In the certain hypothetical radioactive decay process, species a decays into species B and species B decays into species C according to the reactions.  $A\to 2B+particles+energy;$ $B\to 3C +particles+energy.$
The decay constant for the species A is  ${\lambda }_1=1s^{-1}$  and that for the species B is  ${\lambda }_2=100s^{-1}$. Initially ${10}^4$ moles of species A are taken and species B reaches its maximum number at a time $t_0=2\ln \left(10\right)s.$ Then value of the maximum number of moles of B is $(e^{2303} = 10)$