A radiaocatice isotope is being produced at a constant rate `X`. Half-life of the radioactive substance is `Y`. After some time, the number of radioactive nuceli become constant. The value of this constant is .

Options

A. `(X)/(Y)`
B. `XY`
C. `XY ln (2)`
D. `(XY)/(ln(2))`

Answer

D

Explanation

Rate of production, `(dN)/(dt)=lambdaN=X`
Now, N will becomes constant, when
`N=(X)/(lambda)="costant"`
But `lambda=(ln(2))/(T_(1//2))=(ln(2))/(Y) therefore N=(X)/(ln(2)//Y)=(XY)/(ln(2))`