Today we will examine in detail an important topic - we will define the Brownian motion of small pieces of matter in a liquid or gas.
Map and coordinates
Some students, tormented by boring lessons, do not understand why to study physics. Meanwhile, it was this science that once allowed us to discover America!
Let's start from afar. The ancient civilizations of the Mediterranean were lucky in a sense: they developed on the banks of a closed inland water body. The Mediterranean Sea is so called because it is surrounded on all sides by land. And ancient travelers could go quite far with their expedition without losing sight of the coast. Outlines of sushi helped to navigate. And the first maps were drawn up descriptively rather than geographically. Thanks to these relatively short voyages, the Greeks, Phoenicians and Egyptians learned to build ships well. And where the best equipment is, there is the desire to push the boundaries of your world.
Therefore, one fine day, the European powers decided to go into the ocean. During sailing through the vast expanses between the continents, sailors for many months saw only water, and they had to somehow navigate. The invention of an accurate watch and a high-quality compass helped to determine their coordinates.
Clock and compass
The invention of small hand-held chronometers greatly helped the mariners. To determine exactly where they are, they needed to have a simple instrument that measured the height of the sun above the horizon, and to know when it was noon. And thanks to the compass, ship captains knew where they were going. Both the clock and the properties of the magnetic hand were studied and created by physicists. Thanks to this, the whole world was opened to Europeans.
The new continents were terra incognita, uncharted lands. Strange plants grew on them and strange animals were found.
Plants and physics
All natural scientists of the civilized world rushed to study these new strange ecological systems. And of course, they sought to capitalize on them.
Robert Brown was an English nerd. He traveled to Australia and Tasmania, collecting plant collections there. Already at home, in England, he worked hard on the description and classification of the material brought. And this scientist was very meticulous. Once, observing the movement of pollen in the sap of plants, he noticed: small particles constantly make chaotic zigzag movements. This is the definition of Brownian motion of small elements in gases and liquids. Thanks to the discovery, the stunning nerd wrote his name in the history of physics!
Brown and Gooey
In European science, it is customary to call an effect or phenomenon by the name of the one who discovered it. But often this happens by accident. But the person who describes, discovers the importance or explores the physical law in more detail, is in the shadows. So it happened with the Frenchman Louis Georges Guy. It was he who gave the definition to the Brownian motion (the 7th grade doesn’t hear about him when he studies this topic in physics).
Gooey studies and properties of Brownian motion
The French experimenter Louis Georges Guy observed the movement of various types of particles in several liquids, including solutions. The science of that time was already able to accurately determine the size of pieces of matter up to tenths of a micrometer. Studying what Brownian motion is (it was Gouy who defined this phenomenon in physics), the scientist realized that the intensity of particle movement increases if they are placed in a less viscous medium. Being an experimenter of a wide spectrum, he exposed the suspension to the action of light and electromagnetic fields of various powers. The scientist found that these factors have no effect on the chaotic zigzag jumps of particles. Gooey unequivocally showed what Brownian motion proves: thermal movement of liquid or gas molecules.
The team and the mass
And now we will describe in more detail the mechanism of zigzag jumps of small pieces of matter in a liquid.
Any substance consists of atoms or molecules. These elements of the world are very small, not a single optical microscope can see them. In a fluid, they oscillate and move all the time. When any visible particle enters a solution, its mass is thousands of times larger than one atom. Brownian motion of liquid molecules occurs randomly. Nevertheless, all atoms or molecules are a collective, they are connected with each other, like people who joined hands. Therefore, sometimes it happens that liquid atoms on one side of a particle move in such a way that they “press” on it, while a less dense medium is created on the other side of the particle. Therefore, a speck of dust moves in the space of the solution. Elsewhere, the collective motion of liquid molecules randomly acts on the other side of a more massive component. This is how the Brownian motion of particles takes place.
Time and Einstein
If a substance has a nonzero temperature, its atoms undergo thermal vibrations. Therefore, even in a very cold or supercooled liquid, Brownian motion exists. These chaotic hopping of small suspended particles never stop.
Albert Einstein is perhaps the most famous scientist of the twentieth century. Everyone who is at least somewhat interested in physics knows the formula E = mc 2 . Also, many may recall the photoelectric effect, for which he was given the Nobel Prize, and the special theory of relativity. But few people know that Einstein developed a formula for Brownian motion.
Based on the molecular-kinetic theory, the scientist derived the diffusion coefficient of suspended particles in a liquid. And it happened in 1905. The formula is as follows:
D = (R * T) / (6 * N A * a * π * ξ),
where D is the desired coefficient, R is the universal gas constant, T is the absolute temperature (expressed in Kelvin), N A is the Avogadro constant (corresponds to one mole of substance, or about 10 23 molecules), a is the approximate average particle radius, ξ - dynamic viscosity of a liquid or solution.
And already in 1908, the French physicist Jean Perrin and his students experimentally proved the correctness of Einstein's calculations.
One particle in a warrior field
Above, we described the collective effect of the medium on many particles. But even one foreign element in the liquid can give some laws and dependencies. For example, if you observe a Brownian particle for a long time, then you can record all of its movements. And out of this chaos will emerge a harmonious system. The average advance of a Brownian particle along a single direction is proportional to time.
In experiments on a particle in a liquid, the following quantities were specified:
- Boltzmann constant;
- Avogadro number.
In addition to linear motion, a Brownian particle is also characterized by chaotic rotation. And the average angular displacement is also proportional to the observation time.
Sizes and shapes
After such reasoning, a logical question may arise: why is this effect not observed for large bodies? Because when the length of an object immersed in a liquid is more than a certain value, then all these random collective “shocks” of molecules turn into constant pressure, as they are averaged. And the general buoyancy force of Archimedes is already acting on the body. Thus, a large piece of iron is sinking, and metal dust floats in the water.
The particle size, on the example of which the fluctuation of liquid molecules is detected, should not exceed 5 micrometers. As for objects with large sizes, this effect will not be noticeable here.