The diffusion coefficient of some spherical nanoparticles $($radius $=6nm)$ in a liquid solution is measured to be $3\mathrm{.}5*{10}^{-9}\frac{m^2}{s}$ at $22C$ with a nanoparticle concentration of $1\mathrm{.}00*{10}^{-1}M($trial $1).$ The experiment is repeated at $50C$ with a nanoparticle concentration of $1\mathrm{.}00*{10}^{-1}M($trial $2).$ The solvent viscosities are measured to be $1\mathrm{.}2$ Pa$.$s $($trial $1)$ and $3\mathrm{.}4$ Pa$.$s $($trial $2)$ using a rheometer. What value would you expect the diffusion coefficient to have in trial $2?$

A$.$ less than $1\mathrm{.}0*{10}^{-9}\frac{m^2}{s}$

D$.$ between $3\mathrm{.}0*{10}^{-9}\frac{m^2}{s}$ and $4\mathrm{.}0*{10}^{-9}\frac{m^2}{s}$

B$.$ between $1\mathrm{.}0*{10}^{-9}\frac{m^2}{s}$ and $2\mathrm{.}0*{10}^{-9}\frac{m^2}{s}$

E$.$ between $4\mathrm{.}0*{10}^{-9}\frac{m^2}{s}$ and $5\mathrm{.}0*{10}^{-9}\frac{m^2}{s}$

C$.$ between $2\mathrm{.}0*{10}^{-9}\frac{m^2}{s}$ and $3\mathrm{.}0*{10}^{-9}\frac{m^2}{s}$

$D=\frac{**T}{6****r_A**{}_B}$

Where,

${}_B$ is the solvent viscosity $($Pa$*$s$)$

$$ is the Boltzmann constant $(J*K^{-1})$

$r_A$ is the solute particle radius $($m$)$

$T$ is absolute temperature $($K$)$