BROWNIAN MOTION 
Any minute particle suspended in a liquid (or gas) moves chaotically under the action of collisions with surrounding molecules. The intensity of this chaotic motion is increased with an increase in temperature. This experimental fact was discovered by a British scientist R.Brown in 1827.
The main physical principle of Brownian motion is that the mean kinetic energy of any molecule of a liquid (or gas) is equal to the mean kinetic energy of a particle suspended in this ambience. The mean kinetic energy of onward motion < E > can be written as:
< E > = m<v^{2}>/ 2 = 3kT/2
where m is the mass of a particle, v is the velocity of a particle, k is the Boltzman constant, and T is the temperature. We can see from this formula that mean kinetic energy of Brownian motion is proportional to the temperature.
With a random velocity, a Brownian particle will move in a tangled zigzag path, and will progress with time away from its initial location. Calculations show that the meansquare displacement r ^{2 }= x ^{2} + y ^{2} + z ^{2} of a Brownian particle is described by the equation:
< r ^{2} > = 6kTBt
where B is the mobility of the particle, which is inversely proportional to the medium viscosity h and the size of the particle. Observing the Brownian motion under a microscope, the French physicist J.Perren (18701942) measured the Boltzman constant and Avogadro number, which proved to correspond well with the values of these constants found by other methods.
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