In a certain hypothetical radioactive decay process, species $$A$$ decays into species $$B$$ and species $$B$$ decays into species $$C$$ according to the reactions :
$$\eqalign{ & A \to 2B + {\text{particles}} + {\text{energy}} \cr & B \to 3C + {\text{particles}} + {\text{energy}} \cr} $$
The decay constant for species is $${\lambda _1} = 1\,{\sec ^{ - 1}}$$   and that for the species $$B$$ is $${\lambda _2} = 100\,{\sec ^{ - 1}}.$$    Initially $${10^4}$$ moles of species of $$A$$ were present while there was none of $$B$$ and $$C.$$ It was found that species $$B$$ reaches its maximum number at a time $${t_0} = 2\,\ln \left( {10} \right)\sec .$$    Calculate the value of maximum number of moles of $$B.$$