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The Stokes–Einstein relation gives the translational diffusion coefficientat $T=298\mathrm{K}$. For isotropic three-dimensional Brownian motion, the mean squared displacement is $⟨|\Delta \mathbf{r}{|}^2⟩=6Dt$. Thus after one hour the root mean square displacement isThe phrase “on average” needs a convention: the mean displacement vector is zero; the mean displacement magnitude of three-dimensional Brownian motion is $⟨|\Delta \mathbf{r}|⟩=4\sqrt{Dt/\pi }=1.22\mathrm{mm}$, obtained by integrating the three-dimensional Gaussian distribution. These are displacements, not the total microscopic path length. The estimate assumes dilute unconfined water, a spherical hydrodynamic radius and constant temperature.