Question

Suppose that you are observing the Brownian motion of a spherical particle (radius 1 um) at room temperature (295 K). You collect a set of measurements on the 2-dimensional diffusion of these particles. You find that after a time t the particles have typically diffused a distance R from the origin, as follows: t/seconds 100 500 1000 2000 R/microns 10 22.4 31.6 44.8 Plot this data in such a way so as to obtain a linear plot, and estimate the diffusion constant of the spherical particle from your graph.

Answer 1

t (Time) in second	R (Distance from origin) in microns	R (Distance from origin) in meter	(R)^2 (m^2)
100	10	0.00001	1E-10
500	22.4	0.0000224	5.0176E-10
1000	31.6	0.0000316	9.9856E-10
2000	44.8	0.0000448	2.00704E-09

RA2 VS t graph 2.5E-09 2E-09 t (Time) (R)^2 (m^2) 100 1E-10 500 5.0176E-10 1000 9.9856E-10 2000 2.00704E-09 1.5E-09 R^2 in m^2 1E-09 slope = 1.00341E-12 5E-10 500 1000 1500 2000 2500 (t in second