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Physics Question on Nuclei

A radioactive nucleus is being produced at a constant rate α\alpha per second. Its decay constant is λ\lambda. If N0N_0 are the number of nuclei at time t = 0, then the maximum number of nuclei possible are

A

N0+αλN_{0}+\frac{\alpha}{\lambda}

B

N0N_0

C

λα+N0\frac{\lambda}{\alpha}+N_{0}

D

αλ\frac{\alpha }{\lambda }

Answer

αλ\frac{\alpha }{\lambda }

Explanation

Solution

Maximum number of nuclei will be present, when rate of decay = rate of formation λ,N=α,N=αλ\lambda, N=\alpha, N=\frac{\alpha}{\lambda}