A `""^(32)P` radio nuclide with half life T = 14.3 days is produced in a reactor at a constant rate `q = 2.7 xx10^(9)` nuclei per second. How soon after the beginning of production of that nuclide will its activity be equal to `A = 1.0xx10^(9)` dis/s ?

Explanation

According to the problem, the radio nuclide is being produced at a constant rate as well as it decays with rate nuclide is given by `-(dN)/(dt) =lamdaN`. Hence net rate of accumulation of radio nuclide is given by
`(dN)/(dt) = q-lamdaN.......(1)`
(or) `int_(0)^(N) (dN)/(-lamdaN)= int_(0)^(t)dt " (or) " t=(T_(1//2))/(ln2)ln(1-(lamdaN)/q)`
On substituting numerical values we get t = 9.5 days