A radioactive nuclide is produced at the constant rate of n per second. It decays into a stable nucleus with decay constant λ. If N0 is a number of nuclei at t=0, then expected number N of nuclei in existence after t seconds is given by
A
N=nλ+N0e−λt
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B
N=N0e−λt
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C
N=nλ+(N0+nλ)e−λt
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D
N=nλ+(N0−nλ)e−λt
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Solution
The correct option is DN=nλ+(N0−nλ)e−λt The population is increasing by n and simultaneously decreasing by λN.
∴dNdt=n−λN
Integrating the above equation within proper limit,