Calculation of Radioactive Disintegration Constant

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We have, T= 30 days
(a) The radioactive disintegration constant λ = 0.693/T = 0.0231 per day (Ans)

(b) Average life Ta = 1/λ = 1/0.0231 = 43.29 Days (Ans)

(c) Number of atoms disintegrated ¾ N0 and the number of atoms left behind = ¼ N0
N = N0 Exp (-λt)
N/ N0 = Exp (-λt)

But in this case, N/ N0 = ¼
Or Exp (-λt) = ¼ λt = loge (4) = 2.3026 log10 (4)

Substituting the value of λ,
t = 2.3026 x 0.6021 / 0.0231 = 60 days (Ans)

(d) In this case, N/ N0 = 1/8

N/ N0 = Exp (-λt)

Or, t = 2.3026 x log10 (8) / 0.0231
= 90 days (Ans)

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