A radionuclide is produced at constant rate `'q'` having half life `T`. Find time after which activity of nuclei will be `A`, if initially number of nuclei were zero.

Options

A. `(TA)/(q ln(2))`
B. `(T)/(ln(2))ln(A)/(q)`
C. `(T)/(ln(2))ln(1-(A)/(q))`
D. None of these

Answer

C

Explanation

`(dN)/(dt)=R- lambda N rArr (dN)/(R-lambda N)=dt`, solving this equation with initial conditions, we get the desired answer