$.$ In the kinetic study of the inversion of cane sugar according to the below equation, the rotation angle is measured:

$C_{12}{H}_{22}{O}_{11}{?}_{\text{s}\text{u}\text{c}\text{r}\text{o}\text{s}\text{e}}{H}_3{O}^{+}{C}_6{H}_{12}{O}_6{?}_{glucose}+C_6{H}_{12}{O}_6{?}_{\text{f}\text{r}\text{u}\text{c}\text{t}\text{o}\text{s}\text{e}}$

using the reported data and the first$-$order equation of the optically active materials, what will be the rate constant in $s^{-1}?$

Note: The modified first$-$order equation of the optically active materials is given by:

$ln(\frac{{}_0-{}_{}}{{}_t-{}_{}})=kt$

A$)0\mathrm{.}23s^{-1}$

B$)0\mathrm{.}03s^{-1}$

C$)0\mathrm{.}167s^{-1}$

D$)2\mathrm{.}77{10}^{-3}{s}^{-1}$

E$)1\mathrm{.}67{10}^{-3}{s}^{-1}$