A radionuclide having decay constant `lambda` is produced at a constant rate of `alpha` per sec. If `N_(0)` be the number of nucei at t = 0, then maximum number of nuclide possible are :

Options

A. `N_(0) + (alpha)/(beta)`
B. `N_(0) + (lambda)/(alpha)`
C. `(alpha)/(lambda)`
D. `N_(0)`

Answer

C

Explanation

Rate of formation of nuclide, `(dN)/(dt) = alpha - lambda` N (where `lambda` N is its rate of decay )
For maximum number, `(dN)/(dt) = 0 " " therefore alpha - lambda N = 0 or N = (alpha)/(lambda)`