= Solution
Let $U(x)$ be the static potential and $\gamma$ the <drag coefficient>, so terminal <Genetic drift> under <force> $-U'$ is $v=-U'/\gamma$. The <Probability flux>[probability current] is $J=-DU'p/(k_BT)$ only after imposing the desired relation; instead start independently from $J=-Dp'-U'p/\gamma$. At <thermal equilibrium> $p\propto e^{-U/(k_BT)}$ and <detailed balance> requires $J=0$. Substitution yields
$$
\boxed{D=\frac{k_BT}{\gamma}=\frac{k_BT}{6\pi\eta a}.}
$$
At 298 K with $a=0.5\ \mu$m, this gives approximately $4.37\times10^{-13}$ m$^2$ s$^{-1}$. The <argument> assumes an overdamped particle in an <equilibrium> thermal bath, rather than arbitrary driven <diffusion>.
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