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Question:

The half-life of a radioactive substance is 20 minutes. The approximate time interval (t2−t1) between the time t1 when 1/3 of it had decayed and t2 when 2/3 of it had decayed is:

7min

20min

14min

28min

Solution:

Using first order decay equation, Number of remaining nuclei N = N0e−λt
We get Δt = t2−t1 = (1/λ)loge(N1/N2)
Where N1 = (2/3)N0
N2 = (1/3)N0
Also λ = loge2/T1/2 = loge2/20
∴ t2−t1 = T1/2loge2/loge2 = 20 min