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Question
The selling rate of a radioactive isotope is decided by its activity. What will be the second-hand rate of a one month old 32P(t1/2 = 14.3 days) source if it was originally purchased for 800 rupees?
Solution
Given:
Half-life of 32P source, `T_(1"/"2)`= 14.3 days
Time, t = 30 days = 1 month
Here, the selling rate of a radioactive isotope is decided by its activity.
∴ Selling rate = Activity of the radioactive isotope after 1 month
Initial activity, A0 = 800 disintegration/sec
Disintegration constant (`lambda`) is given by
`lambda = 0.693/T_(1"/"2) = 0.693/14.3 "days"^-1`
Activity (A) is given by
`A = A_0e^(-lambdat)`
Here, `lambda` = Disintegration constant
`therefore` Activity of the radioactive isotope after one month (selling rate of the radioactive isotope) (A) is given below .
`A = 800 xx e^(-0.693/14.3) xx 30`
= `800 xx 0.233669`
= 186.935 = Rs 187
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