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A parent radioactive nucleus A (decay constant λ_a) converts into a radio-active nucleus B of decay constant λ_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 N_b is.

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$\frac{{{\lambda _b}{N_a}}}{{{\lambda _a}}}\$

$\frac{{({\lambda _a} + {\lambda _b}){N_a}}}{{{\lambda _b}}}\$

$\frac{{{\lambda _a}{N_a}}}{{{\lambda _b}}}\$

$\frac{{{\lambda _b}}}{{({\lambda _a} + {\lambda _b})}}{N_a}\$

answer is A.

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Detailed Solution

N_b reaches maximum when activity of A will be equal to activity of B.

$i.e.,{\lambda _a}{N_a} = {\lambda _b}{N_b} \Rightarrow \,\,\,{N_b} = \frac{{{\lambda _a}{N_a}}}{{{\lambda _b}}}\$

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