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The activity of a sample of a radio-active material is A1 at time t1 and A2 at time t2 (where t2 > t1) if T its mean life is then

(A) A1t1 = A2t2 

(B) A2 = A1e[{t(1) – t(2)} / T]

(C) A1 – A2 = t2 – t1

(D) A2 = A1e(t1 / t2)T

1 Answer

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Best answer

The correct option is (B) A2 = A1e[{t(1) – t(2)} / T].

Explanation:

mean life time = T = (1 / λ) ......(1)

Activity after time t is A = A0e–λt where A0 = initial activity by given

condition,      A1 = A0e–λt(1)

A2 = A0e–λt(2)

 ∴ Taking ratio (A2 / A1) = eλt(2)+λt(1)

∴ A2 = A1e[t(1) –t(2)]λ

from (1) A2 = A1e[{t(1) –t(2)} / T].

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