A radioactive substance with decay constant of `0.5s^(-1)` is being produced at a constant rate of 50 nuclei per second . If there are no nuclei present initially, the time (in second) after which 25 nuclei will be present is :

Options

A. 1
B. ln 2
C. ln(4/3)
D. 2 ln (4/3)

Answer

D

Explanation

`(dN)/(dt)=50-(N)/(0.5)`
`underset(0)overset(N)int (dN)/(50-2N)=underset(0)overset(t)int dt`
`rArr N= (100(1-e^(-t//2)))`
N=25
`rArr t=2ln ((4)/(3))`