= Nuclear decay constant
{title2=$\lambda$}
In the constant-rate <mathematical model>, an undecayed <atomic nucleus> has conditional probability
$$
\Pr(T\le t+\Delta t\mid T>t)=1-e^{-\lambda\Delta t}
=\lambda\Delta t+O((\lambda\Delta t)^2)
$$
of decaying during the next positive interval $\Delta t$. The <nuclear decay constant> has units of inverse <time>. Its value describes a rate; it does not specify a scheduled death time for one <atomic nucleus>. The conditional probability is independent of the age $t$, the <memorylessness of the exponential distribution>.
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