J. Dalton's theory

The first truly scientific substantiation of the atomic theory, which convincingly demonstrated the rationality and simplicity of the hypothesis that every chemical element consists of the smallest particles, was the work of the English school mathematics teacher J. Dalton (1766-1844), whose article devoted to this problem appeared in 1803 Dalton's atomic postulates had the advantage over the abstract reasoning of the ancient Greek atomists that his laws made it possible to explain and relate the results of real experiments, as well as predict the results of new experiments. He postulated that: 1) all atoms of the same element are identical in all respects, in particular, their masses are the same; 2) atoms of different elements have different properties, in particular, their masses are different; 3) a compound, in contrast to an element, contains a certain integer number of atoms of each of its constituent elements; 4) in chemical reactions, a redistribution of atoms can occur, but not a single atom is destroyed or created again. (In fact, as it turned out at the beginning of the 20th century, these postulates are not strictly fulfilled, since atoms of the same element can have different masses, for example, hydrogen has three such varieties, called isotopes; in addition, atoms can undergo radioactive transformations and even completely collapse, but not in the chemical reactions considered by Dalton.) Based on these four postulates, Dalton's atomic theory provided the simplest explanation of the laws of constant and multiple ratios. However, it did not give any idea about the structure of the atom itself.

Brownian motion

Scottish botanist Robert Brown conducted research on plant pollen in 1827. He was particularly interested in how pollen participates in the process of fertilization. Once he looked under a microscope at elongated cytoplasmic grains isolated from pollen cells suspended in water. Suddenly Brown saw that the smallest solid grains, which could barely be seen in a drop of water, were constantly trembling and moving from place to place. He found that these movements, in his words, “are not associated either with flows in the liquid or with its gradual evaporation, but are inherent in the particles themselves.” The phenomenon observed by Brown was called “Brownian motion.” The explanation of Brownian motion by the movement of invisible molecules was given only in the last quarter of the 19th century, but was not immediately accepted by all scientists. In 1863, descriptive geometry teacher Ludwig Christian Wiener (1826-1896) suggested that the phenomenon was associated with the oscillatory movements of invisible particles.

Discovery of the electron

The real existence of molecules was finally confirmed in 1906 by experiments studying the laws of Brownian motion by the French physicist Jean Perrin.

At the time Perrin carried out his research on cathode and X-rays, no consensus had yet been reached regarding the nature of the cathode rays emitted by the negative electrode (cathode) in a vacuum tube during an electrical discharge. Some scientists believed that these rays were a type of light radiation, but in 1895 Perrin's research showed that they were a stream of negatively charged particles. Atomic theory stated that elements were composed of discrete particles called atoms, and that chemical compounds were composed of molecules, larger particles containing two or more atoms. By the end of the 19th century. atomic theory became widely accepted among scientists, especially among chemists. However, some physicists believed that atoms and molecules are nothing more than fictitious objects that are introduced for reasons of convenience and are useful in numerical processing of the results of chemical reactions.

Joseph John Thomson, modifying Perrin's experiment, confirmed his conclusions and in 1897 determined the most important characteristic of these particles by measuring their charge-to-mass ratio by deflection in the electric and magnetic fields. The mass turned out to be approximately 2 thousand times less than the mass of the hydrogen atom, the lightest among all atoms. Soon the belief began to spread that these negative particles, called electrons, were a constituent part of atoms.

Rice. 8. Brownian motion

Atomic-molecular science was of great importance for chemistry, which, thanks to it, began to develop rapidly and achieved brilliant success in a short time.

However, at the end of the 19th century, when this teaching had already yielded so many valuable results, a reactionary movement arose that fundamentally denied the very existence of atoms and molecules. Under the influence of idealistic philosophy, the so-called “energy” school of chemists appeared in Germany, headed by the famous scientist Ostwald, whose theoretical views were based on the abstract concept of energy not related to matter. Supporters of this school believed that all external phenomena can be explained as processes between energies, and categorically rejected the existence of atoms and molecules as particles inaccessible to direct sensory perception.

Ostwald's energy doctrine was one of the varieties of idealistic philosophical movements aimed against materialism in science. By separating energy, i.e., movement from matter, allowing the existence of immaterial movement, Ostwald's followers thereby tacitly recognized that our consciousness, thought, sensations exist independently, as something primary, not related to matter. They considered chemical elements not as specific ones, but as different forms of chemical energy.

The reactionary essence of Ostwald's teaching was brilliantly revealed by V.I. Lenin in his work “Materialism and Empirio-Criticism.” In ch. V of this work, speaking about the connection of philosophical idealism with some new trends in physics, Lenin dwells on Ostwald’s “philosophy”, proving its inconsistency and the inevitability of its defeat in the fight against materialism.

"…attempt think movement without matter, writes Lenin, drags thought, divorced from matter, and this is philosophical idealism.”

Lenin not only completely revealed the idealistic basis of Ostwald's reasoning, but also showed the internal contradictions contained in them. Putting forward the philosophical idea of ​​the existence of movement without matter, Ostwald rejects the objective existence of matter, but at the same time, as a physical chemist, he himself interprets energy materialistically at every step, relying on the law of conservation and transformation of energy. “The transformation of energy,” states Lenin, “is considered by natural science as an objective process, independent of human consciousness and the experience of mankind, that is, it is considered materialistically. And in Ostwald himself, in the majority of cases, even probably in the vast majority of cases, by energy, of course material movement" .

Soon, new amazing discoveries that marked the beginning of the 20th century so irrefutably proved the reality of atoms and molecules that in the end even Ostwald was forced to admit their existence.

Of the experimental studies devoted to the question of the existence of atoms and molecules, the work of the French physicist Perrin on the study of the distribution and movement of particles in so-called suspensions is of particular interest.

Having prepared a suspension containing particles of the same size, visible under a microscope, Perrin examined the distribution particles in it. As a result of numerous experiments carried out with extraordinary care, he proved that the distribution of suspension particles over height exactly corresponds to the law of decrease in gas concentration with height, derived from the kinetic theory of gases. Thus Perrin showed that suspensions are true models of gases; Consequently, individual molecules also exist in gases, only they are invisible due to their small size.

Even more convincing were the results obtained by Perrin when observing the movement of suspension particles.

When examining a drop of liquid with particles suspended in it under a strong microscope, one can see that the particles do not remain at rest, but do not moving jerkily in all sorts of directions. The movement of particles is extremely disordered. If you trace the path of an individual particle under a microscope, you get a very complex zigzag line, indicating the absence of any regularity in the movement of particles (Fig. 8). This movement can continue for any amount of time without weakening or changing its character.

The described phenomenon was discovered in 1827 by the English botanist Brown and was called Brownian motion. However, an explanation was given to it only in the 60s on the basis of molecular kinetic concepts. According to this explanation, the reason for the visible movement of suspension particles is the invisible thermal movement of the liquid molecules surrounding them. The shocks received by the particles of the suspension from all sides from the molecules of the liquid cannot, of course, exactly balance each other; at every moment the balance is disturbed in favor of one direction or another, as a result of which the particles make their own bizarre path.

Thus, the very fact of the existence of Brownian motion indicates the reality of molecules and gives a picture of their random motion, since suspended particles generally repeat the same movements as liquid molecules. But Perrin in his research he went even further: through long-term observations of the movement of particles under a microscope, he was able to determine the average speed of particle movement. From here, knowing the mass of the particles of the prepared suspension, Perrin calculated their average kinetic energy. The result was amazing. It turned out that the kinetic energy of particles exactly corresponds to the kinetic energy of gas molecules, calculated for the same temperature on the basis of kinetic theory. Perrin particles were approximately 10 12 times heavier than hydrogen molecules, but the kinetic energy of both was the same. Once these facts were established, it was no longer possible to deny the objective reality of molecules.

Currently, Brownian motion is considered both as a consequence of the thermal motion of liquid molecules and as an independent thermal motion of suspension particles. The latter are like giant molecules that participate in thermal motion along with invisible liquid molecules. There is no fundamental difference between the two.

Perrin's experiments not only proved that molecules really exist, but also made it possible to calculate the number of molecules in one gram molecule of gas. This number, which, as we know, has a universal meaning, is called Avogadro's number. According to Perrin's calculations, it turned out to be approximately 6.5 10 23, which was very close to the values ​​​​of this value previously found by other methods. Subsequently, Avogadro's number was determined many times by completely different physical methods, and the results were always very close. This coincidence of results indicates the correctness of the found number and serves as indisputable proof of the real existence of molecules.

Currently, Avogadro's number is taken to be

6,02 10 23

The colossal magnitude of Avogadro's number goes beyond our imagination. Some idea of ​​it can be formed only through comparisons.

Let us assume, for example, that 1 mole, i.e. 18 G, water is evenly distributed over the entire surface of the globe. A simple calculation shows that for every square centimeter of surface there will be about 100,000 molecules.

Let's give another comparison. Let's say that we managed to somehow label all the molecules contained in 18 g of water. If you then pour this water into the sea and wait for it to mix evenly with all the waters of the earth ball, scooping up a glass of water anywhere, we will find in it about 100 molecules we have marked.

Rice. 9. Zinc Oxide Smoke Particles at 20,000x Magnification

Since a gram molecule of any gas occupies a volume of 22.4 liters under normal conditions, then at 1 ml gas contains under these conditions 2.7 10 19 molecules. If we bring the rarefaction of gas in any vessel even to the extreme limit that the best pumps can achieve (approximately to one ten-billionth part of an atmosphere), i.e., to obtain what we practically consider “airless space,” then still in 1 cm 3 of this molecular space remains significantly more than all the people on the globe. From this one can judge how insignificant the sizes of molecules and atoms must be if such a huge number of them fit into 1 cm 3. And yet, physicists have calculated these dimensions in various ways. It turns out that if you imagine molecules in the form of tiny balls, then their diameter will be measured in hundred-millionths of a centimeter. For example, the diameter of an oxygen molecule is approximately 3.2 10 -8 cm, diameter of a hydrogen molecule 2.6 10 -8 cm and the diameter of the hydrogen atom is 1 10 -8 cm.

To express such small quantities, it is very convenient to take one hundred millionth of a centimeter (10 -8 cm). This unit was proposed by the Swedish physicist Ångström to measure the wavelengths of light and was named Ångström after him. It is designated by the symbol A or A. The linear dimensions of atoms and molecules are usually expressed in several angstroms.

Knowing the number of molecules in one gram molecule, and therefore the number of atoms in one gram atom, one can calculate the weight of an atom of any element in grams. For example, dividing by the gram of hydrogen by Avogadro’s number, we get the weight of the hydrogen atom in grams:

Mountains, stars, people - everything we see around us is made of tiny atoms. Atoms are small. Very, very. Since childhood, we know that all matter is made up of clusters of these tiny things. We also know that they cannot be seen with the naked eye. We are forced to blindly believe these statements without being able to verify them. Atoms interact with each other and, brick by brick, make up our world. How do we know this? Many people do not like to take scientists' statements at face value. Let's go together with science along the path from awareness of atoms to direct proof of their existence.

It might seem that there is an easy way to prove the existence of atoms: put them under a microscope. But this approach won't work. Even the most powerful light-focusing microscopes cannot image a single atom. An object becomes visible because it reflects light waves. The atoms are so much smaller than the wavelength of visible light that they do not interact at all. In other words, atoms are invisible even to light. However, atoms do have observable effects on some things that we can see.

50 years later, in 1827, Scottish botanist Robert Brown described something remarkably similar. By studying pollen granules under a microscope, Brown discovered that some granules emitted tiny particles - which then moved away from the pollen in a random, nervous dance.

At first, Brown thought the particles were some unknown organism. He repeated the experiment with other substances, such as stone dust, which was clearly inanimate, and again saw a strange movement.

It took almost a hundred years for science to find an explanation. Einstein came along and developed a mathematical formula that predicted that very special type of motion - then called Brownian motion, after Robert Brown. Einstein's theory was that pollen granule particles were constantly moving as millions of tiny water molecules - molecules made of atoms - crashed into them.

"He explained that this neural movement that you see was actually caused by the action of individual water molecules on dust particles or what have you," explains Harry Cliff of the University of Cambridge, also a curator at the Science Museum in London.

By 1908, observations, supported by calculations, showed that atoms were real. In ten years, physicists have made significant progress. By stretching individual atoms, they began to understand their internal structure.

The surprise was that atoms could be divided - especially since the name "atom" itself came from the Greek "atomos", meaning "indivisible". But physicists now know that atoms are far from the building blocks. They consist of three main parts: protons, neutrons and electrons. Imagine that the protons and neutrons together form a “sun,” or nucleus, at the center of the system. Electrons are in orbit around this nucleus, like planets.

But how did we know those particles were there? The answer is that although they are small, they have a big impact. British physicist Thomson, who discovered electrons, used a wonderful method to prove their existence in 1897.

He had a Crookes tube - a funny-shaped piece of glass from which almost all the air had been sucked out by the machine. A negative electric charge was applied to one end of the tube. This charge was enough to knock out some of the electrons from the molecules of the gas remaining in the tube. The electrons were negatively charged, so they flew to the other end of the tube. Thanks to the partial vacuum, electrons flew through the tube without encountering large atoms on their way.

The electrical charge caused the electrons to travel very quickly - about 59,500 kilometers per second - until they crashed into the glass at the far end, knocking out even more electrons that were hidden in its atoms. Amazingly, the collision between these mind-bogglingly tiny particles produced so much energy that it produced a fantastic green-yellow glow.

“It was, in a sense, one of the first particle accelerators,” Cliff says. “It accelerates the electrons at one end of the tube to the other, and they crash into the screen at the other end, producing a phosphorescent glow.”

Because Thomson discovered that he could control beams of electrons using magnets and electric fields, he knew that these were not just strange rays of light - they were charged particles.

And if you're wondering how these electrons can fly independently of their atoms, it's thanks to the process of ionization, in which - in this case - an electrical charge changes the structure of the atom, knocking electrons out into space nearby.

In particular, because electrons are so easy to manipulate and move, electrical circuits became possible. The electrons in a copper wire move like a train from one copper atom to another - that's why the wire is transmitted through the wire. Atoms, as we have already said, are not solid pieces of matter, but systems that can be modified or disassembled into structural elements.

The early 20th century identified these positively charged particles and at the same time revealed the internal structure of the atom - similar to the solar system.

Ernest Rutherford and his colleagues took a very thin piece of metal foil and exposed it to a beam of positively charged radiation - a stream of tiny particles. Most of the powerful radiation passed through, as Rutherford expected, given the thickness of the foil. But, to the surprise of scientists, part of it bounced off.

Rutherford theorized that the atoms in the metal foil must contain small, dense regions of positive charge—nothing else would have sufficient potential to reflect such powerful radiation. He discovered positive charges in the atom - and at the same time proved that they are all connected in a dense mass, unlike electrons. In other words, he demonstrated the existence of a dense nucleus in the atom.

There was still a problem. By that time, they could already calculate the mass of an atom. But given the evidence of how heavy the particles in the nucleus must have been, the idea that they were all positively charged did not make sense.

"Carbon has six electrons and six protons in its nucleus - six positive charges and six negative charges," Cliff explains. “But a carbon nucleus doesn’t weigh six protons, it weighs the equivalent of 12 protons.”

It was first suggested that there were six other nuclear particles in the nucleus with the mass of a proton, but negatively charged: neutrons. But no one could prove it. In fact, neutrons weren't discovered until the 1930s.

Several years earlier, other physicists had experimented with radiation. They fired positively charged radiation - the type used by Rutherford in his search for the nucleus - into beryllium atoms. Beryllium emitted its own radiation: radiation that was not positively or negatively charged and could penetrate deep into the material.

By this time, others had figured out that gamma radiation was neutral and penetrated deeply, so physicists believed that it was emitted by beryllium atoms. But Chadwick didn't think so.

He produced new radiation on his own and directed it at a substance that he knew was rich in protons. Unexpectedly, it turned out that the protons were knocked out of the material as if by particles with identical mass - like billiard balls by other balls.

Gamma rays cannot reflect protons in this way, so Chadwick decided that the particles he was looking for must have the mass of a proton, but a different electrical charge: and these are neutrons.

All the basic particles of the atom have been found, but the story does not end there.

Although we learned a lot more about atoms than we knew before, they were difficult to visualize. In the 1930s, no one had pictures of them - and many people wanted to see them in order to accept their existence.

It's important to note, however, that the methods used by scientists like Thomson, Rutherford and Chadwick paved the way for new equipment that eventually helped us produce these images. The beams of electrons that Thomson generated in his Crookes tube experiment proved particularly useful.

Today, such beams are generated by electron microscopes, and the most powerful of these microscopes can actually take pictures of individual atoms. That's because an electron beam has a wavelength thousands of times shorter than a beam of light—so short, in fact, that electron waves can bounce off tiny atoms and produce a picture that light beams cannot.

Neil Skipper of University College London says such images are useful for people who want to study the atomic structure of special substances - like those used in the production of batteries for electric vehicles, for example. The more we know about their atomic structure, the better we can design batteries to make them efficient and reliable.

You can also figure out what atoms look like just by poking them. This is essentially how atomic force microscopy works.

Skipper adds that many atomic scientists study how the structure of things changes when exposed to high pressure or temperature. Most people know that when a substance is heated, it often expands. The atomic changes that occur can now be detected, which is often useful.

“When you heat a liquid, you can see its atoms take on a disordered configuration,” Skipper says. “You can see this directly from the structure map.”

Skipper and other physicists can also work with atoms using neutron beams, first discovered by Chadwick in the 1930s.

“We fire a lot of beams of neutrons into samples of materials, and from the scattering pattern that emerges, you can tell that you're scattering neutrons into nuclei,” he says. “You can roughly estimate the mass and size of the object that was illuminated.”

But atoms don't always just sit there in a stable state, waiting to be studied. Sometimes they decay - that is, they are radioactive.

There are many naturally occurring radioactive elements. This process generates the energy that forms the basis of nuclear power - and nuclear bombs. Nuclear physicists typically try to better understand reactions in which a nucleus goes through fundamental changes like these.

“The types of detectors you should use are detectors that will allow you to measure both the presence of radiation and the radiation energy that has been deposited,” she says. “This is because all nuclei have a special imprint.”

Because all types of atoms can be present in an area where radiation has been detected, especially after a large nuclear reaction, it is important to know exactly which radioactive isotopes are present. Such detection is usually carried out at nuclear plants or in areas where a nuclear disaster has occurred.

Harkness-Brennan and her colleagues are now working on detection systems that can be placed in such locations to show in three dimensions where radiation may be present in a particular room. “You need techniques and tools that can map the space in three dimensions and tell you where the radiation is in this room, in this pipe,” she says.

It is also possible to visualize radiation in a cloud chamber. In this special experiment, alcohol vapor cooled to -40 degrees Celsius is sprayed into a cloud over a radioactive source. Charged radiation particles flying from the radiation source knock electrons out of the alcohol molecules. The alcohol condenses into a liquid next to the path of emitted particles. The results of this type of detection are impressive.

We haven't worked much directly with atoms except to realize that they are beautiful, complex structures that can undergo amazing changes, many of which occur in nature. By studying atoms in this way, we improve our own technology, extract energy from nuclear reactions, and better understand the natural world around us. We also have the opportunity to protect ourselves from radiation and study how substances change under extreme conditions.

“Given how small an atom is, it’s incredible how much physics we can extract from it,” Harkness-Brennan aptly observes. Everything we see around us consists of these tiny particles. And it’s good to know that they are there, because it was thanks to them that everything around us became possible.

Based on materials from the BBC

Rice. 8. Brownian motion

Atomic-molecular science was of great importance for chemistry, which, thanks to it, began to develop rapidly and achieved brilliant success in a short time.

However, at the end of the 19th century, when this teaching had already yielded so many valuable results, a reactionary movement arose that fundamentally denied the very existence of atoms and molecules. Under the influence of idealistic philosophy, the so-called “energy” school of chemists appeared in Germany, headed by the famous scientist Ostwald, whose theoretical views were based on the abstract concept of energy not related to matter. Supporters of this school believed that all external phenomena can be explained as processes between energies, and categorically rejected the existence of atoms and molecules as particles inaccessible to direct sensory perception.

Ostwald's energy doctrine was one of the varieties of idealistic philosophical movements aimed against materialism in science. By separating energy, i.e., movement from matter, allowing the existence of immaterial movement, Ostwald's followers thereby tacitly recognized that our consciousness, thought, sensations exist independently, as something primary, not related to matter. They considered chemical elements not as specific ones, but as different forms of chemical energy.

The reactionary essence of Ostwald's teaching was brilliantly revealed by V.I. Lenin in his work “Materialism and Empirio-Criticism.” In ch. V of this work, speaking about the connection of philosophical idealism with some new trends in physics, Lenin dwells on Ostwald’s “philosophy”, proving its inconsistency and the inevitability of its defeat in the fight against materialism.

"…attempt think movement without matter, writes Lenin, drags thought, divorced from matter, and this is philosophical idealism.”

Lenin not only completely revealed the idealistic basis of Ostwald's reasoning, but also showed the internal contradictions contained in them. Putting forward the philosophical idea of ​​the existence of movement without matter, Ostwald rejects the objective existence of matter, but at the same time, as a physical chemist, he himself interprets energy materialistically at every step, relying on the law of conservation and transformation of energy. “The transformation of energy,” states Lenin, “is considered by natural science as an objective process, independent of human consciousness and the experience of mankind, that is, it is considered materialistically. And in Ostwald himself, in the majority of cases, even probably in the vast majority of cases, by energy, of course material movement" .

Soon, new amazing discoveries that marked the beginning of the 20th century so irrefutably proved the reality of atoms and molecules that in the end even Ostwald was forced to admit their existence.

Of the experimental studies devoted to the question of the existence of atoms and molecules, the work of the French physicist Perrin on the study of the distribution and movement of particles in so-called suspensions is of particular interest.

Having prepared a suspension containing particles of the same size, visible under a microscope, Perrin examined the distribution particles in it. As a result of numerous experiments carried out with extraordinary care, he proved that the distribution of suspension particles over height exactly corresponds to the law of decrease in gas concentration with height, derived from the kinetic theory of gases. Thus Perrin showed that suspensions are true models of gases; Consequently, individual molecules also exist in gases, only they are invisible due to their small size.

Even more convincing were the results obtained by Perrin when observing the movement of suspension particles.

When examining a drop of liquid with particles suspended in it under a strong microscope, one can see that the particles do not remain at rest, but do not moving jerkily in all sorts of directions. The movement of particles is extremely disordered. If you trace the path of an individual particle under a microscope, you get a very complex zigzag line, indicating the absence of any regularity in the movement of particles (Fig. 8). This movement can continue for any amount of time without weakening or changing its character.

The described phenomenon was discovered in 1827 by the English botanist Brown and was called Brownian motion. However, an explanation was given to it only in the 60s on the basis of molecular kinetic concepts. According to this explanation, the reason for the visible movement of suspension particles is the invisible thermal movement of the liquid molecules surrounding them. The shocks received by the particles of the suspension from all sides from the molecules of the liquid cannot, of course, exactly balance each other; at every moment the balance is disturbed in favor of one direction or another, as a result of which the particles make their own bizarre path.

Thus, the very fact of the existence of Brownian motion indicates the reality of molecules and gives a picture of their random motion, since suspended particles generally repeat the same movements as liquid molecules. But Perrin in his research he went even further: through long-term observations of the movement of particles under a microscope, he was able to determine the average speed of particle movement. From here, knowing the mass of the particles of the prepared suspension, Perrin calculated their average kinetic energy. The result was amazing. It turned out that the kinetic energy of particles exactly corresponds to the kinetic energy of gas molecules, calculated for the same temperature on the basis of kinetic theory. Perrin particles were approximately 10 12 times heavier than hydrogen molecules, but the kinetic energy of both was the same. Once these facts were established, it was no longer possible to deny the objective reality of molecules.

Currently, Brownian motion is considered both as a consequence of the thermal motion of liquid molecules and as an independent thermal motion of suspension particles. The latter are like giant molecules that participate in thermal motion along with invisible liquid molecules. There is no fundamental difference between the two.

Perrin's experiments not only proved that molecules really exist, but also made it possible to calculate the number of molecules in one gram molecule of gas. This number, which, as we know, has a universal meaning, is called Avogadro's number. According to Perrin's calculations, it turned out to be approximately 6.5 10 23, which was very close to the values ​​​​of this value previously found by other methods. Subsequently, Avogadro's number was determined many times by completely different physical methods, and the results were always very close. This coincidence of results indicates the correctness of the found number and serves as indisputable proof of the real existence of molecules.

Currently, Avogadro's number is taken to be

6,02 10 23

The colossal magnitude of Avogadro's number goes beyond our imagination. Some idea of ​​it can be formed only through comparisons.

Let us assume, for example, that 1 mole, i.e. 18 G, water is evenly distributed over the entire surface of the globe. A simple calculation shows that for every square centimeter of surface there will be about 100,000 molecules.

Let's give another comparison. Let's say that we managed to somehow label all the molecules contained in 18 g of water. If you then pour this water into the sea and wait for it to mix evenly with all the waters of the earth ball, scooping up a glass of water anywhere, we will find in it about 100 molecules we have marked.

Rice. 9. Zinc Oxide Smoke Particles at 20,000x Magnification

Since a gram molecule of any gas occupies a volume of 22.4 liters under normal conditions, then at 1 ml gas contains under these conditions 2.7 10 19 molecules. If we bring the rarefaction of gas in any vessel even to the extreme limit that the best pumps can achieve (approximately to one ten-billionth part of an atmosphere), i.e., to obtain what we practically consider “airless space,” then still in 1 cm 3 of this molecular space remains significantly more than all the people on the globe. From this one can judge how insignificant the sizes of molecules and atoms must be if such a huge number of them fit into 1 cm 3. And yet, physicists have calculated these dimensions in various ways. It turns out that if you imagine molecules in the form of tiny balls, then their diameter will be measured in hundred-millionths of a centimeter. For example, the diameter of an oxygen molecule is approximately 3.2 10 -8 cm, diameter of a hydrogen molecule 2.6 10 -8 cm and the diameter of the hydrogen atom is 1 10 -8 cm.

To express such small quantities, it is very convenient to take one hundred millionth of a centimeter (10 -8 cm). This unit was proposed by the Swedish physicist Ångström to measure the wavelengths of light and was named Ångström after him. It is designated by the symbol A or A. The linear dimensions of atoms and molecules are usually expressed in several angstroms.

Knowing the number of molecules in one gram molecule, and therefore the number of atoms in one gram atom, one can calculate the weight of an atom of any element in grams. For example, dividing by the gram of hydrogen by Avogadro’s number, we get the weight of the hydrogen atom in grams:

FEDERAL AGENCY FOR EDUCATION

RUSSIAN FEDERATION

VORONEZH STATE UNIVERSITY

DEPARTMENT OF ONTOLOGY AND THEORY OF COGNITION

The theory of Brownian motion and experimental proof of the real existence of atoms and molecules

Completed by: graduate student

Faculty of Physics

Krisilov A.V.

Voronezh 2010

Atomic structure of matter

Robert Brown's discovery

Brownian motion theory

1Albert Einschnein - the first theory of Brownian motion

2Mariann Smoluchowski - the origin of the laws of probability in physics

Evidence of the real existence of atoms and molecules

1Jean Baptiste Perrin - decisive experiments

2Theodor Svedberg - determining the size of a protein molecule

Modern science and Brownian motion

Literature

1.Atomic structure of matter

matter Brownian molecule atom

An essential feature of what we designate as chance in everyday life and in science can be briefly defined as follows: small causes - large consequences.

M. Smoluchowski

It is well known that ancient thinkers repeatedly suggested the discrete nature of matter. They came to this based on the philosophical idea that it is impossible to comprehend the infinite divisibility of matter and when considering ever smaller quantities it is necessary to stop somewhere. For them, the atom was the last indivisible part of matter, after which there was nothing left to look for. Modern physics also starts from the idea of ​​the atomic structure of matter, but from its point of view, the atom is something completely different from what ancient thinkers understood by this word. According to modern concepts, the atom, being an integral part of matter, has a very complex structure. Real atoms in the sense of the ancients are, from the point of view of modern physics, elementary particles, for example electrons, which are considered today (perhaps temporarily) as the last indivisible components of atoms and, therefore, matter.

The concept of an atom was introduced into modern science by chemists. The study of the chemical properties of various bodies led chemists to the idea that all substances are divided into two classes: one of them includes complex or composite substances that, through appropriate operations, can be decomposed into simpler substances, the other includes simpler substances that can no longer be broken down into its component parts. These simple substances are often also called elements. According to this theory, the decomposition of complex substances into their constituent elements consists of breaking the bonds that unite various atoms into molecules and separating the substances into their component parts.

The atomic hypothesis turned out to be very fruitful not only for explaining basic chemical phenomena, but also for constructing new physical theories. In fact, if all substances really consist of atoms, then many of their physical properties can be predicted based on the idea of ​​their atomic structure. For example, the well-known properties of a gas should be explained by representing the gas as a collection of an extremely large number of atoms or molecules in a state of rapid, continuous motion. The pressure of the gas on the walls of the container containing it must be caused by the impacts of atoms or molecules on the walls; its temperature must be related to the average speed of movement of the particles, which increases with increasing temperature of the gas. A theory based on such ideas, called the kinetic theory of gases, made it possible to derive theoretically the basic laws that gases obey and which had already been obtained experimentally. Moreover, if the assumption about the atomic structure of substances corresponds to reality, then it follows that in order to explain the properties of solids and liquids it is necessary to assume that in these physical states the atoms or molecules that make up the substance must be at much smaller distances from each other each other and be much more closely connected with each other than in the gaseous state. The large magnitude of interaction forces between extremely closely spaced atoms or molecules, which must be assumed, must explain the elasticity, incompressibility and some other properties characterizing solid and liquid bodies. The theories that emerged and developed on this basis encountered a number of difficulties along the way (most of which were eliminated with the advent of quantum theory). However, the results obtained in this theory were sufficiently satisfactory to consider that it is developing along the right path.

Despite the fact that the hypothesis about the atomic structure of matter for some physical theories turned out to be very fruitful, for its final confirmation it was necessary to carry out a more or less direct experiment confirming the atomic structure of matter.

The first step towards this experiment was the experience of botanist Robert Brown, who discovered the random movement of pollen particles suspended in liquid. But recognition of the significance of this discovery for science came more than half a century later.

To prove the reality of molecules, it was necessary to determine their size or mass. In 1865, Loschmidt obtained, on a gas-kinetic basis, the first estimate of the size of air molecules and the number of gas molecules in 1 cubic meter. cm under normal conditions, and presented the results obtained in the famous work “Zur Gr ö sse der Luftmolek ü le" .

Seven years later in 1872, Van der Waals calculated Avogadro's constant NA (the number of molecules in a sample in which the number of grams of a substance is equal to its molecular weight). Van der Waals found an approximate value for the number N of 6.2 1023. Theory of gas at high pressures and consequences arising from it

the results were widely admired, but due to the large number of assumptions underlying both the theory and the calculation of NA, the resulting value for Avogadro's number was not particularly trusted.

2.Robert Brown's discovery

During his lifetime, the Scottish botanist Robert Brown, as the best plant expert, received the title “Prince of Botanists.” He made many wonderful discoveries. In 1805, after a four-year expedition to Australia, he brought to England about 4,000 species of Australian plants unknown to scientists and spent many years studying them. Described plants brought from Indonesia and Central Africa. He studied plant physiology and for the first time described in detail the nucleus of a plant cell. But the name of the scientist is now widely known not because of these works.

In 1827 Brown conducted research on plant pollen. He was particularly interested in how pollen participates in the process of fertilization. Once, under a microscope, he examined elongated cytoplasmic grains suspended in water from pollen cells of the North American plant Clarkia pulchella. Suddenly Brown saw that the smallest solid grains, which could barely be seen in a drop of water, were constantly trembling and moving from place to place. He found that these movements, in his words, “are not associated either with flows in the liquid or with its gradual evaporation, but are inherent in the particles themselves.”

Brown's observation was confirmed by other scientists. The smallest particles behaved as if they were alive, and the “dance” of the particles accelerated with increasing temperature and decreasing particle size and clearly slowed down when replacing water with a more viscous medium. This amazing phenomenon never stopped: it could be observed for as long as desired. At first, Brown even thought that living beings actually fell into the field of the microscope, especially since pollen is the male reproductive cells of plants, but there were also particles from dead plants, even from those dried a hundred years earlier in herbariums. Then Brown wondered if these were the “elementary molecules of living beings” that the famous French naturalist Georges Buffon (1707-1788), author of the 36-volume Natural History, spoke about. This assumption fell away when Brown began to examine apparently inanimate objects; at first it was very small particles of coal, as well as soot and dust from the London air, then finely ground inorganic substances: glass, many different minerals. “Active molecules” were everywhere: “In every mineral,” wrote Brown, “which I have succeeded in grinding into dust to such an extent that it could for some time be suspended in water, I have found, in greater or lesser quantities, these molecules."

For about 30 years, Brown's discovery did not attract the interest of physicists. The new phenomenon was not given much importance, considering that it was explained by the trembling of the preparation or similar to the movement of dust particles, which is observed in the atmosphere when a ray of light falls on them, and which, as was known, is caused by the movement of air. But if the movements of Brownian particles were caused by any flows in the liquid, then such neighboring particles would move in concert, which contradicts observational data.

An explanation of Brownian motion (as this phenomenon was called) by the movement of invisible molecules was given only in the last quarter of the 19th century, but was not immediately accepted by all scientists. In 1863, a teacher of descriptive geometry from Karlsruhe (Germany), Ludwig Christian Wiener (1826-1896), suggested that the phenomenon was associated with the oscillatory movements of invisible atoms. It is important that Wiener saw the opportunity to use this phenomenon to penetrate the secrets of the structure of matter. He was the first to try to measure the speed of movement of Brownian particles and its dependence on their size. But Wiener's conclusions were complicated by the introduction of the concept of "atoms of ether" in addition to atoms of matter. In 1876, William Ramsay, and in 1877, the Belgian Jesuit priests Carbonel, Delso and Thirion, and finally, in 1888, Guy, clearly showed the thermal nature of Brownian motion [5].

“Over a large area,” wrote Delso and Carbonelle, “the impacts of the molecules, which are the cause of the pressure, do not cause any shaking of the suspended body, because they together create a uniform pressure on the body in all directions. But if the area is not sufficient to compensate for the unevenness, it is necessary to take into account the inequality of pressures and their continuous change from point to point. The law of large numbers no longer reduces the effect of collisions to an average uniform pressure; their resultant will no longer be equal to zero, but will continuously change its direction and its magnitude.”

If we accept this explanation, then the phenomenon of thermal motion of liquids, postulated by the kinetic theory, can be said to be proven ad oculos (visually). Just as it is possible, without distinguishing waves in the distance at sea, to explain the rocking of a boat on the horizon by waves, in the same way, without seeing the movement of molecules, one can judge it by the movement of particles suspended in a liquid.

This explanation of Brownian motion is significant not only as a confirmation of the kinetic theory, it also entails important theoretical consequences. According to the law of conservation of energy, a change in the speed of a suspended particle must be accompanied by a change in temperature in the immediate vicinity of this particle: this temperature increases if the speed of the particle decreases, and decreases if the speed of the particle increases. Thus, the thermal equilibrium of a liquid is a statistical equilibrium.

An even more significant observation was made in 1888 by Guy: Brownian motion, strictly speaking, does not obey the second law of thermodynamics. In fact, when a suspended particle rises spontaneously in a liquid, part of the heat of its surroundings spontaneously turns into mechanical work, which is prohibited by the second law of thermodynamics. Observations, however, have shown that the lifting of a particle occurs less often, the heavier the particle. For particles of matter of normal size, this probability of such a rise is practically zero.

Thus, the second law of thermodynamics becomes a law of probability rather than a law of necessity. No previous experience has supported this statistical interpretation. It was enough to deny the existence of molecules, as was done, for example, by the school of energetics, which flourished under the leadership of Mach and Ostwald, for the second law of thermodynamics to become a law of necessity. But after the discovery of Brownian motion, a strict interpretation of the second law became impossible: there was real experience that showed that the second law of thermodynamics is constantly violated in nature, that a perpetual motion machine of the second kind is not only not excluded, but is constantly being realized right before our eyes.

Therefore, at the end of the last century, the study of Brownian motion acquired enormous theoretical significance and attracted the attention of many theoretical physicists, and in particular Einstein.

3.Brownian motion theory

Since the very first physical studies of Brownian motion, attempts have been made to determine the average speed of suspended particles. However, the estimates obtained contained gross errors, since the trajectory of the particle is so complex that it cannot be traced: the average speed varies greatly in magnitude and direction, without tending to any specific limit with increasing observation time. It is impossible to determine the tangent to the trajectory at any point, because the trajectory of the particle does not resemble a smooth curve, but the graph of some function that does not have a derivative.

Horizontal projection (enlarged) of successive positions occupied every 30 seconds by three gum particles with a diameter of slightly more than 1 micron. (Les Atomes - Nature, Volume 91, Issue 2280, pp. 473 (1913)).

3.1Einschnein - the first theory of Brownian motion

In 1902, after graduating from the Federal Institute in Zurich, Einstein became an expert at the Swiss Patent Office in Bern, where he served for seven years. These were happy and productive years for him. Although the salary was barely enough, work in the patent office was not particularly burdensome and left Einstein enough energy and time for theoretical research. His first works were devoted to the forces of interaction between molecules and applications of statistical thermodynamics. One of them, “A New Determination of Molecular Sizing,” was accepted as a doctoral dissertation by the University of Zurich. That same year, Einstein published a small series of papers that not only showed his strength as a theoretical physicist, but also changed the face of physics.

One of these works was devoted to explaining the Brownian motion of particles suspended in a liquid. Einstein related the motion of particles observed in a microscope to the collisions of these particles with molecules; in addition, he predicted that the observation of Brownian motion makes it possible to calculate the mass and number of molecules present in a given volume. This was confirmed several years later by Jean Perrin. This work of Einstein was of particular importance because the existence of molecules, considered nothing more than a convenient abstraction, was still being questioned at that time.

3.2Smoluchowski - origin of the laws of probability in physics

Einstein, who himself conducted brilliant research on Brownian motion around the same years, wrote in his obituary to the memory of Smoluchowski (1917): The kinetic theory of heat achieved general recognition only in 1905-1906, when it was proven that it could quantitatively explain the long-discovered chaotic motion of suspended microscopic particles, i.e. Brownian motion. Smoluchowski created a particularly elegant and visual theory of this phenomenon, based on the kinetic law of uniform distribution of energy... Knowledge of the essence of Brownian motion led to the sudden disappearance of any doubts about the reliability of Boltzmann's understanding of thermodynamic laws [ 9].

The most important thing in the work of Einstein and Smoluchowski on Brownian motion is to establish a connection between the laws of motion of visible and directly measurable Brownian particles suspended in a liquid and the laws of motion of invisible molecules. It turned out that gas laws apply to suspended Brownian particles; their distribution in the gravity field (barometric formula) is the same as the distribution of gases; their average kinetic energy is equal to the average kinetic energy of the molecules of the liquid in which they are suspended. This means that in the Brownian motion of observed particles we have a clear and measurable picture of the kinetic motion of molecules. All this has opened up rich possibilities for various methods of experimental testing of quantities characterizing molecular systems that previously looked only hypothetical. Thus, the results of the study of Brownian motion gave many ways to measure the number of particles in a gram molecule (Avogadro's number) - through measuring the viscosity of gases, the distribution of particles, the diffusion of soluble bodies, the phenomenon of opalescence, the phenomenon of blueness of the sky, etc. In all cases, the results turned out to be surprisingly consistent, within the experimental errors. Jean Perrin, in a report on Brownian motion and molecules, read at the French Physical Society on April 15, 1909, said: It seems to me impossible that a mind free from prejudice should not be greatly impressed by the thought of the extraordinary variety of phenomena which tend so accurately to give the same number, while for each of these phenomena, without being guided by molecular theory, one could expect any value between zero and infinity. From now on it will be difficult to defend with reasonable arguments the hostility to molecular hypotheses . The importance of research into Brownian motion was well understood by Smoluchowski, who at the congress in Münster in 1912 said: ...Here for the first time, Maxwell’s law of velocity distribution and the general idea of ​​heat as a process of motion are taken seriously, while previously all this was usually considered as a kind of poetic comparison .

Studies of Brownian motion and fluctuations inevitably pose methodological problems for scientists about the role of randomness in physics, as Smoluchowski wrote in an article published after his death On the concept of randomness and the origin of the laws of probability in physics .

4.Evidence of the real existence of atoms and molecules

1Jean Baptiste Perrin - decisive experiments.

During studies of cathode rays emitted by a negative electrode (cathode) in a vacuum tube during an electrical discharge, Jean Baptiste Perrin showed in 1895 that they are a stream of negatively charged particles. Soon the belief began to spread that these negative particles, called electrons, were a constituent part of atoms.

Atomic theory stated that elements were composed of discrete particles called atoms, and that chemical compounds were composed of molecules, larger particles containing two or more atoms. By the end of the 19th century. atomic theory became widely accepted among scientists, especially among chemists. However, some physicists believed that atoms and molecules are nothing more than fictitious objects that are introduced for reasons of convenience and are useful in numerical processing of the results of chemical reactions. The Austrian physicist and philosopher Ernst Mach believed that the question of the primary structure of matter is fundamentally unsolvable and should not be the subject of research by scientists. For supporters of atomism, confirmation of the discreteness of matter was one of the fundamental questions that remained unresolved in physics.

Continuing to develop atomic theory, Perrin put forward the hypothesis in 1901 that the atom was a miniature solar system, but could not prove it.

In 1905, Albert Einstein published a paper on Brownian motion, which provided theoretical justification for the molecular hypothesis. He made certain quantitative predictions, but the experiments needed to verify them required such great precision that Einstein doubted their feasibility. From 1908 to 1913, Perrin (at first unaware of Einstein's work) made subtle observations of Brownian motion that confirmed Einstein's predictions.

Perrin realized that if the motion of suspended particles is caused by collisions with molecules, then, based on the well-known gas laws, it is possible to predict their average displacements over a certain period of time, if one knows their size, density and certain characteristics of the liquid (for example, temperature and density). All that was required was to correctly reconcile these predictions with measurements, and then there would be strong evidence for the existence of molecules. However, obtaining particles of the required size and uniformity was not so easy. After many months of painstaking centrifugation, Perrin was able to isolate a few tenths of a gram of homogeneous particles of gum (a yellowish substance obtained from the milky sap of plants). After measuring the characteristics of the Brownian motion of these particles, the results turned out to be quite consistent with molecular theory.

Distribution of the end points of horizontal displacements of a gum particle, transferred parallel to themselves so that the origins of all displacements are in the center of the circle, published in the work of Perrin Brownian motion and the reality of molecules .

Perrin also studied the sedimentation, or settling, of minute suspended particles. If the molecular theory was correct, he reasoned, particles smaller than a certain size would not sink to the bottom of the vessel at all: the upward component of the momentum resulting from collisions with molecules would constantly counteract the downward force of gravity. If the suspension is not subject to disturbance, sedimentation equilibrium will eventually be established, after which the concentration of particles at different depths will not change. If the properties of the suspension are known, then the equilibrium vertical distribution can be predicted.

Perrin made several thousand observations, using microscopic techniques in a very sophisticated and ingenious way and counting the number of particles at different depths in one drop of liquid with a depth step of only twelve hundredths of a millimeter. He discovered that the concentration of particles in a liquid decreases exponentially with decreasing depth, and the numerical characteristics agreed so well with the predictions of molecular theory that the results of his experiments were widely accepted as decisive confirmation of the existence of molecules. Later, he came up with ways to measure not only the linear displacements of particles in Brownian motion, but also their rotation. Perrin's research allowed him to calculate the sizes of molecules and Avogadro's number, i.e. the number of molecules in one mole (the amount of a substance whose mass, expressed in grams, is numerically equal to the molecular weight of this substance). He tested his value for Avogadro's number using five different types of observations and found that it satisfied them all, subject to minimal experimental error. (The currently accepted value of this number is approximately 6.02 1023; Perrin obtained a value 6% higher.) By 1913, when he summarized the already numerous evidence of the discrete nature of matter in his book Les Atomes - “Atoms” the reality of the existence of both atoms and molecules was almost universally accepted.

In 1926, Perrin received the Nobel Prize in Physics “for his work on the discrete nature of matter and especially for his discovery of sedimentation equilibrium.”

4.2Theodor Svedberg - determination of the size of a protein molecule

Swedish chemist Theodor Svedberg, just 3 years after entering Uppsala University, receives a doctorate for his dissertation on colloidal systems.

Colloidal systems are a mixture in which tiny particles of one substance are dispersed in another substance. Colloidal particles are larger than those of true solutions, but not so large that they can be viewed under a microscope or that they precipitate under the influence of gravity. Their sizes vary from 5 nanometers to 200 nanometers. Examples of colloidal systems are Indian ink (coal particles in water), smoke (solid particles in the air), and butterfat (tiny globules of fat in a water solution). In his doctoral dissertation, Svedberg described a new method of using oscillatory electrical discharges between metal electrodes located in a liquid in order to obtain relatively pure colloidal solutions of metals. The previously adopted method using direct current was characterized by a high degree of contamination.

In 1912, Svedberg became the first teacher of physical chemistry at Uppsala University and remained in this position for 36 years. His careful study of diffusion and Brownian motion of colloidal particles (the random movement of tiny particles suspended in a liquid) became further evidence in favor of Jean Perrin's 1908 experimental confirmation of the theoretical work of Albert Einstein and Marian Smoluchowski, who established the presence of molecules in solution. Perrin proved that the size of large colloidal particles could be determined by measuring the rate at which they precipitated. Most colloidal particles, however, settle so slowly in their environment that this method was impractical.

To determine the size of particles in colloidal solutions, Svedberg used an ultramicroscope designed by Richard Zsigmondy. He believed that the sedimentation of colloidal particles would be accelerated under the stronger gravitational field created by a high-speed centrifuge. During his stay at the University of Wisconsin in 1923, where he was a visiting professor for 8 months, Swedberg began building an optical centrifuge in which the deposition of particles would be recorded by photography. Since the particles moved, not only by settling, but also under the influence of conventional currents, Svedberg could not determine the particle sizes using this method. He knew that hydrogen's high thermal conductivity could help eliminate temperature differences and therefore convection currents. By constructing a wedge-shaped cell and placing a rotating cell in a hydrogen atmosphere, Svedberg, back in Sweden in 1924, together with his colleague Hermann Rinde, achieved deposition without convection. In January 1926, the scientist tested a new model of ultracentrifuge with oil rotors, in which he achieved 40,100 revolutions per minute. At such a speed, a force 50,000 times greater than the force of gravity acted on the settling system.

In 1926, Svedberg was awarded the Nobel Prize in Chemistry “for his work in the field of dispersed systems.” In his opening speech on behalf of the Royal Swedish Academy of Sciences, H. G. Söderbaum said: “The movement of particles suspended in a liquid ... clearly demonstrates the real existence of molecules, and therefore of atoms - a fact all the more significant since until quite recently the influential a school of scientists declared these material particles to be figments of the imagination.”

5.Modern science of Brownian motion

The fundamental problem of the relationship between the reversibility of the equations of classical and quantum mechanics and the irreversibility of thermodynamic processes is closely related to the concept of chaos and the applicability of a probabilistic description. Of the many solutions to the equations of dynamics, only those that are resistant to interaction with the environment of the physical system are realized, thus irreversibility is a property of open systems. Any system can be considered closed only approximately (since there is always external noise), therefore irreversibility has a universal character.

Currently the term Brownian motion has a very broad meaning and the theory of Brownian motion is a branch of open systems physics associated with stochastic processes, self-organization processes and dynamic chaos.

In the statistical theory of nonequilibrium processes atoms , as microscopic structural units, are used only at the stage of constructing a model of the macroscopic system under consideration. Next, dissipative nonlinear equations are applied continuum mechanics for deterministic functions. There are three levels of description - kinetic, hydrodynamic and chemical kinetics. Separately, we can distinguish stochastic equations (for example, equations of the theory of turbulence) for random functions. Refinement of the theory is possible by taking into account fluctuations, which was first done by Langevin when considering the linear dissipative dynamic equation of motion of a Brownian particle. In various systems the role Brownian particles distribution functions, hydrodynamic functions and concentrations can play.

Taking into account fluctuations is necessary when studying molecular light scattering and nonequilibrium phase transitions, the sequences of which form self-organization processes. The applications of the nonlinear theory of Brownian motion are extremely extensive: from ecology and finance to methods for controlled movement of nanoparticles - Brownian motors . Brownian motors associated with dissipative dynamics in nonequilibrium quantum systems.

The development of a mathematical description of stochastic processes stimulated progress in various fields, leading to the emergence of the modern formulation of quantum mechanics based on path integrals and new directions of research, such as quantum chaos and quantum Brownian noise. Experimental progress in the field of high-energy physics and astrophysics has stimulated interest in the processes of relativistic diffusion and the construction of relativistic statistical mechanics; at present, many questions still remain open.

Since its discovery, Brownian motion has evolved from an object of private scientific curiosity into a key concept of modern science.

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