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(t_1/2 = 14.3 days) source if it was originally purchased for 800 rupees?

Answer 1

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