= Potassium-argon dating
{title2=$t=\lambda^{-1}\ln[1+N_{\mathrm{Ar}}/(bN_{\mathrm K})]$}
{wiki=Potassium–argon_dating}
With no initial radiogenic <argon-40> and complete daughter retention, the surviving <potassium-40> population is $N_K=N_{K,0}e^{-\lambda t}$ and the accumulated daughter population is $N_{\mathrm{Ar}}=b(N_{K,0}-N_K)$. Here $\lambda$ is the total <nuclear decay constant> and $b$ is the argon-producing <branching fraction>. Their ratio gives the displayed age. The result measures closure of the mineral's isotope system under those assumptions.
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