Definition of Brownian Motion

In the second half of the twentieth century, a serious debate on the nature of atoms flared up in the scientific community. On one side were irrefutable authorities such as Ernst Mach (see Shock Waves) who argued that atoms are simply mathematical functions that successfully describe the observed physical phenomena and do not have a real physical basis. On the other hand, scientists of the new wave – in particular, Ludwig Boltzmann (see Boltzmann’s Constant) – insisted that atoms are physical realities. And neither of the two sides realized that tens of years before the start of their dispute, experimental results had been obtained, once and for all deciding the question in favor of the existence of atoms as a physical reality, although they were obtained in a related discipline of natural science by the botanist Robert Brown.

As early as the summer of 1827, Brown, studying the behavior of flower pollen under a microscope (he was studying the aqueous suspension of the pollen of the Clarkia pulchella plant), suddenly discovered that some spores were making completely chaotic impulsive movements. He determined for sure that these movements are not connected in any way with the turbulence and currents of the water, or with its evaporation, after which, having described the nature of the particle motion, he honestly signed his own impotence to explain the origin of this chaotic movement. However, being a meticulous experimenter, Brown established that such a chaotic motion is characteristic of any microscopic particles, whether it be pollen of plants, suspension of minerals, or, in general, any ground substance.

Only in 1905, none other than Albert Einstein, first realized that this mysterious, at first glance, a phenomenon is the best experimental confirmation of the correctness of the atomic theory of the structure of matter. He explained it approximately like this: a water-weighted dispute is constantly bombarded by chaotically moving water molecules. On average, the molecules act on it from all sides with equal intensity and at regular intervals. However, no matter how small the dispute, due to purely random deviations, it first receives a pulse from the side of the molecule that struck it from one side, then from the side of the molecule that struck it on the other, etc. As a result of averaging such collisions, that at some point the particle “jerks” in one direction, then, if on the other hand it is “pushed” more molecules – into another, and so on. Using the laws of mathematical statistics and the molecular-kinetic theory of gases, Einstein derived an equation describing the dependence of the mean square displacement of a Brownian particle on macroscopic exponents. (An interesting fact: in 1905 three articles of Einstein were published in one of the volumes of the German journal Annals of Physics (Annalen der Physik): an article with a theoretical explanation of the Brownian motion, an article on the foundations of the special theory of relativity, and finally an article describing the theory of photoelectric effect.) It was during the last Albert Einstein that he was awarded the Nobel Prize in Physics in 1921.)

In 1908 the French physicist Jean-Baptiste Perrin (Jean-Baptiste Perrin, 1870-1942) conducted a brilliant series of experiments that confirmed the correctness of the Einstein explanation of the phenomenon of Brownian motion. It became finally clear that the observed “chaotic” motion of Brownian particles is a consequence of intermolecular collisions. Since “useful mathematical conventions” (according to Mach) can not lead to observable and completely real displacements of physical particles, it became finally clear that the dispute about the reality of the atoms is over: they exist in nature. As a “bonus game”, Perrin got the formula derived by Einstein, which allowed the Frenchman to analyze and estimate the average number of atoms and/or molecules that collide with a particle suspended in a liquid for a given period of time and, through this indicator, calculate the molar numbers of different liquids. This idea was based on the fact that at any given time the acceleration of the suspended particle depends on the number of collisions with the molecules of the medium (see Newton’s laws of mechanics), and hence on the number of molecules per unit volume of the liquid. And this is nothing more than Avogadro’s number (see Avogadro’s Law) – one of the fundamental constants that determine the structure of our world.

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