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A radioactive element decay by $β$ emission. A detector records $n$ beta particles in 2 second and in next 2 seconds it records $0.75 n$ beta particles. Find mean life, correct to nearest whole number. (In sec) Given ln2 = 0.6931 and ln3 = 1.0986

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Detailed Solution

We know that $N = N_{0} e^{- λt}$ After 2 second $N_{1} = N_{0} e^{- λ \times 2}$ After (2+2) second, $N_{2} = N_{0} e^{- λ \times 4}$

According to given conditions, $N_{0} - N_{1} = n or N_{0} - N_{0} e^{- 2 λ} = n$ And $N_{0} e^{- 2 λ} - N_{0} e^{- 4 λ} = 0 .75 n$ ....... (ii)

After solving above equations, we get $λ = 0 .145 s$ Mean life $T = 1 / λ = 6 .9 s$

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