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In the certain hypothetical radioactive decay process, species a decays into species B and species B decays into species C according to the reactions. $A \to 2 B + p a r t i c l e s + e n e r g y;$ $B \to 3 C + p a r t i c l e s + e n e r g y .$
The decay constant for the species A is $λ_{1} = 1 s^{- 1}$ and that for the species B is $λ_{2} = 100 s^{- 1}$ . Initially $10^{4}$ moles of species A are taken and species B reaches its maximum number at a time $t_{0} = 2 \ln (10) s .$ Then value of the maximum number of moles of B is $(e^{2303} = 10)$

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Detailed Solution

$\frac{d B}{d t} = 2 (- \frac{d A}{d t}) - λ_{2} B$

when maximum $\frac{d B}{d t} = 0$

$\begin{array}{l} ∴ B = \frac{2}{λ_{2}} \times 10^{4} {λ_{1 e}}^{- λ t} \\ = 2 \end{array}$

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