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Question:

A radioactive nucleus is being produced at a constant rate α per second. Its decay constant is λ. If N₀ is the number of nuclei at t=0, then the maximum number of nuclei possible are:

N₀ + α/λ

N₀

λ/α + N₀

α/λ

Solution:

The rate of production of the nuclei is
dN/dt = α − λN
When the number of nuclei are maximum, i.e., N is maximum, dN/dt = 0
⇒ α − λNmax = 0
⇒ Nmax = α/λ