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Question

A radioactive sample is undergoing α decay. At any time t1, its activity is A and at another time t2, the activity is A/5. What is the average lifetime for the sample?


A

(t2t1)/ln5

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B

ln(t2+t1)/2

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C

(t1t2)/ln5

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D

ln5/(t2t1)

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Solution

The correct option is A

(t2t1)/ln5


Step 1: Given data

Decay =α decay

Activity at time t1 =A

Activity at time t2 =A/5

Initial activity=A0

Step 2: Find average life

Let Average life =1λ

For activity of radioactive sample,

A=A0e-λt1(1)A/5=A0e-λt2(2)

On dividing (1) by (2), we get

5=e-λ(t1-t2)ln(5)=(t2-t1)λλ=ln(5)/t2t1

Average life =1λ=(t2-t1)/ln(5)

Hence, option A is correct.


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