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Question
Obtain an expression for the half-lifetime of radioactive material. Hence state the relation between an average life and half lifetime of radioactive material.
Solution
Expression for half-life period (T1/2):
From the law of radioactive decay, N(t) = N0 e−λt
at t = T1/2, N(t) = `"N"_0/2`
∴ `"N"_0/2 = "N"_0 "e"^{-λ"T"(1"/"2)}`
∴ `e^{lambda"T"(1"/"2)}` = 2
∴ `lambda"T"_{1"/"2} = log_"e"2 = 0.693`
∴ `"T"_{1"/"2} = 0.693/lambda`
Relation between average life (τ) and a half lifetime of radioactive material:
`"T"_{1"/"2} = tau "In" 2 = 0.693 tau`
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