Question

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

Answer 1

Concentration of A after time t=$A_0{e}^{-{\lambda }_{1}t}$

Thus after time $t_0$, concentration of A=${10}^4\left(\frac{1}{100}\right)=100moles$

Rate of formation of B=${\lambda }_1{C}_A-{\lambda }_2\frac{C_B}{2}=0$ when species reaches its maximum number.

Thus $C_A=50C_B$ at that moment.

Thus $C_B=2moles$