A 1-micrometre oil droplet (r = 0.5 x 10^-6 m) in water (viscosity eta = 10^-3 Pa s) at 300 K shows Brownian motion. (a) Compute its diffusion coefficient. (b) Estimate its rms displacement in 10 s along one axis. Solution: (a) D = kT/(6 pi eta r) = (1.38x10^-23 x 300)/(6 x 3.1416 x 10^-3 x 0.5x10^-6) = 4.14x10^-21/9.42x10^-9 = 4.4 x 10^-13 m^2/s. (b) <x^2> = 2Dt = 2 x 4.4x10^-13 x 10 = 8.8 x 10^-12 m^2, so x_rms = 3.0 x 10^-6 m = 3 micrometres - visible under a microscope, as Brown saw.