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

To solve the problem step by step, we need to analyze the situation involving the radioactive decay of radionuclide X and its effect on the brightness of the bulb.

### Step 1: Understand the Decay Process
The radionuclide X decays into a stable daughter nuclide Y, releasing energy (ΔE) in the process. The decay follows the equation:
\[ X \overset{\lambda}{\rightarrow} Y + \Delta E \]
where λ is the decay constant.

### Step 2: Initial Conditions
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