Question

What are the characteristics for random motion? Explain how different or similar it is to directed motion.

If the average total displacement in either the x- or the y-direction is zero for all times, why is the displacement NOT zero? How does the displacement change with time?

Answer 1

there is no preferred direction for the random oscillations, then over a period of time the particles will tend to be spread evenly throughout the medium. Thus, if A and B are two adjacentregions and, at time t, A contains twice as many particles as B, at that instant the probability of a particle’s leaving A to enter B is twice as great as the probability that a particle will leave B to enter A. The physical process in which a substance tends to spread steadily from regions of high concentration to regions of lower concentration is called diffusion.

Over a period of time, the particle would tend to drift from its starting point, and, on the basis of kinetic theory, it is possible to compute the probability (P) of a particle’s moving a certain distance (x) in any given direction (the total distance it moves will be greater than x) during a certain time interval (t) in a medium whose coefficient of diffusion (D) is known, D being equal to one-half the average of the square of the displacement in the x-direction. This formula for probability “density” allows P to be plotted against x.