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A radioactive isotope has a half-life of...

A radioactive isotope has a half-life of 10 years. How long will it take for the activity to reduce to 3.125% ?

Text Solution

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Activity ,`A=lambdaN`
Given , A=3.125% of `A_0=(3.125A_0)/100=A_0/32`
or , `A/A_0 = (1/2)^5`
`therefore N/N_0 =(1/2)^5`
So the activity will reduce to 3.125% after 5 half-lives. Hence required time = 5 x 10 =50 years .
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