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Question

# After 280 days, the activity of a radioactive sample is 6000 dps. The activity reduces to 3000 dps after another 140 days. The initial activity of the sample (in dps) is,

A
6000
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B
9000
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C
3000
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D
24000
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Solution

## The correct option is D 24000t1=280 days, Activity A1=6000 dps t2=140 days, Activity A2=3000 dps Let, initial activity is A0. Now, for the interval (0→t1) A1=A0e−λt1 6000=A0 e−280λ −(i) And, for the interval t1→t2 A2=A1e−λt2 3000=6000 e−140λ −(ii) Dividing (i) by (ii), we get, 60003000=A0 e−280 λ6000 e−140 λ 2=A0 e−140 λ6000 −(iii) From (ii), we can write, e−140 λ=30006000=12 Putting this value in (iii), we get, 2=A06000×12 ∴A0=24,000 dps Hence, (D) is the correct answer.

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