In a radioactive reactor, radionuclide X are being injected at a rate of r atoms/sec which decay to a stable daughter nuclide Y according to equation.
`Xoverset(lambda)toY+DeltaE`
The energy released in each decay process is transformed to electricity and used to light up a bulb. If the process starts at t = 0 then :(At t = 0 The number of radionuclide X = 0)

Options

A. Brightness of bulb increases with time in the beginning and then becomes constatnt
B. ) Brightness of bulb decreases with time in the beginning and then becomes constatnt
C. Brightness first increases then decreases later
D. Brightness first decreases then increases later

Explanation

The rate of accumulation of nuclei of X in the reactor can be given as
`(dN_(X))/(dt)=r-lambdaN_(x)`
`implies N_(x)=r/(lambda)(1-e^(-lambdat))`
Thus amount of `N_(X)` continuously increases with time hence brightness of bulb will continuously increases.