Brownian motion apart once the particle is in motion. Also, there would be a distribution of different possible Δ"V"s instead of always just one in a realistic situation. The diffusion equation yields an approximation of the time evolution of the probability density function associated to the position of the particle going under a Brownian movement under the physical definition. The approximation is valid on short timescales. The time evolution of the position of the Brownian particle itself is best described using Langevin equation, an equation which involves a random force field representing the effect of the thermal fluctuations of the solvent on
Brownian motion square root of the total population. Suppose that a Brownian particle of mass "M" is surrounded by lighter particles of mass "m" which are traveling at a speed "u". Then, reasons Smoluchowski, in any collision between a surrounding and Brownian particles, the velocity transmitted to the latter will be "mu"/"M". This ratio is of the order of 10 cm/s. But we also have to take into consideration that in a gas there will be more than 10 collisions in a second, and even greater in a liquid where we expect that there will be 10 collision in one second. Some