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A parent radioactive nucleus \mathrm{A} (decay constant \lambda_{\mathrm{a}} ) converts into a radio-active nucleus B of decay constant \lambda_b, Initially, number of atoms of B is zero. At any time N_a, N_b are number of atoms of nuclei A and B respectively then maximum value of \mathrm{N}_b is :

Option: 1

\frac{\lambda_a N_a}{\lambda_b}


Option: 2

\frac{\lambda_b N_a}{\lambda_a}


Option: 3

\frac{\left(\lambda_{\mathrm{a}}+\lambda_{\mathrm{b}}\right) \mathrm{N}_{\mathrm{a}}}{\lambda_{\mathrm{b}}}


Option: 4

\frac{\lambda_{\mathrm{b}}}{\left(\lambda_{\mathrm{a}}+\lambda_{\mathrm{b}}\right)} \mathrm{N}_{\mathrm{a}}


Answers (1)

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\mathrm{N}_{\mathrm{b}} reaches maximum when activity of \mathrm{A} will be equal to activity of \mathrm{B} . 

\text { i.e., } \lambda_{\mathrm{a}} \mathrm{N}_{\mathrm{a}}=\lambda_{\mathrm{b}} \mathrm{N}_{\mathrm{b}} \Rightarrow \mathrm{N}_{\mathrm{b}}=\frac{\lambda_{\mathrm{a}} \mathrm{N}_{\mathrm{a}}}{\lambda_{\mathrm{b}}}

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