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Half-life \(t_{1/2}\) is the time in which there is a 50% chance that a nucleus will decay. The number of nuclei \(N\) as a function of time is \[N = N_0e^{-\lambda t},\] where \(N_0\) is the number present at \(t = 0\), and \(\lambda\) is the decay constant, related to the half-life by \[\lambda = \dfrac{0.693}{t_{1/2}}.\]
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