In the second half of the nineteenth century, the study of Brownian (chaotic) molecular motion aroused keen interest among many theoretical physicists of that time. The substance developed by the Scottish scientist James, although it was generally recognized in European scientific circles, existed only in a hypothetical form. There was no practical confirmation of it at that time. The movement of molecules remained inaccessible to direct observation, and measuring their speed seemed like an insoluble scientific problem.
That is why experiments capable of proving in practice the very fact of the molecular structure of a substance 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 practical substantiation and proof of the validity of one of the most progressive theories of that time - molecular kinetic theory.
By the beginning of the twentieth century, world science had reached a sufficient level of development for the emergence of real opportunities for experimental verification of Maxwell's theory. The German physicist Otto Stern in 1920, using the method of molecular beams, 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 accuracy of the assessment of atoms, which followed from the hypothetical assumptions made by Maxwell. True, Stern's experience was able to give only 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 discs that had radial holes and were displaced relative to each other by a certain angle. By varying the rotation speed of the unit and the angle between the holes, Lammert was able to isolate individual molecules from the beam, which have different speed indicators. 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 setup was created, necessary for conducting experiments of this kind. It consisted of a pair of cylinders designed by Stern himself. A thin platinum rod with a silver coating 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 turn through a certain angle. In this way, Stern determined the speed of their movement.
But this is not Otto Stern's only scientific achievement. A year later, together with Walter Gerlach, he conducted an experiment that confirmed the presence of spin in atoms and proved the fact of their spatial quantization. The Stern-Gerlach experience required the creation of a special experimental setup with a powerful one at its core. Under the influence of the magnetic field generated by this powerful component, they deflected according to the orientation of their own magnetic spin.
The assumption that the molecules of a body can have any speed was first theoretically proved in 1856 by an English physicist J. Maxwell... He believed that the speed of molecules at a given moment in time is random, and therefore their distribution over speeds is statistical in nature ( Maxwell distribution).
The nature of the distribution of molecules over velocities established by him is graphically represented by the curve shown in Fig. 1.17. The presence of a maximum (bump) in it indicates that the velocities of most molecules fall within a certain interval. It is asymmetric, since there are fewer molecules with high speeds than with low ones.
Fast molecules determine the course of many physical processes under normal conditions. For example, thanks to them, the evaporation of liquids occurs, because at room temperature, most molecules do not have enough energy to break the bond with other molecules (it is much higher (3/2). KT), and for molecules with high speeds it is sufficient.
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| Rice. 1.18. O. Stern's experience |
The distribution of molecules by the velocities of McSwell for a long time remained experimentally unconfirmed, and only in 1920 the German scientist O. Stern managed to experimentally measure the rate of thermal motion of molecules.
On a horizontal table, which could rotate around a vertical axis (Fig. 1.18), there were two coaxial cylinders A and B. From which air was pumped out to a pressure of about 10 -8 Pa. A platinum wire C covered with a thin layer of silver was located along the axis of the cylinders. When an electric current passed through the wire, it heated up, and silver evaporated intensively from its surface, which mainly settled on the inner surface of cylinder A. Part of the silver molecules passed through a narrow slot in cylinder A to the outside, falling on cylinder B. If the cylinders did not rotate, the silver molecules, moving straight-linearly, settled opposite the slot in the circumference of point D. When the system was set in motion with an angular velocity of about 2500-2700 rpm, the image shifted to point E, and its edges “eroded”, forming a hillock with gentle slopes.
In science Stern's experience finally confirmed the validity of the molecular kinetic theory.
Considering that the offset l =v. t = ω R A t, and the flight time of molecules t = (R B -R A) /v, we get:
l =ω(R B -R A)R A /v.
As can be seen from the formula, the mixing of a molecule from point D depends on the speed of its movement. Calculating the velocity of silver molecules from the data Stern's experience at a spiral temperature of about 1200 ° C, they gave values in the range from 560 to 640 m / s, which was in good agreement with the theoretically determined average molecular speed of 584 m / s.
The average rate of thermal motion of gas molecules can be found using the equation p =nm 0v̅ 2 x:
E̅ = (3/2). kT = m 0 v̅ 2/2.
Hence, the average square of the speed of the gradual movement of the molecule is:
v̅ 2 = 3kT /m 0, or v̅ =√(v̅ 2) =√(3 kT /m 0). Material from the site
The square root of the mean square of the velocity of the molecule is called mean square speed.
Taking into account that k = R / N A and m 0 = M / N A, from the formula v̅ =√(3 kT /m 0) we get:
v̅ =√ (3RT / M).
Using this formula, you can calculate the root mean square velocity of molecules for any gas. For example, at 20 ° C ( T= 293K) for oxygen it is 478 m / s, for air - 502 m / s, for hydrogen - 1911 m / s. Even at such significant speeds (approximately equal to the speed of propagation of sound in a given gas), the movement of gas molecules is not so rapid, since numerous collisions occur between them. Therefore, the trajectory of motion of a molecule resembles the trajectory of motion of a Brownian particle.
The mean square velocity of a molecule does not differ significantly from the average velocity of its thermal motion - it is approximately 1.2 times greater.
On this page material on topics:
Molecular physics report
Grade 10 Physics Molecular Speed Stern's Experience
Stern's experience in summary
Abstract about Stern's experience
Physics report Stern's experiment
Questions about this material:
Lecture 15
Molecular physics
Questions
1. Maxwell's law of the distribution of ideal gas molecules in terms of velocities and energies.
2. Ideal gas in a uniform gravitational field.
Barometric formula. Boltzmann distribution.
3. Average number of collisions and average mean free path of molecules.
4. Phenomena of transport in gases.
1. Maxwell's law of molecular distribution
ideal gas for velocities and energies
In a gas in equilibrium, a stationary velocity distribution of molecules is established, which obeys Maxwell's law.
Clausius equation 
, (1)
Mendeleev - Clapeyron equation 
(2)
, (3)
those. root mean square velocity is proportional to the square root of the absolute temperature of the gas.
Maxwell's law is described by the function f(v) called molecular velocity distribution function . If we divide the range of molecular velocities into small intervals equal to d v, then for each velocity interval there will be a certain number of molecules d N(v), having the speed included in this interval. Function f(v) determines the relative number of molecules d N(v)/ N, whose speeds lie in the range from v before v + d v, i.e.
Maxwellian velocity distribution function
, where 
.
Applying the methods of probability theory, Maxwell found the function f(v) –the law for the velocity distribution of ideal gas molecules:
.
(4)
.
(5)
Most likely speedv c is the speed near which the largest number of molecules falls on a unit interval of speed.
Average Molecule Velocity
(arithmetic mean speed):
(7)
Mean square velocity
(8)
From formula (6) it follows that as the temperature rises, the maximum of the velocity distribution function of molecules shifts to the right (the value of the most probable velocity becomes higher). However, the area bounded by the curve remains unchanged; therefore, as the temperature rises, the velocity distribution curve of molecules stretches and decreases.
Stern's experience
.
(9)
2. Ideal gas in a uniform gravitational field. Barometric formula. Boltzmann distribution
If there was no thermal motion, then all the molecules of atmospheric air would fall to the Earth; if there was no gravitation, the atmospheric air would be scattered throughout the universe. Gravity and thermal motion bring the gas into a state in which its concentration and pressure decrease with height.
Let's get the law of pressure change with height.
Differential pressure R and p + d p is equal to the weight of the gas enclosed in the volume of a cylinder with a base area equal to one and a height d h
p–
(p + d p)
=
g d h
d p = - g d h
(10)
From the equation of state for an ideal gas:
(11)
(11)
(10)
,
(12)
where R and R 0 - gas pressure at altitudes h and h= 0.
Formula (12) is called barometric... It follows from it that the pressure decreases exponentially with height.
Barometric formula allows you to determine altitude h using a barometer. A specially calibrated barometer for direct reading of the height above sea level is called altimeter... It is widely used in aviation and mountain climbing.
Generalization of the barometric formula
, because 
.
, Is the Boltzmann distribution (13)
where n and n 0 - concentration of molecules at heights h0 and h= 0, respectively.
Special cases
1.
, i.e. thermal motion tends to scatter particles evenly throughout the volume.
2.
(no thermal movement), i.e. all particles would occupy a state with minimum (zero) potential energy (in the case of the Earth's gravitational field, the molecules would collect on the Earth's surface).
3. Average number of collisions and average mean free path of molecules
The mean free path of molecules
is called the path that a molecule travels between two successive collisions with other molecules. Effective molecule diameterd is called the smallest distance at which the centers of two molecules approach each other in a collision.
BROWN Robert (), English botanist Described the nucleus of the plant cell and the structure of the ovule. In 1828 he published "A Brief Report on Observations in a Microscope ...", in which he described the motion of Brownian particles discovered by him. Described the nucleus of a plant cell and the structure of the ovule. In 1828 he published "A Brief Report on Observations in a Microscope ...", in which he described the motion of Brownian particles discovered by him.
Brownian motion - this is the thermal movement of particles suspended in a liquid or gas - for a year, I observed the phenomenon by examining the spores of a lymphoid suspended in a microscope through a microscope. Brownian motion never stops, particles move randomly. This is a heat movement.
PERRIN Jean Baptiste (), French physicist. Experimental studies by Perrin of Brownian motion () finally proved the reality of the existence of molecules. Nobel Prize (1926).
Perrin's experiments Observed Brownian particles in very thin layers of liquid He concluded that the concentration of particles in a gravity field should decrease with height according to the same law as the concentration of gas molecules. The advantage is that the mass of Brownian particles is faster due to the large mass. Based on the counting of these particles at different heights, determining the Avogadro constant in a new way.
MAXWELL James Clerk ((), English physicist, creator of classical electrodynamics, one of the founders of statistical physics Maxwell was the first to state the statistical nature of the laws of nature.In 1866 he discovered the first statistical law of the distribution of molecules by velocities (Maxwell's distribution).
BOLZMAN Ludwig (), Austrian physicist, one of the founders of statistical physics and physical kinetics. Derived the distribution function, named after him, and the basic kinetic equation of gases. Boltzmann generalized the law of the distribution of the velocities of molecules in gases in an external force field, and established a formula for the distribution of gas molecules over coordinates in the presence of an arbitrary potential field ().
STERN Otto (), physicist. Born in Germany, from 1933 he lived in the USA. Otto Stern measured (1920) the rate of thermal motion of gas molecules (Stern's experiment). The experimental determination of the rates of thermal motion of gas molecules, carried out by O. Sterno, confirmed the correctness of the foundations of the kinetic theory of gases. Nobel Prize, 1943.
Stern's experiment The cylinders began to rotate at a constant angular velocity. Now the atoms that passed through the slot were no longer settling directly in front of the slot, but displaced by a certain distance, since during their flight the outer cylinder had time to turn through a certain angle. When the cylinders rotated at a constant speed, the position of the strip formed by the atoms on the outer cylinder was displaced by a certain distance.
Stern's experiment Knowing the values of the radii of the cylinders, the speed of their rotation and the magnitude of the displacement, it is easy to find the speed of motion of the atoms. The flight time of an atom t from the slot to the wall of the outer cylinder can be found by dividing the path traveled by the atom and equal to the difference in the radii of the cylinders by the atom's velocity v. During this time, the cylinders turned through an angle φ, the value of which we find by multiplying the angular velocity ω by the time t. Knowing the value of the angle of rotation and the radius of the outer cylinder R 2, it is easy to find the value of the displacement L and obtain an expression from which the speed of motion of the atom can be expressed
Think ... Multiple repetitions of Stern's experiment made it possible to establish that with an increase in temperature, the section of the strip with the maximum thickness shifts towards the beginning. What does it mean? Answer: with an increase in temperature, the velocities of molecules increase, and then the most probable velocity is in the region of high temperatures.
Year. The experiment was one of the first practical proofs of the consistency of the molecular kinetic theory of the structure of matter. It directly measured the velocities of the thermal motion of molecules and confirmed the presence of a velocity distribution of gas molecules.
To carry out the experiment, Stern prepared a device consisting of two cylinders of different radii, the axis of which coincided, and a platinum wire with a deposited layer of silver was located on it. A sufficiently low pressure was maintained in the space inside the cylinders by continuous evacuation of air. When an electric current was passed through the wire, the melting point of silver was reached, because of 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 temperature of silver. A narrow slit was made in the inner cylinder through which atoms could freely fly further. The walls of the cylinders were specially cooled, which facilitated the settling of the atoms falling on them. In this state, on the inner surface of the large cylinder, a fairly clear narrow strip of silver plaque was formed, located directly opposite the slit of the small cylinder. Then the whole system began to rotate with a certain sufficiently large angular velocity ω ... In this case, the plaque band shifted in the direction opposite to the direction of rotation and lost its sharpness. Measuring the offset s In the darkest part of the strip from its position, when the system was at rest, Stern determined the flight time through which he found the speed of the molecules:
,
where s- strip shift, l is 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 in favor of the fact that the speeds of atoms are different and distributed according to a certain law - Maxwell's distribution law: atoms, those who moved faster, displaced relative to the strip obtained at rest by smaller distances than those that moved more slowly.
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Literature
- A short dictionary of physical terms / Comp. A. I. Bolsun, rec. M.A.Elyashevich. - Mn. : Higher school, 1979. - S. 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) (unavailable link - history) ... Retrieved April 5, 2008.
- Stern's experience- an article from the Great Soviet Encyclopedia.
Excerpt from Stern's Experience
So he lay and now on his bed, leaning his heavy, large disfigured head on his chubby hand, thinking, peering into the darkness with one eye open.Since Bennigsen, who corresponded with the sovereign and had the most strength in the headquarters, avoided him, Kutuzov was calmer in the sense that he and the troops would not be forced to again participate in useless offensive operations. The lesson of the Tarutino battle and the eve of it, painfully remembered by Kutuzov, should also have worked, he thought.
“They need to understand that we can only lose by acting offensively. Patience and time, here are my warriors, heroes! " Thought Kutuzov. He knew not to pick the apple while it was green. It will fall by itself when it is ripe, and you pick the green, spoil the apple and the tree, and set your teeth on edge. He, as an experienced hunter, knew that the beast was wounded, wounded as much as the entire Russian force could hurt, but lethally or not, this was not yet an clarified question. Now, from the dispatches of Loriston and Bertelemi and from the reports of the partisans, Kutuzov almost knew that he was mortally wounded. But more proof was needed, it was necessary to wait.
“They want to run to see how they killed him. Wait, you will see. All maneuvers, all offensives! He thought. - For what? All to excel. It’s like there’s something fun about fighting. They are like children, from whom you cannot get a sense, as was the case, because everyone wants to prove how they can fight. But 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 Petersburg), they invented them all. And they are all innumerable! "
The unresolved question of whether the wound inflicted in Borodino was fatal or not, has been hanging over Kutuzov's head for a whole month. On the one hand, the French occupied Moscow. On the other hand, undoubtedly with all his being, Kutuzov felt that the terrible blow in which he, together with all the Russian people, strained all his strength, was bound to be fatal. But in any case, proofs were needed, and he had been waiting for them for a month, and the further time passed, the more impatient he became. Lying on his bed in his sleepless nights, he did what these young generals did, the very thing for which he reproached them. He invented all possible accidents in which this true, already accomplished death of Napoleon would be expressed. He invented these accidents 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 he imagined. He invented all kinds of movements for the Napoleonic army, all or parts of it - towards Petersburg, towards it, bypassing it, and invented (which he was most afraid of) the chance that Napoleon would fight against him with his own weapon, that he would remain in Moscow waiting for him. Kutuzov even invented the movement of Napoleon's army back to Medyn and Yukhnov, but one thing that he could not foresee was what happened, that crazy, convulsive throwing of Napoleon's army during the first eleven days of his march from Moscow - the throwing that made it possible something that Kutuzov still did not dare to think about: the complete extermination of the French. Dorokhov's reports about Brusier's division, news from the partisans about the calamities of Napoleon's army, rumors about preparations for a march from Moscow - all 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 how much weight should be attributed to rumors, he knew how people who want something are capable of grouping all the news so that they seem to confirm what they want, and he knew how, in this case, they willingly let go of everything that contradicts. And the more Kutuzov wanted this, the less he allowed himself to believe it. This question occupied all his mental strength. All the rest was for him only the habitual fulfillment of life. Such a habitual execution and subordination of life were his conversations with the staff, letters to m me Stael, which he wrote from Tarutin, reading novels, distributing awards, correspondence with St. Petersburg, etc. But the death of the French, foreseen by him alone, was his soul's only desire.
