  The Stokes-Einstein (SE) relation has been widely applied to quantitatively
describe the Brownian motion. Notwithstanding, here we show that even for a
simple fluid, the SE relation may not be completely applicable. Namely,
although the SE relation could be a good approximation for a large enough
Brownian particle, we find that it induces significant error for a smaller
Brownian particle, and the error increases with the decrease of the Brownian
particle's size, till the SE relation fails completely when the size of
Brownian particle is comparable with that of a fluid molecule. The cause is
rooted in the fact that the kinetic and the hydrodynamic effects depend on the
size of the Brownian particle differently. By excluding the kinetic
contribution to the diffusion coefficient, we propose a revised Stokes-Einstein
relation and show that it expands significantly the applicable range.
