11-17 Diffusion can be regarded as a random walk problem in which the successive

Question

11-17 Diffusion can be regarded as a random walk problem in which the successive displacements of a gas molecule are statistically independent. In this model. the distance 1 traveled by a molecule after N displacements is related to the mean free path ( by the expression L-= N. and the time I required to move a dis- tance L is given by 1 - Nt/v. Using these relations. estimate how long it would take a molecule in a room of macroscopically "still" air with uniform tempera ture and pressure to move a distance of 5 meters.

Explanation / Answer

Distance traveled by the particle after N displacements, L = 5 meters.

Since L2 = N x l2 , the average velocity is the total distance traveled by the particle/ time taken taken to travel the distance, therefore

v(average) = 5/t . taking t as 1 sec, therefore, '

v(average) = 5/1 = 5 m/sec, therefore, the time will be, for one molecule since N = 1,

t = Nl/v(average) = 1 x 5/ 5 = 1 units or sec.

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