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Question

Two radioactive samples A and B have half lives T1 and T2 (T1>T2) respectively. At t=0, the activity of B was twice the activity of A. Their activity will become equal after a time-

A
T1T22
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B
T1+T22
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C
T1T2T1+T2
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D
T1T2T1T2
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Solution

The correct option is D T1T2T1T2
Given, 2RA=RB

2λ1N1=λ2N2 .......(1)

Radio activity of sample A and B becomes equal after some time t.

λ1N1eλ1t=λ2N2eλ2t ......(2)

Dividing (1) by (2) we get,

2eλ1t=eλ2t

2=e(λ2λ1)t

Taking log on both sides we get,

ln2=(λ2λ1)t

ln2=λT

0.693=0.693[1T21T1]t

t=T1T2T1T2

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, (D) is the correct answer.

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