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Question

An activity of a radioactive sample decreases to (1/3)rd of its original value in 3 days. Then, in 9 days its activity will become:

A
(1/27) of the original value
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B
(1/9) of the original value
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C
(1/18) of the original value
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D
(1/3) of the original value
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Solution

The correct option is D (1/27) of the original value
RR0=eλt
Activity of a radioactive sample decreases to one third of its original value in 3 days.
13=eλ×3=e3λ ....... (1)
Let activity in 9 days be R′. Then
RR0=eλ×9
RR0=eλ×3×3
RR0=(e3λ)3
Substitute equation (1) in the above equation.
RR0=(13)3
RR0=127
R=R027
Then, in 9 days its activity will become (1/27)th of the original value.

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