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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 24000
t1=280 days, Activity A1=6000 dps
t2=140 days, Activity A2=3000 dps

Let, initial activity is A0.

Now, for the interval (0t1)
A1=A0eλt1

6000=A0 e280λ (i)

And, for the interval t1t2
A2=A1eλt2

3000=6000 e140λ (ii)

Dividing (i) by (ii), we get,

60003000=A0 e280 λ6000 e140 λ

2=A0 e140 λ6000 (iii)

From (ii), we can write,
e140 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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