The activity of a radioactive sample is $9750 \mathrm{counts} {\min }^{-1}$ at $t=0$ and $975 \mathrm{counts} {\min }^{-1}$ at $t=5 \min$. The decay constant is approximately $({\log }_{e}10=2.3)$

Two radioactive materials, $A_1$ and $A_2$, have decay constants of $10{\lambda }_0$ and ${\lambda }_0$, respectively. If initially they have the same number of nuclei, the ratio of number of their undecayed nuclei will be $\left(\frac{1}{e}\right)$ after a time