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A radioactive substance X decays into another radioactive substance Y. Initially only X was present. $λ_{x}$ and $λ_{y}$ are the disintegration constants of X and Y. $N_{x}$ amd $N_{y}$ are the number of nuclei of X and Y at any time t. Number of nuclei $N_{y}$ will be maximum when

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$\frac{N_{y}}{N_{x} - N_{y}} = \frac{λ_{y}}{λ_{x} - λ_{y}}$

$\frac{N_{x}}{N_{x} - N_{y}} = \frac{λ_{x}}{λ_{x} - λ_{y}}$

$λ_{y} N_{y} = λ_{x} N_{x}$

$λ_{y} N_{x} = λ_{x} N_{y}$

answer is C.

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Detailed Solution

At radioactive equilibrium,

$\frac{d N_{A}}{d t} = \frac{d N_{B}}{d t} \Rightarrow λ_{X} N_{Y} = λ_{X} N_{Y}$

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