The decay constant of a radioactive sample is λ. The half-life and the average-life of the sample are respectively

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(ln 2/λ) and 1/λ The half-life of a radioactive sample (t_(1"/"2)) is defined as the time elapsed before half the active nuclei decays. Let the initial number of the active nuclei present in the sample be N_0 . `N_0/2 = N_0e^(-lambdat_"$\frac{1}{2}$") $\Rightarrow$ t_"$\frac{1}{2}$" = ("In 2")/lambda` Average life of the nuclei, t_(av) = S/N_0 = 1/lambda Here, S is the sum of all the lives of all the N nuclei that were active at t = 0 and lambda is the decay constant of the sample.

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