Einstein\'s estimate of Brownian motion and Avogadro\'s number. Einstein assumed

Question

Einstein's estimate of Brownian motion and Avogadro's number. Einstein assumed that a particle of radius 5 times 10^minus5 cm could be observed to undergo Brownian motion under a microscope (Investigations on the Theory of Brownian Movement. Dover Publications, New York, 1956). He computed the squareroot-mean-square distance lsaquox^2rsaquo^1/2 that the particle would move in one minute in a one-dimensional walk in water, eta asymp1 cP at about T = 300 K. Compute lsaquox^2rsaquo^1/2. Show how the argument can be turned around to give Avogadro's number.

Explanation / Answer

a.

D=KT/f =diffusion coefficient D

D=KT/6*n*r=1.38*10^-23*300/6*0.001*5*10^-5 =4.39*10^-15 m2/s

< x2 >=6Dt= 6*4.39*10^-15*60=1.580*10^-12 m2

ROOT < x2 >=1.2572*10^-6 m

b.

< x2 >=6Dt=6KT*t/6*n*r =KT*t/*n*r but K=R/Na

< x2 >=RT*t/*n*r*Na

Na = RT*t/*n*r*< x2 >

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