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Question
The decay constant of a radioactive sample is λ. The half-life and the average-life of the sample are respectively
Options
1/λ and (In 2/λ)
(In 2/λ) and 1/λ
λ(In 2) and 1/λ
λ/(In 2) and 1/λ.
Solution
(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_"1/2")`
⇒ `t_"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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