Conditions for performing the stern experiment. Stern experience. The essence of the stern experience

From formulas

we obtain a formula for calculating the root mean square speed of movement of molecules of a monatomic gas:

where R is the universal gas constant.

Thus depends on the temperature and nature of the gas. So, at 0°C for hydrogen it is equal to 1800 m/s. for nitrogen - 500 m/s.

O. Stern was the first to experimentally determine the speed of molecules. In the chamber from which air has been evacuated, there are two coaxial cylinders 1 and 2 (Fig. 1), which can rotate around an axis at a constant angular velocity.

A silver-plated platinum wire is stretched along the axis, through which an electric current is passed. It heats up and the silver evaporates. Silver atoms enter cylinder 1 through slot 4 in the wall of cylinder 2 and settle on its inner surface, leaving a trace in the form of a narrow strip parallel to the slot. If the cylinders are stationary, then the strip is located opposite the slot (point B in Fig. 2, a) and has the same thickness.

When the cylinder rotates uniformly with angular velocity, the strip moves in the direction opposite to the rotation by a distance s relative to point B (Fig. 2, b). Point B of cylinder 1 has shifted by this distance in time t, which is necessary for the silver atoms to travel a distance equal to R - r, where R and r are the radii of cylinders 1 and 2.

where is the linear speed of points on the surface of cylinder 1. Hence

Speed ​​of silver atoms

Knowing R, r, and having measured s experimentally, using this formula one can calculate the average speed of movement of silver atoms. In the Stern experiment. This value coincides with the theoretical value of the root mean square speed of molecules. This serves as experimental proof of the validity of formula (1), and consequently, formula (3).

In Stern's experiment, it was discovered that the width of the strip on the surface of a rotating cylinder is much larger than the geometric image of the slit and its thickness is not the same in different places (Fig. 3, a). This can only be explained by the fact that the silver atoms move at different speeds. Atoms flying at a certain speed reach point B'. Atoms flying faster end up at a point lying in Figure 2 above point B’, and atoms flying slower end up below point B’. Thus, each point in the image corresponds to a certain speed, which can be easily determined from experience. This explains the fact that the thickness of the layer of silver atoms deposited on the surface of the cylinder is not the same everywhere. The greatest thickness is in the middle part of the layer, and at the edges the thickness decreases.

Studying the cross-sectional shape of a strip of deposited silver using a microscope showed that it has a shape approximately corresponding to that shown in Figure 3, b. Based on the thickness of the deposited layer, one can judge the velocity distribution of silver atoms.

Let us divide the entire range of experimentally measured velocities of silver atoms into small ones. Let be one of the speeds of this interval. Using the density of the layer, we calculate the number of atoms having a speed in the range from , and plot the function

where N is the total number of silver atoms deposited on the surface of the cylinder. We obtain the curve shown in Figure 4. It is called the velocity distribution function of molecules.

The area of ​​the shaded area is

those. equal to the relative number of atoms having a speed within

We see that the numbers of particles with speeds from different intervals are sharply different. There is some speed, around the value of which are the speeds at which the largest number of molecules move. It is called the most probable speed, and it corresponds to the maximum in Figure 4. This curve corresponds well to the curve obtained by J. Maxwell, who, using the statistical method, theoretically proved that in gases that are in a state of thermodynamic equilibrium, a certain value is established that does not change with time, the distribution of molecules by speed, which obeys a well-defined statistical law, graphically depicted by the curve. The most probable speed, as Maxwell showed, depends on the temperature of the gas and the mass of its molecules according to the formula

correctness of the basics kinetic theory of gases . The gas under study in the experiment was rarefied silver vapor, which was obtained by evaporation of a layer of silver deposited on a platinum wire heated by an electric current. The wire was located in a vessel from which the air was pumped out, so the silver atoms freely scattered in all directions from the wire. To obtain a narrow beam of flying atoms, a barrier with a slit was installed in their path, through which the atoms fell onto a brass plate that was at room temperature. Silver atoms were deposited on it in the form of a narrow strip, forming a silver image of the slit. A special device was used to set the entire device into rapid rotation around an axis parallel to the plane of the plate. Due to the rotation of the device, the atoms fell into another place on the plate: while they flew the distance l from the slot to the plate, the plate shifted. The displacement increases with the angular velocity w of the device and decreases with increasing speed v silver atoms. Knowing w And l, can be determined v. Since atoms move at different speeds, the strip blurs out and becomes wider when the device is rotated. The density of the deposit at a given location on the strip is proportional to the number of atoms moving at a certain speed. The highest density corresponds to the most probable speed of the atoms. Received in Stern experience the values ​​of the most probable speed are in good agreement with the theoretical value obtained based on Maxwell distribution molecules by speed.

Article about the word " Stern experience" in the Great Soviet Encyclopedia was read 5742 times

In the second half of the nineteenth century, the study of Brownian (chaotic) motion of molecules aroused keen interest among many theoretical physicists of that time. The substance developed by the Scottish scientist James, although it was generally accepted in European scientific circles, existed only in a hypothetical form. There was no practical confirmation of it then. The movement of molecules remained inaccessible to direct observation, and measuring their speed seemed simply an insoluble scientific problem.

That is why experiments capable of proving in practice the very fact of the molecular structure of matter and determining the speed of movement of its invisible particles were initially perceived as fundamental. The decisive importance of such experiments for physical science was obvious, since it made it possible to obtain a practical justification and proof of the validity of one of the most progressive theories of that time - molecular kinetics.

By the beginning of the twentieth century, world science had reached a sufficient level of development for the emergence of real possibilities for experimental verification of Maxwell's theory. The German physicist Otto Stern in 1920, using the molecular beam method, which was invented by the Frenchman Louis Dunoyer in 1911, was able to measure the speed of movement of gas molecules of silver. Stern's experiment irrefutably proved the validity of the law. The results of this experiment confirmed the correctness of the assessment of atoms, which followed from the hypothetical assumptions made by Maxwell. True, Stern’s experience could only provide very approximate information about the very nature of the speed gradation. Science had to wait another nine years for more detailed information.

Lammert was able to verify the distribution law with greater accuracy in 1929, who somewhat improved Stern’s experiment by passing a molecular beam through a pair of rotating disks that had radial holes and were shifted relative to each other by a certain angle. By changing the rotation speed of the unit and the angle between the holes, Lammert was able to isolate individual molecules from the beam that have different speed characteristics. But it was Stern’s experience that laid the foundation for experimental research in the field of molecular kinetic theory.

In 1920, the first experimental installation necessary for conducting experiments of this kind was created. It consisted of a pair of cylinders designed personally by Stern. A thin platinum rod coated with silver was placed inside the device, which evaporated when the axis was heated with electricity. Under vacuum conditions that were created inside the installation, a narrow beam of silver atoms passed through a longitudinal slit cut on the surface of the cylinders and settled on a special external screen. Of course, the unit was in motion, and during the time the atoms reached the surface, it managed to rotate through a certain angle. In this way, Stern determined the speed of their movement.

But this is not the only scientific achievement of Otto Stern. A year later, he, together with Walter Gerlach, conducted an experiment that confirmed the presence of spin in atoms and proved the fact of their spatial quantization. The Stern-Gerlach experiment required the creation of a special experimental setup with power at its core. Under the influence of the magnetic field generated by this powerful component, they were deflected according to the orientation of their own magnetic spin.

Year. The experiment was one of the first practical proofs of the validity of the molecular kinetic theory of the structure of matter. It directly measured the speed of thermal motion of molecules and confirmed the presence of a distribution of gas molecules by speed.

To conduct the experiment, Stern prepared a device consisting of two cylinders of different radii, the axis of which coincided and a platinum wire coated with a layer of silver was placed on it. A sufficiently low pressure was maintained in the space inside the cylinders through continuous pumping of air. When an electric current was passed through the wire, the melting point of silver was reached, due to which the silver began to evaporate and the silver atoms flew to the inner surface of the small cylinder uniformly and rectilinearly at a speed v, determined by the heating temperature of the platinum wire, i.e., the melting point of silver. A narrow slit was made in the inner cylinder, through which atoms could fly further without hindrance. The walls of the cylinders were specially cooled, which contributed to the settling of atoms falling on them. In this state, a fairly clear narrow strip of silver plaque formed on the inner surface of the large cylinder, located directly opposite the slit of the small cylinder. Then the entire system began to rotate with a certain sufficiently high angular velocity ω . In this case, the plaque band shifted in the direction opposite to the direction of rotation and lost its clarity. By measuring the displacement s the darkest part of the strip from its position when the system was at rest, Stern determined the flight time, after which he found the speed of movement of the molecules:

$t=\backslash frac(s)(u)=\backslash frac(l)(v)\; \backslash Rightarrow\; v=\backslash frac(ul)(s)=\backslash frac(\backslash omega\; R\_(big)\; (R\_(big)-R\_(small\; )))(s)$,

Where s- stripe offset, l- the distance between the cylinders, and u- the speed of movement of the points of the outer cylinder.

The speed of movement of silver atoms found in this way coincided with the speed calculated according to the laws of molecular kinetic theory, and the fact that the resulting strip was blurred testified to the fact that the speeds of the atoms are different and distributed according to a certain law - Maxwell’s distribution law: atoms, those moving faster shifted relative to the strip obtained at rest by shorter distances than those moving more slowly.

Write a review of the article "Stern Experience"

Literature

• Brief dictionary of physical terms / Comp. A. I. Bolsun, rector. M. A. Elyashevich. - Mn. : Higher School, 1979. - P. 388. - 416 p. - 30,000 copies.

Links

• Landsberg. Elementary physics textbook. Volume 1. Mechanics. Heat. Molecular physics. - 12th ed. - M.: FIZMATLIT, 2001. - ISBN 5-9221-0135-8.
• Internet school Prosveshchenie.ru.(Russian) (inaccessible link - story) . Retrieved April 5, 2008.
• Stern experience- article from the Great Soviet Encyclopedia.

Excerpt characterizing the Stern Experiment

So he lay now on his bed, leaning his heavy, large, disfigured head on his plump arm, and thought, with one eye open, peering into the darkness.
Since Bennigsen, who corresponded with the sovereign and had the most power in the headquarters, avoided him, Kutuzov was calmer in the sense that he and his troops would not be forced to again participate in useless offensive actions. The lesson of the Tarutino battle and its eve, painfully memorable for Kutuzov, should also have had an effect, he thought.
“They must understand that we can only lose by acting offensively. Patience and time, these are my heroes!” – thought Kutuzov. He knew not to pick an apple while it was green. It will fall on its own when it is ripe, but if you pick it green, you will spoil the apple and the tree, and you will set your teeth on edge. He, as an experienced hunter, knew that the animal was wounded, wounded as only the entire Russian force could wound, but whether it was fatal or not was a question that had not yet been clarified. Now, according to the dispatches of Lauriston and Berthelemy and according to the reports of the partisans, Kutuzov almost knew that he was mortally wounded. But more evidence was needed, we had to wait.
“They want to run and see how they killed him. Wait and see. All maneuvers, all attacks! - he thought. - For what? Everyone will excel. There's definitely something fun about fighting. They are like children from whom you can’t get any sense, as was the case, because everyone wants to prove how they can fight. That's not the point now.
And what skillful maneuvers all these offer me! It seems to them that when they invented two or three accidents (he remembered the general plan from St. Petersburg), they invented them all. And they all have no number!”
The unresolved question of whether the wound inflicted in Borodino was fatal or not fatal had been hanging over Kutuzov’s head for a whole month. On the one hand, the French occupied Moscow. On the other hand, undoubtedly with his whole being Kutuzov felt that that terrible blow, in which he, together with all the Russian people, strained all his strength, should have been fatal. But in any case, proof was needed, and he had been waiting for it for a month, and the more time passed, the more impatient he became. Lying on his bed on his sleepless nights, he did the very thing that these young generals did, the very thing for which he reproached them. He came up with all possible contingencies in which this certain, already accomplished death of Napoleon would be expressed. He came up with these contingencies in the same way as young people, but with the only difference that he did not base anything on these assumptions and that he saw not two or three, but thousands. The further he thought, the more of them appeared. He came up with all kinds of movements of the Napoleonic army, all or parts of it - towards St. Petersburg, against it, bypassing it, he came up with (which he was most afraid of) and the chance that Napoleon would fight against him with his own weapons, that he would remain in Moscow , waiting for him. Kutuzov even dreamed up the movement of Napoleon’s army back to Medyn and Yukhnov, but one thing he could not foresee was what happened, that crazy, convulsive rushing of Napoleon’s army during the first eleven days of his speech from Moscow - the throwing that made it possible something that Kutuzov still did not dare to think about even then: the complete extermination of the French. Dorokhov's reports about Broussier's division, news from the partisans about the disasters of Napoleon's army, rumors about preparations for departure from Moscow - everything confirmed the assumption that the French army was defeated and was about to flee; but these were only assumptions that seemed important to young people, but not to Kutuzov. With his sixty years of experience, he knew what weight should be attributed to rumors, he knew how capable people who want something are of grouping all the news so that they seem to confirm what they want, and he knew how in this case they willingly miss everything that contradicts. And the more Kutuzov wanted this, the less he allowed himself to believe it. This question occupied all his mental strength. Everything else was for him just the usual fulfillment of life. Such habitual fulfillment and subordination of life were his conversations with staff, letters to m me Stael, which he wrote from Tarutin, reading novels, distributing awards, correspondence with St. Petersburg, etc. n. But the death of the French, foreseen by him alone, was his spiritual, only desire.

The study of diffusion and Brownian motion provides some insight into the speed of chaotic movement of gas molecules. One of the simplest and most visual experiments for its determination is the experiment of O. Stern, performed by him in 1920. The essence of this experiment is as follows.

On a horizontal table, which can rotate around the O axis (Fig. 3.2), cylindrical surfaces A and B are strengthened perpendicular to the table. Surface B is solid, and in surface A there is a narrow slot parallel to the O axis. A silver-plated platinum wire is located vertically along the O axis, which is included in the electrical circuit. When current is passed through, the wire glows and silver evaporates from its surface. Silver molecules fly in all directions and mainly settle on the inner side of the cylindrical surface A. Only a narrow beam of silver molecules flies through the gap in this

surface and settles in area M on surface B. The width of the deposit in M ​​is determined by the width of the gap in surface A. To prevent silver molecules from being scattered during collisions with air molecules, the entire installation is covered with a cap, from under which air is pumped out. The narrower the gap in surface A, the narrower the coating in area M and the more accurately the speed of movement of molecules can be determined.

The very definition of speed is based on the following idea. If the entire installation is brought into rotation around the O axis with a constant angular velocity, then during the time during which the molecule flies from the slit to surface B, the latter will have time to rotate and the deposit will shift from region M to region K. Consequently, the flight time of the molecule along the radius and the time the displacement of point M of surface B by the same distance. Since the molecule flies uniformly, then

where is the desired speed, is the radius of the cylindrical surface A. Since the linear speed of points on surface B is equal to south, time can be expressed by another formula:

Thus,

Since during the experiment they remain constant and are determined in advance, then by measuring you can find the speed of the molecule. In Stern's experiment it turned out to be close to 500 m/s.

Since the deposit in region K appears blurred, we can conclude that the silver molecules fly to surface B at different speeds. The average molecular speeds can be expressed mathematically by the formula

As an example, we note that at 0 °C the average speed of hydrogen molecules is 1840 m/s, and that of nitrogen is 493 m/s. The change in plaque thickness in the K region gives an idea of ​​the distribution of molecules according to the speed of their movement. It turns out that a small number of molecules have speeds several times higher than the average speed.

(Think where in Fig. 3.2 they left a trace of molecules whose speeds are greater than the average speed and how the position of the deposit will change if the current in the wire O is increased.)