= Radioactive decay constant
{title2=$\lambda$}
The <radioactive decay constant> $\lambda$ is the probability per unit time that one surviving <atomic nucleus> decays in the simple constant-rate model. It gives $d\overline N/dt=-\lambda\overline N$ and hence $\overline N(t)=N_0e^{-\lambda t}$ for the mean surviving population.
The <radioactive activity> is $\lambda\overline N$, the <mean lifetime> is $1/\lambda$, and the <half-life> is $\ln2/\lambda$. These are different quantities: a large sample can have high <radioactive activity> even when each <atomic nucleus> has a small decay rate. Counting successive time intervals tests the exponential model, but background, <detection efficiency> and daughter <radioactive activity> affect the observed counts. A constant decay constant describes stochastic individual events, not a scheduled time at which each <atomic nucleus> must decay.
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