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  • A radioactive isotope has a half-life of T years. How long will it take the activity to reduce to a) 3.125%, b) 1% of its original value?

Q. 13.7  A radioactive isotope has a half-life of T years. How long will it take the activity to reduce to a) 3.125%, b)  1% of its original value?

Answers (1)

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(a) The activity is proportional to the number of radioactive isotopes present

The number of half years in which the number of radioactive isotopes reduces to x% of its original value is n.

n=log_{2}(\frac{100}{x})

In this case

 n=log_{2}(\frac{100}{3.125})=log_{2}32=5

It will take 5T years to reach 3.125% of the original activity.

(b) In this case

n=log_{2}(\frac{100}{1})=log_{2}100=6.64

It will take 6.64T years to reach 1% of the original activity.

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