An unstable element is produced in nuclear reaction at a constant rate `R`. Its disintergration constant is `lambda`. Find number of nuclei after time `'t'` if initialy it was Zero

Options

A. `(R )/(lambda)e^(-lambda t)`
B. `(R )/(lambda)(1-e^(-lambdat))`
C. `(R )/(lambda)(1+e^(lambdat))`
D. None of these

Answer

B

Explanation

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