after two half-lives, 25%; after three, 12.5%; and so on.
Carbon-14 has a half-life of about 5,730 years and is used in radiocarbon dating to estimate the age of organic materials up to about 50,000 years old.
Yes. Half-life is used in pharmacokinetics (drug elimination from the body), biology (enzyme activity), and finance (describing exponential decay processes).
After about 10 half-lives, less than 0.1% of the original substance remains. In practice, 7-10 half-lives is often considered effectively zero for most purposes.
The decay constant lambda = ln(2) / t_half. It represents the probability per unit time that an atom will decay. The decay formula can also be written as N = N0 x e^(-lambda x t).