Determination of the elementary electric charge by electrolysis. Methods for determining the elementary electric charge - abstract Laboratory work measuring the charge of an electron

Methodical note. The electron is already known to students from the course of chemistry and the corresponding section of the program of grade VII. Now you need to deepen your understanding of the first elementary particle of matter, recall what has been studied, connect it with the first topic of the section "Electrostatics" and move on to a higher level of interpretation of the elementary charge. It should be borne in mind the complexity of the concept of electric charge. The proposed digression can help to reveal this concept and get to the heart of the matter.

The electron has a complicated history. To reach the goal in the shortest way, it is advisable to lead the story as follows.

The discovery of the electron was the result of numerous experiments. By the beginning of the XX century. the existence of the electron has been established in a number of independent experiments. But, despite the colossal experimental material accumulated by entire national schools, the electron remained a hypothetical particle, because experience had not yet answered a number of fundamental questions.

First of all, there was not a single experiment in which individual electrons would participate. The elementary charge was calculated on the basis of measurements of the microscopic charge under the assumption that a number of hypotheses were correct.

There were skeptics who generally ignored the discovery of the electron. Academician A.F. Ioffe wrote in his memoirs about his teacher V.K. needs".

The question of the mass of the electron has not been resolved, it has not been proved that both on conductors and on dielectrics the charges consist of electrons. The concept of "electron" did not have an unambiguous interpretation, because the experiment had not yet revealed the structure of the atom (Rutherford's planetary model appeared in 1911, and Bohr's theory in 1913).

The electron has not yet entered the theoretical constructions. Lorentz's electron theory featured a continuously distributed charge density. In the theory of metallic conductivity developed by Drude, it was about discrete charges, but these were arbitrary charges, on the value of which no restrictions were imposed.

The electron has not yet left the framework of "pure" science. Recall that the first electronic lamp appeared only in 1907.

To move from faith to conviction, it was necessary first of all to isolate the electron, to invent a method for directly and accurately measuring the elementary charge.

Such a problem was solved by the American physicist Robert Millikan (1868-1953) in a series of subtle experiments that began in 1906.

Robert Milliken was born in 1868 in Illinois into a poor family of a priest. He spent his childhood in the provincial town of Makvoket, where much attention was paid to sports and badly taught. The principal of a high school who taught physics, for example, said to his young students: "How can you make sound out of waves? Nonsense, boys, all this is nonsense!"

Oberdeen College was no better, but Millikan, who did not have material support, had to teach physics in high school himself. In America at that time there were only two textbooks on physics translated from French, and the talented young man had no difficulty in studying them and successfully teaching them. In 1893 he entered Columbia University, then went to study in Germany.

Millikan was 28 years old when he received an offer from A. Michelson to take an assistant position at the University of Chicago. At the beginning, he was engaged here almost exclusively in pedagogical work, and only at the age of forty did he begin scientific research, which brought him worldwide fame.

The first experiments were as follows. Between the plates of a flat capacitor, to which a voltage of 4000 V was applied, a cloud was created, consisting of water droplets that settled on the ions. First, the fall of the cloud top was observed in the absence of an electric field. Then a cloud was created with the voltage turned on. The fall of the cloud occurred under the action of gravity and electrical force.

The ratio of the force acting on a drop in a cloud to the speed it acquires is the same in the first and second cases. In the first case, the force is equal to mg, in the second, mg + qE, where q is the charge of the drop, E is the electric field strength. If the speed in the first case is equal to v 1 in the second v 2, then

Knowing the dependence of the cloud fall velocity v on the air viscosity, we can calculate the desired charge q. However, this method did not give the desired accuracy because it contained hypothetical assumptions that were beyond the control of the experimenter.

In order to increase the measurement accuracy, it was necessary first of all to find a way to take into account cloud evaporation, which inevitably occurred during the measurement process.

Reflecting on this problem, Millikan came up with the classical drop method, which opened up a number of unexpected possibilities. Let's leave the author to tell the story of the invention:

“Realizing that the rate of evaporation of the drops remained unknown, I tried to think of a method that would completely eliminate this uncertain value. My plan was as follows. In previous experiments, the electric field could only slightly increase or decrease the speed of the fall of the top of the cloud under the influence of gravity. Now but I wanted to strengthen that field so that the upper surface of the cloud remained at a constant height. In this case, it was possible to accurately determine the evaporation rate of the cloud and take it into account in the calculations. " To implement this idea, Milliken designed a small battery that gave a voltage of up to 104 V (for that time it was an outstanding achievement of the experimenter). She had to create a field strong enough to keep the cloud, like the "coffin of Mohammed", in a suspended state.

“When I had everything ready,” says Milliken, “and when the cloud formed, I turned the switch, and the cloud was in an electric field. And in that instant it melted before my eyes, in other words, not even a small piece was left of the whole cloud , which could be observed with the help of a control optical device, as Wilson did and I was going to do. As it seemed to me at first, the disappearance of the cloud without a trace in the electric field between the upper and lower plates meant that the experiment ended without results ... "

However, as so often in the history of science, failure gave birth to a new idea. She led to the famous method of drops. "Repeated experiments," Millikan writes, "showed that after the cloud dissipated in a powerful electric field, several separate water drops could be distinguished in its place" (emphasized by me. - V.D.).

The "unfortunate" experience led to the discovery of the possibility of keeping in equilibrium and observing individual droplets for a sufficiently long time.

But during the observation period, the mass of the water drop changed significantly as a result of evaporation, and Millikan, after many days of searching, switched to experiments with oil drops.

The experimental procedure turned out to be simple. Adiabatic expansion between the plates of the capacitor forms a cloud. It consists of droplets having charges of different modulus and sign. When the electric field is turned on, the drops with the same charges as the charge of the upper plate of the capacitor fall rapidly, and the drops with the opposite charge are attracted by the upper plate. But a certain number of drops have such a charge that the force of gravity is balanced by the electric force.

After 7 or 8 minutes, the cloud dissipates, and a small number of drops remain in the field of view, the charge of which corresponds to the said balance of forces.

Millikan observed these drops as distinct bright dots. “The history of these drops usually goes like this,” he writes. “In the case of a slight predominance of gravity over the force of the field, they begin to slowly fall, but as they gradually evaporate, their downward movement soon stops, and they become motionless for quite a long time. Then the field begins to predominate, and the drops begin to rise slowly. Toward the end of their life in the space between the plates, this upward movement becomes very strongly accelerated, and they are attracted with great speed to the upper plate. "

The scheme of the Millikan installation, with the help of which decisive results were obtained in 1909, is shown in Figure 17.

In chamber C was placed a flat capacitor made of round brass plates M and N with a diameter of 22 cm (the distance between them was 1.6 cm). A small hole p was made in the center of the top plate, through which drops of oil passed. The latter were formed by blowing a jet of oil with a sprayer. The air was previously cleaned of dust by passing through a pipe with glass wool. The oil droplets had a diameter of about 10-4 cm.

A voltage of 104 V was applied from the battery B to the capacitor plates. Using a switch, it was possible to short-circuit the plates and thereby destroy the electric field.

Drops of oil falling between plates M and N were illuminated by a strong source. The behavior of drops was observed perpendicular to the direction of the rays through the telescope.

The ions necessary for the condensation of the droplets were created by radiation from a piece of radium weighing 200 mg, located at a distance of 3 to 10 cm to the side of the plates.

With the help of a special device, the gas was expanded by lowering the piston. In 1–2 s after the expansion, the radium was removed or covered with a lead screen. Then the electric field was turned on and the observation of drops into the telescope began.

The pipe had a scale by which it was possible to count the path traveled by a drop over a certain period of time. The time was fixed by an accurate clock with a cage.

In the process of observations, Millikan discovered a phenomenon that served as the key to the entire series of subsequent accurate measurements of individual elementary charges.

“While working on suspended drops,” writes Milliken, “I forgot several times to close them from radium rays. Then I happened to notice that from time to time one of the drops suddenly changed its charge and began to move along the field or against it, obviously, capturing in the first case a positive, and in the second case a negative ion.This opened up the possibility of measuring with certainty not only the charges of individual drops, as I had done up to that time, but also the charge of an individual atmospheric ion.

Indeed, by measuring the velocity of the same drop twice, once before and the second time after the capture of the ion, I obviously could completely exclude the properties of the drop and the properties of the medium and operate with a quantity proportional only to the charge of the captured ion.

The elementary charge was calculated by Millikan on the basis of the following considerations. The speed of the drop is proportional to the force acting on it and does not depend on the charge of the drop.

If the drop fell between the plates of the capacitor under the action of only gravity with a speed v 1, then

When the field directed against gravity is turned on, the acting force will be the difference qE = mg, where q is the charge of the drop, E is the modulus of the field strength.

The drop speed will be:

v 2 \u003d k (qE - mg) (2)

If we divide equality (1) by (2), we get

Let the drop captured the ion and its charge became equal to q′ and the speed of motion v 2 ′. Let us denote the charge of this trapped ion by e. Then e = q′ - q.

Using (3), we get

The value is constant for a given drop.

Therefore, any charge captured by the drop will be proportional to the difference in velocities (v′ 2 -v 2), in other words, proportional to the change in the speed of the drop due to ion capture!

So, the measurement of the elementary charge was reduced to the measurement of the path traveled by the drop and the time during which this path was traveled.

Numerous observations have shown the validity of formula (4). It turned out that the value of e can only change in jumps! Charges e, 2e, 3e, 4e, etc. are always observed.

“In many cases,” Millikan writes, “the drop was observed for five or six hours, and during this time it captured not eight or ten ions, but hundreds of them. In total, I observed the capture of many thousands of ions in this way, and in all cases, the captured charge ... was either exactly equal to the smallest of all the trapped charges, or it was equal to a small integer multiple of this value.This is a direct and irrefutable proof that the electron is not a "statistical average", but that all electric charges on ions are either exactly equal to the charge of the electron, or are small integer multiples of this charge.

So, atomism, discreteness, or, in modern terms, the quantization of electric charge has become an experimental fact. Now it was important to show that the electron is, so to speak, omnipresent. Any electric charge in a body of any nature is the sum of the same elementary charges.

Millikan's method made it possible to unambiguously answer this question.

In the first experiments, the charges were created by the ionization of neutral gas molecules by a stream of radioactive radiation. The charge of the ions captured by the drops was measured.

When a liquid is sprayed with an atomizer, the droplets are electrified due to friction. This was well known in the 19th century. Are these charges as quantized as the ion charges?

Millikan "weighs" the droplets after spraying and makes charge measurements in the manner described above. Experience reveals the same discreteness of electric charge.

Sprinkling drops of oil (dielectric), glycerin (semiconductor), mercury (conductor), Millikan proves that the charges on bodies of any physical nature in all cases without exception consist of separate elementary portions of a strictly constant value.

In 1913, Milliken summed up the results of numerous experiments and gave the following value for the elementary charge: e=4.774·10 -10 units. charge SGSE.

Thus, one of the most important constants of modern physics was established. Determining the electric charge has become a simple arithmetic problem.

Electron visualization. A great role in strengthening the idea of the reality of the electron was played by the discovery by G. A. Wilson of the effect of condensation of water vapor on ions, which led to the possibility of photographing particle tracks.

They say that A. Compton at the lecture could not convince the skeptical listener of the reality of the existence of microparticles. He insisted that he would believe only when he saw them with his own eyes.

Then Compton showed a photograph with an α-particle track, next to which was a fingerprint. "Do you know what it is?" asked Compton. "Finger," the listener replied. "In that case," Compton solemnly declared, "this luminous band is the particle."

Photographs of electron tracks not only testified to the reality of electrons. They confirmed the assumption about the small size of electrons and made it possible to compare with experiment the results of theoretical calculations, in which the electron radius appeared. Experiments initiated by Lenard in the study of the penetrating power of cathode rays showed that very fast electrons emitted by radioactive substances give tracks in a gas in the form of straight lines. The track length is proportional to the energy of the electron. Photographs of high-energy α-particle tracks show that the tracks consist of a large number of dots. Each dot is a water drop that appears on an ion, which is formed as a result of the collision of an electron with an atom. Knowing the size of an atom and their concentration, we can calculate the number of atoms through which an alpha particle must pass at a given distance. A simple calculation shows that an α-particle must pass about 300 atoms before it meets one of the electrons that make up the shell of the atom on the way and produces ionization.

This fact convincingly indicates that the volume of electrons is a negligible fraction of the volume of an atom. The track of an electron with low energy is curved, therefore, a slow electron is deflected by the intra-atomic field. It produces more ionization events on its way.

From the theory of scattering, data can be obtained for estimating the deflection angles as a function of the electron energy. These data are well confirmed by the analysis of real tracks. The coincidence of theory with experiment strengthened the idea of the electron as the smallest particle of matter.

The measurement of an elementary electric charge opened up the possibility of accurately determining a number of important physical constants.

Knowing the value of e automatically makes it possible to determine the value of the fundamental constant - the Avogadro constant. Prior to Millikan's experiments, there were only rough estimates of the Avogadro constant, which were given by the kinetic theory of gases. These estimates were based on calculations of the average radius of an air molecule and varied within a fairly wide range from 2·10 23 to 20·10 23 1/mol.

Let us assume that we know the charge Q that has passed through the electrolyte solution and the amount of substance M that has deposited on the electrode. Then, if the charge of the ion is equal to Ze 0 and its mass is m 0, then the equality

If the mass of the deposited substance is equal to one mole, then Q = F is Faraday's constant, and F = N 0 e, whence N 0 = F / e. Obviously, the accuracy of determining the Avogadro constant is given by the accuracy with which the electron charge is measured.

Practice required an increase in the accuracy of determining the fundamental constants, and this was one of the incentives to continue improving the technique for measuring the electric charge quantum. This work, which is already purely metrological in nature, continues to this day.

The most accurate values are currently:

e \u003d (4.8029 ± 0.0005) 10 -10 units. charge SGSE;

N 0 \u003d (6.0230 ± 0.0005) 10 23 1 / mol.

Knowing N 0, it is possible to determine the number of gas molecules in 1 cm 3, since the volume occupied by 1 mole of gas is a known constant.

Knowledge of the number of gas molecules in 1 cm 3 made it possible in turn to determine the average kinetic energy of the thermal motion of the molecule.

Finally, the charge of the electron can be used to determine the Planck constant and the Stefan-Boltzmann constant in the law of thermal radiation.

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;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">ELEMENTARY CHARGE AND THE MILLIKEN EXPERIENCE

;font-family:"Arial"" xml:lang="uk-UA" lang="uk-UA">Robot target;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">:;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">study of the movement of charged drops in electric and gravitational fields (Milliken's experiment). Definition of elementary charge.

;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">Equipment;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">: Milliken device, multimeter, voltage source 0÷600 V, micrometer 1 mm 100 divisions, 2 stopwatches, glasses 18 x 18 mm, switch, tripod, tube.

;font-family:"Arial";text-decoration:underline" xml:lang="en-EN" lang="en-EN">Determining the radii and charges of charged drops. Measuring the velocities of drops at various voltages and directions of the electric field .

;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">1. Turn on the optical system of the Millikan installation and calibrate the micrometer using a special graduation glass.

;font-family:"Arial"" xml:lang="ru-GB" lang="ru-GB">2. Set the voltage to 300 V on the Millikan setup. Inject drops of oil into the observation space in the setup. Adjusting the optical system slightly, observe the movement of oil droplets.To change the direction of movement of the drops, change the direction of the electric field with the switch.From the visible drops, select the one that moves strictly vertically and at a low speed.Since the size of the resulting droplets is small, it can be considered with a high degree of accuracy that the observed movement is already established (the drop moves at a constant speed).

;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">3. Use a stopwatch to determine the time of movement;font-family:"Arial"" xml:lang="en-US" lang="en-US">t;font-family:"Arial";vertical-align:sub" xml:lang="en-EN" lang="en-EN">1;font-family:"Arial"" xml:lang="en-EN" lang="en-EN"> of the selected drop upwards when passing a certain distance;font-family:"Arial"" xml:lang="en-US" lang="en-US">S;font-family:"Arial";vertical-align:sub" xml:lang="en-EN" lang="en-EN">1;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">, as well as the movement time;font-family:"Arial"" xml:lang="en-US" lang="en-US">t;font-family:"Arial";vertical-align:sub" xml:lang="en-EN" lang="en-EN">2;font-family:"Arial"" xml:lang="en-EN" lang="en-EN"> the same drop down when passing a certain distance;font-family:"Arial"" xml:lang="en-US" lang="en-US">S;font-family:"Arial";vertical-align:sub" xml:lang="en-EN" lang="en-EN">2;font-family:"Arial"" xml:lang="en-EN" lang="en-EN"> The distance traveled by a drop is determined as the product of the price of a micrometer division (see Item 1 of the task) by the number of divisions of the scale passed. Enter the data in Table 1. Repeat the experiment with a few drops (4÷6 drops).

;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">Table 1.

;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">drop number	;font-family:"Arial"" xml:lang="en-US" lang="en-US">U;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">, В	;font-family:"Arial"" xml:lang="en-US" lang="en-US">S;font-family:"Arial";vertical-align:sub" xml:lang="en-US" lang="en-US">1;font-family:"Arial"" xml:lang="en-US" lang="en-US">,;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">mm	;font-family:"Arial"" xml:lang="en-US" lang="en-US">t;font-family:"Arial";vertical-align:sub" xml:lang="en-US" lang="en-US">1;font-family:"Arial"" xml:lang="en-US" lang="en-US">,;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">с	;font-family:"Arial"" xml:lang="en-US" lang="en-US">S;font-family:"Arial";vertical-align:sub" xml:lang="en-US" lang="en-US">2;font-family:"Arial"" xml:lang="en-US" lang="en-US">,;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">mm	;font-family:"Arial"" xml:lang="en-US" lang="en-US">t;font-family:"Arial";vertical-align:sub" xml:lang="en-EN" lang="en-EN">2;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">, with

;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">4. Repeat the experiment for several drops (4÷6 drops) at Millikan voltages of 400 V and 500 V. Enter the data in table 1.

;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">5. Using the data in Table 1, calculate the speeds;font-family:"Arial"" xml:lang="en-US" lang="en-US">v;font-family:"Arial";vertical-align:sub" xml:lang="en-EN" lang="en-EN">1;font-family:"Arial"" xml:lang="en-EN" lang="en-EN"> and;font-family:"Arial"" xml:lang="en-US" lang="en-US">v;font-family:"Arial";vertical-align:sub" xml:lang="en-EN" lang="en-EN">2;font-family:"Arial"" xml:lang="en-EN" lang="en-EN"> drops according to formulas (6) and (7) and, then, radii and charges of drops according to formulas (8) and (9) Since the charge of the drop is an integer;font-family:"Arial"" xml:lang="en-US" lang="en-US">n;font-family:"Arial"" xml:lang="en-EN" lang="en-EN"> elementary charge;font-family:"Arial"" xml:lang="en-US" lang="en-US">e;font-family:"Arial"" xml:lang="en-EN" lang="en-EN"> (electron charge):

;font-family:"Arial"" xml:lang="en-EN" lang="en-EN"> (;font-family:"Arial"" xml:lang="en-US" lang="en-US">1;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">)

;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">then you can define this elementary charge. Fill in table 2.

;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">Table 2.

;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">drop number	;font-family:"Arial"" xml:lang="en-US" lang="en-US">v;font-family:"Arial";vertical-align:sub" xml:lang="en-EN" lang="en-EN">1;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">, m/s	;font-family:"Arial"" xml:lang="en-US" lang="en-US">v;font-family:"Arial";vertical-align:sub" xml:lang="en-EN" lang="en-EN">2;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">, m/s	;font-family:"Arial"" xml:lang="en-US" lang="en-US">Q;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">, cl	;font-family:"Arial"" xml:lang="en-US" lang="en-US">r;font-family:"Arial"" xml:lang="en-US" lang="en-US">,;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">m	;font-family:"Arial"" xml:lang="en-US" lang="en-US">n	;font-family:"Arial"" xml:lang="en-US" lang="en-US">e;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">, Cl

;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">6. Mathematically process the obtained results. Set up the graph. An example of the experiment is shown in Fig. 1.

;font-family:"Arial"" xml:lang="en-EN" lang="en-EN"> 7. Analyze the results obtained and formulate conclusions in accordance with guidelines... Pay attention to the compliance of the conclusions with the goal.

;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">Fig. 1.;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">An example of an experiment to determine the charge of various drops;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">.

;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">
Brief theoretical materials

;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">The idea of the discreteness of the electric charge was first expressed by B. Franklin (1752) Experimentally, the discreteness of charges was substantiated by M. Faraday (1834) based on the laws of electrolysis.The numerical value of the elementary charge (the smallest electric charge found in nature) was theoretically calculated using the Avogadro number.Direct experimental measurement of the elementary charge was made by R. Millikan (1908÷1916) using oil drop method The method is based on the study of the motion of charged oil droplets in a uniform electric field of known intensity;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">Ē;font-family:"Arial"" xml:lang="en-EN" lang="en-EN"> According to the basic concepts of electron theory, the charge of a body changes as a result of a change in the number of electrons contained in it (or, in some phenomena, ions whose charge is a multiple of the charge of an electron.) Therefore, the charge of any body must change abruptly and in such portions that contain an integer number of electron charges.

;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">Milliken measured the electric charge concentrated on individual small spherical droplets that were formed by an atomizer;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">P;font-family:"Arial"" xml:lang="en-EN" lang="en-EN"> and acquired an electric charge by electrification due to friction against the walls of the atomizer, as shown in Fig. 2. Through a small hole in the top plate flat capacitor;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">K;font-family:"Arial"" xml:lang="en-EN" lang="en-EN"> they fell into the space between the plates. The movement of the drop was observed through a microscope;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">M;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">.

;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">Fig. 2:;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">Installation scheme: P - droplet atomizer, K - capacitor, IP - power supply, M - microscope, h;font-family:"Symbol"" xml:lang="en-EN" lang="en-EN">;font-family:"Arial"" xml:lang="en-EN" lang="en-EN"> - radiation source, P - table surface.

;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">
In order to protect droplets from convection air currents, the condenser was enclosed in a protective casing, the temperature and pressure of which were maintained constant. When performing experiments, it was necessary to observe the following conditions:

;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">1. The droplets must be microscopic in order to:

;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">the electrostatic force acting on a charged drop exceeded the force of gravity when the electric field was on;
;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">droplet charge, as well as its changes during irradiation (using an ionizer) were equal to a fairly small number of elementary charges.

;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">This makes it easier to set the multiplicity of the charge of a drop to an elementary charge;

;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">2. Drop density;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">ρ;font-family:"Arial"" xml:lang="en-US" lang="en-US">=1;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">,03*10;font-family:"Arial";vertical-align:super" xml:lang="en-EN" lang="en-EN">3;font-family:"Arial"" xml:lang="en-EN" lang="en-EN"> kg/m;font-family:"Arial";vertical-align:super" xml:lang="en-EN" lang="en-EN">3;font-family:"Arial"" xml:lang="en-EN" lang="en-EN"> -;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">should be greater than the density of the viscous medium;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">ρ;font-family:"Arial";vertical-align:sub" xml:lang="en-EN" lang="en-EN">0;font-family:"Arial"" xml:lang="en-EN" lang="en-EN"> in which it moves (air -;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">ρ;font-family:"Arial";vertical-align:sub" xml:lang="en-EN" lang="en-EN">0;font-family:"Arial"" xml:lang="en-US" lang="en-US">=1;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">,293 kg/m;font-family:"Arial";vertical-align:super" xml:lang="en-EN" lang="en-EN">3;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">);

;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">3. The mass of the drop should not change during the entire experiment. For this, the oil that makes up the drop should not evaporate (oil evaporates much more slowly than water).

;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">If the capacitor plates were not charged (electric field strength;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">Ē;font-family:"Arial"" xml:lang="en-EN" lang="en-EN"> = 0), then the drop slowly fell, moving from the top plate to the bottom one.

;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">As soon as the capacitor plates were charged, changes occurred in the movement of the drop: in the case of a negative charge on the drop and a positive charge on the upper capacitor plate the fall of the drop slowed down, and at some point in time it changed the direction of motion to the opposite - it began to rise towards the upper plate.

Drop equation

;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">Knowing the rate of fall of the drop in the absence of an electrostatic field (its charge did not play a role) and the rate of fall of the drop in a given and known electrostatic field, Millikan could calculate the charge of the drop.To determine the charge, it is necessary to first consider the movement of the drop in the absence of an electrostatic field (the plates are not charged,;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">Ē;font-family:"Arial"" xml:lang="en-EN" lang="en-EN"> = 0;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">).The balance of power is shown in Fig. 3.

;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">In this case, three forces act on the drop (see Fig. 3.a):

;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">gravity;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">mg, g;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">=;font-family:"Arial"" xml:lang="en-EN" lang="en-EN"> 9.81 m/s;font-family:"Arial";vertical-align:super" xml:lang="en-EN" lang="en-EN">2;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">;
;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">archimedean force;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">ρ;font-family:"Arial";vertical-align:sub" xml:lang="en-EN" lang="en-EN">0;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">Vg;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">=;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">m;font-family:"Arial";vertical-align:sub" xml:lang="en-EN" lang="en-EN">0;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">g;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">=;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">F;font-family:"Arial";vertical-align:sub" xml:lang="en-EN" lang="en-EN">A;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">,

;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">where;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">ρ;font-family:"Arial";vertical-align:sub" xml:lang="en-EN" lang="en-EN">0;font-family:"Arial"" xml:lang="en-EN" lang="en-EN"> - air density,;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">V;font-family:"Arial"" xml:lang="en-EN" lang="en-EN"> = (4/3);font-family:"Arial"" xml:lang="en-EN" lang="en-EN">πr;font-family:"Arial";vertical-align:super" xml:lang="en-EN" lang="en-EN">3;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">- drop volume,;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">ρ;font-family:"Arial";vertical-align:sub" xml:lang="en-EN" lang="en-EN">0;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">V;font-family:"Arial"" xml:lang="en-EN" lang="en-EN"> =;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">m;font-family:"Arial";vertical-align:sub" xml:lang="en-EN" lang="en-EN">0;font-family:"Arial"" xml:lang="en-EN" lang="en-EN"> - mass of air displaced by the drop;

;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">viscous drag force expressed by the Stokes formula;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">kv;font-family:"Arial"" xml:lang="en-EN" lang="en-EN"> =;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">-;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">6;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">πηrv;font-family:"Arial"" xml:lang="en-EN" lang="en-EN"> =;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">FC;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">, where;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">η;font-family:"Arial"" xml:lang="en-EN" lang="en-EN"> = 1.82*10;font-family:"Arial";vertical-align:super" xml:lang="en-EN" lang="en-EN">-5;font-family:"Arial"" xml:lang="en-EN" lang="en-EN"> kg/m*s - air viscosity,;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">r;font-family:"Arial"" xml:lang="en-EN" lang="en-EN"> - drop radius,;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">v;font-family:"Arial"" xml:lang="en-EN" lang="en-EN"> - drop speed.

;font-family:"Arial";text-decoration:underline" xml:lang="en-EN" lang="en-EN">Note;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">: The Stokes formula is valid for a ball moving in gas, provided that the radius of the ball is many times greater than the mean free path gas molecules. In Millikan's experiment, the drops were so small that he had to introduce the necessary corrections into the calculations. In addition, it was necessary to take into account that with a significant decrease in the size of the drop, when its radius becomes comparable to the thickness of the layer of air molecules adsorbed on the surface of the drop, the effective density of a drop can differ significantly from the density of its substance.

;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">2 Newton's law in the projection onto the axis;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">X;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">for the case corresponding to Fig. 3.a:

;font-family:"Arial"" xml:lang="en-US" lang="en-US">-;font-family:"Arial"" xml:lang="en-US" lang="en-US">(;font-family:"Arial"" xml:lang="en-US" lang="en-US">m;font-family:"Arial"" xml:lang="en-US" lang="en-US">;font-family:"Arial"" xml:lang="en-US" lang="en-US">-;font-family:"Arial"" xml:lang="en-US" lang="en-US">;font-family:"Arial"" xml:lang="en-US" lang="en-US">m;font-family:"Arial";vertical-align:sub" xml:lang="en-US" lang="en-US">0;font-family:"Arial"" xml:lang="en-US" lang="en-US">);font-family:"Arial"" xml:lang="en-US" lang="en-US">g;font-family:"Arial"" xml:lang="en-US" lang="en-US"> +;font-family:"Arial"" xml:lang="en-US" lang="en-US">kv;font-family:"Arial"" xml:lang="en-US" lang="en-US">g;font-family:"Arial"" xml:lang="en-US" lang="en-US"> =;font-family:"Arial"" xml:lang="en-US" lang="en-US">-ma;font-family:"Arial"" xml:lang="en-US" lang="en-US">(2)

;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">where;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">a;font-family:"Arial"" xml:lang="en-EN" lang="en-EN"> - acceleration with which the drop falls.

;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">Due to viscous resistance, the drop acquires a constant (steady) speed almost immediately after the start of movement or a change in movement conditions and moves uniformly .Because of this;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">a;font-family:"Arial"" xml:lang="en-EN" lang="en-EN"> = 0, and from (1) we can find the velocity of the drop. Let us denote the module of the steady velocity in the absence of an electrostatic field;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">v;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">g;font-family:"Arial"" xml:lang="en-EN" lang="en-EN"> Then:

;font-family:"Arial"" xml:lang="en-US" lang="en-US">v;font-family:"Arial"" xml:lang="en-US" lang="en-US">g;font-family:"Arial"" xml:lang="en-US" lang="en-US"> = (;font-family:"Arial"" xml:lang="en-US" lang="en-US">m;font-family:"Arial"" xml:lang="en-US" lang="en-US">;font-family:"Arial"" xml:lang="en-US" lang="en-US">-;font-family:"Arial"" xml:lang="en-US" lang="en-US">;font-family:"Arial"" xml:lang="en-US" lang="en-US">m;font-family:"Arial";vertical-align:sub" xml:lang="en-US" lang="en-US">0;font-family:"Arial"" xml:lang="en-US" lang="en-US">);font-family:"Arial"" xml:lang="en-US" lang="en-US">g;font-family:"Arial"" xml:lang="en-US" lang="en-US">;font-family:"Arial"" xml:lang="en-US" lang="en-US">/;font-family:"Arial"" xml:lang="en-US" lang="en-US">;font-family:"Arial"" xml:lang="en-US" lang="en-US">k;font-family:"Arial"" xml:lang="en-US" lang="en-US">(3)

;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">If you close the electrical circuit of a capacitor (Fig. 3.b), it will charge and an electrostatic field will be created in it;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">Ē;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">.;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">q;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">(let it be positive) there will be an additional force to those listed;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">qE;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">, directed upwards (Fig. 3.b).

" xml:lang="uk-UA" lang="uk-UA">strength from electric field (charged capacitor field), where is the charge of the drop,Ē - electric field strength, U is the voltage across the capacitor plates, d is the distance between the plates.

;font-family:"Arial"" xml:lang="en-EN" lang="en-EN"> a);font-family:"Arial"" xml:lang="en-EN" lang="en-EN">;font-family:"Arial"" xml:lang="en-EN" lang="en-EN"> b);font-family:"Arial"" xml:lang="en-EN" lang="en-EN">;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">

;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">Fig. 3:;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">Forces acting on the drop:;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">a);font-family:"Arial"" xml:lang="en-EN" lang="en-EN"> in the absence of an electrostatic field;;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">b);font-family:"Arial"" xml:lang="en-EN" lang="en-EN"> in the presence of an electrostatic field.

;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">As in the case of a free fall of a drop, consider the steady state of motion. Newton's law in the projection onto the axis;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">X;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">and taking into account that;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">a;font-family:"Arial"" xml:lang="en-EN" lang="en-EN"> = 0, becomes:

;font-family:"Arial"" xml:lang="en-US" lang="en-US">-;font-family:"Arial"" xml:lang="en-US" lang="en-US">(;font-family:"Arial"" xml:lang="en-US" lang="en-US">m;font-family:"Arial"" xml:lang="en-US" lang="en-US">;font-family:"Arial"" xml:lang="en-US" lang="en-US">-;font-family:"Arial"" xml:lang="en-US" lang="en-US">;font-family:"Arial"" xml:lang="en-US" lang="en-US">m;font-family:"Arial";vertical-align:sub" xml:lang="en-US" lang="en-US">0;font-family:"Arial"" xml:lang="en-US" lang="en-US">);font-family:"Arial"" xml:lang="en-US" lang="en-US">g;font-family:"Arial"" xml:lang="en-US" lang="en-US"> +;font-family:"Arial"" xml:lang="en-US" lang="en-US">qE;font-family:"Arial"" xml:lang="en-US" lang="en-US"> +;font-family:"Arial"" xml:lang="en-US" lang="en-US">kv;font-family:"Arial";vertical-align:sub" xml:lang="en-US" lang="en-US">E;font-family:"Arial"" xml:lang="en-US" lang="en-US"> = 0 (4)

;font-family:"Arial"" xml:lang="en-US" lang="en-US">v;font-family:"Arial";vertical-align:sub" xml:lang="en-US" lang="en-US">E;font-family:"Arial"" xml:lang="en-US" lang="en-US"> = [;font-family:"Arial"" xml:lang="en-US" lang="en-US">-q;font-family:"Arial"" xml:lang="en-US" lang="en-US">;font-family:"Arial"" xml:lang="en-US" lang="en-US">E;font-family:"Arial"" xml:lang="en-US" lang="en-US">;font-family:"Arial"" xml:lang="en-US" lang="en-US">-;font-family:"Arial"" xml:lang="en-US" lang="en-US"> (;font-family:"Arial"" xml:lang="en-US" lang="en-US">m;font-family:"Arial"" xml:lang="en-US" lang="en-US">;font-family:"Arial"" xml:lang="en-US" lang="en-US">-;font-family:"Arial"" xml:lang="en-US" lang="en-US">;font-family:"Arial"" xml:lang="en-US" lang="en-US">m;font-family:"Arial";vertical-align:sub" xml:lang="en-US" lang="en-US">0;font-family:"Arial"" xml:lang="en-US" lang="en-US">);font-family:"Arial"" xml:lang="en-US" lang="en-US">g;font-family:"Arial"" xml:lang="en-US" lang="en-US"> ];font-family:"Arial"" xml:lang="en-US" lang="en-US">/;font-family:"Arial"" xml:lang="en-US" lang="en-US">;font-family:"Arial"" xml:lang="en-US" lang="en-US">k;font-family:"Arial"" xml:lang="en-US" lang="en-US">(5)

;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">where;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">v;font-family:"Arial";vertical-align:sub" xml:lang="en-EN" lang="en-EN">E;font-family:"Arial"" xml:lang="en-EN" lang="en-EN"> - the steady velocity of the oil drop in the electrostatic field of the capacitor:;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">v;font-family:"Arial";vertical-align:sub" xml:lang="en-EN" lang="en-EN">1;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">< ;font-family:"Arial"" xml:lang="en-EN" lang="en-EN"> 0 if the drop is moving down,;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">v;font-family:"Arial";vertical-align:sub" xml:lang="en-EN" lang="en-EN">2;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">>;font-family:"Arial"" xml:lang="en-EN" lang="en-EN"> 0 if the drop is moving up.

" xml:lang="en-EN" lang="en-EN"> (6)

" xml:lang="en-EN" lang="en-EN"> (7)

;font-family:"Arial";color:#000000" xml:lang="en-EN" lang="en-EN">From formulas (6) and (7) one can obtain formulas for determining the charge and radius of drops through drop speed up and down:

;font-family:"Arial";color:#000000" xml:lang="en-EN" lang="en-EN">,;font-family:"Arial";color:#000000" xml:lang="en-US" lang="en-US">;font-family:"Arial";color:#000000" xml:lang="en-EN" lang="en-EN"> (8)

;font-family:"Arial";color:#000000" xml:lang="en-EN" lang="en-EN">where kg m;font-family:"Arial";vertical-align:super;color:#000000" xml:lang="en-EN" lang="en-EN">0.5;font-family:"Arial";color:#000000" xml:lang="en-EN" lang="en-EN"> with;font-family:"Arial";vertical-align:super;color:#000000" xml:lang="en-EN" lang="en-EN">-0.5;font-family:"Arial";color:#000000" xml:lang="en-EN" lang="en-EN"> and

;font-family:"Arial";color:#000000" xml:lang="en-EN" lang="en-EN">where (ms);font-family:"Arial";vertical-align:super;color:#000000" xml:lang="en-EN" lang="en-EN">0.5

;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">Determining the elementary charge through a computational experiment

;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">It follows from equation (5) that by measuring steady-state speeds;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">v;font-family:"Arial";vertical-align:sub" xml:lang="en-EN" lang="en-EN">g;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">and;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">v;font-family:"Arial";vertical-align:sub" xml:lang="en-EN" lang="en-EN">E;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">in the absence of an electrostatic field and in its presence, respectively, it is possible to determine the droplet charge if the coefficient is known;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">k;font-family:"Arial"" xml:lang="en-US" lang="en-US">;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">=;font-family:"Arial"" xml:lang="en-US" lang="en-US">;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">6;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">πηr;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">. It would seem that in order to find;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">k;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">it is enough to measure the radius of the drop (air viscosity is known from other experiments). However, direct measurement of this radius with a microscope is impossible:;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">r;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">has an order of magnitude of 10;font-family:"Arial";vertical-align:super" xml:lang="en-EN" lang="en-EN">-;font-family:"Arial";vertical-align:super" xml:lang="en-EN" lang="en-EN">4;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">÷;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">10;font-family:"Arial";vertical-align:super" xml:lang="en-EN" lang="en-EN">-;font-family:"Arial";vertical-align:super" xml:lang="en-EN" lang="en-EN">6;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">cm, which is comparable to the wavelength of light. Therefore, the microscope gives only a diffraction image of the drop, not allowing to measure its actual size. Information about the drop radius can be obtained from experimental data on its motion in the absence of an electrostatic field.;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">v;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">g;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">and given that;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">m - m;font-family:"Arial";vertical-align:sub" xml:lang="en-EN" lang="en-EN">0;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">=4;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">/;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">3;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">πr;font-family:"Arial";vertical-align:super" xml:lang="en-EN" lang="en-EN">3;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">(;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">ρ - ρ;font-family:"Arial";vertical-align:sub" xml:lang="en-EN" lang="en-EN">0;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">);font-family:"Arial"" xml:lang="en-EN" lang="en-EN">;

;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">where;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">ρ;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">- oil drop density, from (3) we get:

;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">(10)

;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">In his experiments, Millikan changed the charge of the drop by bringing a piece of radium to the condenser. At the same time, radium radiation ionized the air in the chamber (Fig. .;font-family:"Arial"" xml:lang="en-US" lang="en-US">;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">1), as a result of which the drop could capture an additional positive or negative charge. If before that the drop was negatively charged, then it is clear that with a greater probability it will attach positive ions to itself.On the other hand, the addition of negative ions is not excluded.In both cases, the charge of the droplet will change and -;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">hopping;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">- speed of her movement;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">v;font-family:"Arial";vertical-align:super" xml:lang="en-US" lang="en-US">I;font-family:"Arial";vertical-align:sub" xml:lang="en-EN" lang="en-EN">E;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">.;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">q;font-family:"Arial";vertical-align:sub" xml:lang="en-EN" lang="en-EN">0;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">changed droplet charge in accordance with (5) is determined by the relation:

;font-family:"Arial"" xml:lang="en-US" lang="en-US">q;font-family:"Arial";vertical-align:sub" xml:lang="en-US" lang="en-US">0;font-family:"Arial"" xml:lang="en-US" lang="en-US"> =(;font-family:"Arial"" xml:lang="en-US" lang="en-US">v;font-family:"Arial";vertical-align:super" xml:lang="en-US" lang="en-US">I;font-family:"Arial";vertical-align:sub" xml:lang="en-US" lang="en-US">E;font-family:"Arial"" xml:lang="en-US" lang="en-US">;font-family:"Arial"" xml:lang="en-US" lang="en-US">+;font-family:"Arial"" xml:lang="en-US" lang="en-US">v;font-family:"Arial"" xml:lang="en-US" lang="en-US">g;font-family:"Arial"" xml:lang="en-US" lang="en-US">);font-family:"Arial"" xml:lang="en-US" lang="en-US">k;font-family:"Arial"" xml:lang="en-US" lang="en-US">;font-family:"Arial"" xml:lang="en-US" lang="en-US">/;font-family:"Arial"" xml:lang="en-US" lang="en-US">;font-family:"Arial"" xml:lang="en-US" lang="en-US">E;font-family:"Arial"" xml:lang="en-US" lang="en-US">(11)

;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">From (5) and (11) the amount of charge attached to the droplet is determined:

;font-family:"Arial"" xml:lang="en-US" lang="en-US">Δ;font-family:"Arial"" xml:lang="en-US" lang="en-US">q;font-family:"Arial"" xml:lang="en-US" lang="en-US"> =;font-family:"Arial"" xml:lang="en-US" lang="en-US">q;font-family:"Arial"" xml:lang="en-US" lang="en-US">;font-family:"Arial"" xml:lang="en-US" lang="en-US">-;font-family:"Arial"" xml:lang="en-US" lang="en-US">;font-family:"Arial"" xml:lang="en-US" lang="en-US">q;font-family:"Arial";vertical-align:sub" xml:lang="en-US" lang="en-US">0;font-family:"Arial"" xml:lang="en-US" lang="en-US"> =;font-family:"Arial"" xml:lang="en-US" lang="en-US">k;font-family:"Arial"" xml:lang="en-US" lang="en-US">(;font-family:"Arial"" xml:lang="en-US" lang="en-US">v;font-family:"Arial";vertical-align:super" xml:lang="en-US" lang="en-US">I;font-family:"Arial";vertical-align:sub" xml:lang="en-US" lang="en-US">E;font-family:"Arial"" xml:lang="en-US" lang="en-US">;font-family:"Arial"" xml:lang="en-US" lang="en-US">-;font-family:"Arial"" xml:lang="en-US" lang="en-US">;font-family:"Arial"" xml:lang="en-US" lang="en-US">v;font-family:"Arial";vertical-align:sub" xml:lang="en-US" lang="en-US">E;font-family:"Arial"" xml:lang="en-US" lang="en-US">) /;font-family:"Arial"" xml:lang="en-US" lang="en-US">E;font-family:"Arial"" xml:lang="en-US" lang="en-US"> =;font-family:"Arial"" xml:lang="en-US" lang="en-US">k;font-family:"Arial"" xml:lang="en-US" lang="en-US">Δ;font-family:"Arial"" xml:lang="en-US" lang="en-US">v;font-family:"Arial";vertical-align:sub" xml:lang="en-US" lang="en-US">E;font-family:"Arial"" xml:lang="en-US" lang="en-US">;font-family:"Arial"" xml:lang="en-US" lang="en-US">/;font-family:"Arial"" xml:lang="en-US" lang="en-US">;font-family:"Arial"" xml:lang="en-US" lang="en-US">E;font-family:"Arial"" xml:lang="en-US" lang="en-US">(12)

;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">Comparing the charge values of the same drop, you can make sure that the charge change and the drop charge itself are multiples of one and the same value;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">e;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">- elementary charge. In his numerous experiments, Millikan obtained various values of charges;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">q;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">and;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">q;font-family:"Arial";vertical-align:sub" xml:lang="en-EN" lang="en-EN">0;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">, but they always represented a multiple of the value;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">e;font-family:"Arial"" xml:lang="en-US" lang="en-US">;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">≈;font-family:"Arial"" xml:lang="en-US" lang="en-US">;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">1;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">,;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">7*10;font-family:"Arial";vertical-align:super" xml:lang="en-EN" lang="en-EN">-;font-family:"Arial";vertical-align:super" xml:lang="en-EN" lang="en-EN">19;font-family:"Arial"" xml:lang="en-US" lang="en-US">;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">Cl according to (1). Hence, Milliken concluded that the value;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">e;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">represents the smallest possible amount of electricity in nature, that is, "a portion or an atom of electricity.

;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">The modern meaning of the "atom" of electricity;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">e;font-family:"Arial"" xml:lang="en-US" lang="en-US">;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">=;font-family:"Arial"" xml:lang="en-US" lang="en-US">;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">1;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">,;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">602*10;font-family:"Arial";vertical-align:super" xml:lang="en-EN" lang="en-EN">-;font-family:"Arial";vertical-align:super" xml:lang="en-EN" lang="en-EN">19;font-family:"Arial"" xml:lang="en-US" lang="en-US">;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">Cl. This value is the elementary electric charge, the carriers of which are an electron with a negative charge;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">-;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">e;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">and a proton with a charge;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">e;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">.

;font-family:"Arial";text-decoration:underline" xml:lang="en-EN" lang="en-EN">Note;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">:;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">subnuclear particles called "quarks have charges modulo 2/3;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">e;font-family:"Arial"" xml:lang="en-EN" lang="en-EN"> and 1/3;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">e;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">. So 1/3 should be considered a quantum of electric charge;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">e;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">. But in atomic and molecular processes, all charges are multiples;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">e;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">.

" xml:lang="en-US" lang="en-US">Experimental installation

Millikan measured the electric charge on spherical droplets that were formed by the atomizer and charged by friction against the walls of the atomizer. Through a hole in the upper plate of the capacitor, the drops fell into the space between the plates and were observed with a microscope. If the plates were not charged, the drop fell slowly. When the plates were charged, the movement of the drop slowed down and changed direction.

Laboratory work is fully consistent with the experience of Millikan. The experiment is recommended for two students. Assemble the setup as shown in Fig. four.

;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">Connect permanent (300;font-family:"Arial"" xml:lang="en-US" lang="en-US">;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">В;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">) and variable (from 0 to;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">300;font-family:"Arial"" xml:lang="en-US" lang="en-US">;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">В;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">) voltage source outputs so that you can get voltage within;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">300÷600;font-family:"Arial"" xml:lang="en-US" lang="en-US">;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">В;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">. Through the field direction switch, the source is connected to the Millikan installation. A voltmeter is connected in parallel. The optical system of the Millikan installation is connected to the output;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">6,3;font-family:"Arial"" xml:lang="en-US" lang="en-US">;font-family:"Arial"" xml:lang="en-EN" lang="en-EN">В;font-family:"Arial'" xml:lang="en-EN" lang="en-EN"> voltage source.

;font-family:'Arial'" xml:lang="en-EN" lang="en-EN">Fig. 4. Modern experimental setup for determining the elementary charge using the Millikan device

;font-family:'Arial';text-decoration:underline" xml:lang="en-EN" lang="en-EN">Pay attention;font-family:'Arial'" xml:lang="en-EN" lang="en-EN">;font-family:'Arial'" xml:lang="en-EN" lang="en-EN">-;font-family:'Arial'" xml:lang="en-EN" lang="en-EN">in the microscope field (Fig.;font-family:'Arial'" xml:lang="en-US" lang="en-US">;font-family:'Arial'" xml:lang="en-EN" lang="en-EN">5) the image is reversed.

;font-family:'Arial'" xml:lang="en-EN" lang="en-EN">Fig.;font-family:'Arial'" xml:lang="en-US" lang="en-US">;font-family:'Arial'" xml:lang="en-EN" lang="en-EN">5. Oil drops (white dots) between the capacitor plates. The distance between graduation glass divisions in the eyepiece field is 0.029;font-family:'Arial'" xml:lang="en-US" lang="en-US">;font-family:'Arial'" xml:lang="en-EN" lang="en-EN">mm.

" xml:lang="uk-UA" lang="uk-UA">Control" xml:lang="en-EN" lang="en-EN">" xml:lang="uk-UA" lang="uk-UA">" xml:lang="en-EN" lang="en-EN">questions" xml:lang="uk-UA" lang="uk-UA">" xml:lang="en-EN" lang="en-EN">and" xml:lang="uk-UA" lang="uk-UA"> is set" xml:lang="en-EN" lang="en-EN">and" xml:lang="uk-UA" lang="uk-UA">i

;font-family:'Arial'" xml:lang="en-EN" lang="en-EN">1. Formulate the law of charge discreteness.

;font-family:'Arial'" xml:lang="en-EN" lang="en-EN">2. Formulate Stokes' law.

;font-family:'Arial'" xml:lang="en-EN" lang="en-EN">3. What is the physical meaning of viscosity η? From what physical law can its dimension be derived?

;font-family:'Arial'" xml:lang="en-EN" lang="en-EN">4. What forces act on the drop in Millikan's experiment?

;font-family:'Arial'" xml:lang="en-EN" lang="en-EN">5. How to calculate the force acting on a charged particle in the electric field of a capacitor?

;font-family:'Arial'" xml:lang="en-EN" lang="en-EN">6. Why can the speed of the drop be considered constant in this experiment?

;font-family:'Arial'" xml:lang="en-EN" lang="en-EN">7. Why is the air in the condenser exposed to X-rays, ultraviolet rays or radiation from radioactive preparations?

;font-family:'Arial'" xml:lang="en-EN" lang="en-EN">8. Why does the steady-state velocity of a drop change by a specific value during irradiation?

;font-family:'Arial'" xml:lang="en-EN" lang="en-EN">9. Get formula (6).

;font-family:'Arial'" xml:lang="en-EN" lang="en-EN">10. Get formula (7).

;font-family:'Arial'" xml:lang="en-EN" lang="en-EN">11. Why, when irradiated, can a droplet capture a charge of the same sign as its own charge, because similar charges repel each other? Does the frequency of capture by a drop of the same charge depend on temperature, on the charge of the drop, on the charge of the captured ion?

;font-family:'Arial'" xml:lang="en-EN" lang="en-EN">12. Why can't the radius of a drop be measured directly with a microscope?

;font-family:'Arial'" xml:lang="en-EN" lang="en-EN">13. Stokes formula;font-family:'Arial'" xml:lang="en-EN" lang="en-EN">F;font-family:'Arial'" xml:lang="en-US" lang="en-US">;font-family:'Arial'" xml:lang="en-EN" lang="en-EN">=;font-family:'Arial'" xml:lang="en-US" lang="en-US">;font-family:'Arial'" xml:lang="en-EN" lang="en-EN">6πη;font-family:'Arial'" xml:lang="en-EN" lang="en-EN">rv;font-family:'Arial'" xml:lang="en-EN" lang="en-EN">is not applicable if the drop radius is less than the mean free path of molecules;font-family:'Arial'" xml:lang="en-EN" lang="en-EN">λ;font-family:'Arial'" xml:lang="en-EN" lang="en-EN">. Estimate the mean free path at atmospheric pressure and room temperature. After calculating the droplet radius from experimental data, evaluate whether the condition is satisfied , which is the radius of the drop;font-family:'Arial'" xml:lang="en-EN" lang="en-EN">r;font-family:'Arial'" xml:lang="en-US" lang="en-US">;font-family:'Arial'" xml:lang="en-EN" lang="en-EN">>>;font-family:'Arial'" xml:lang="en-US" lang="en-US">;font-family:'Arial'" xml:lang="en-EN" lang="en-EN">λ;font-family:'Arial'" xml:lang="en-EN" lang="en-EN">(that is, the Stokes formula is applicable and data processing according to formulas (5 and 11) is acceptable.

;font-family:'Arial'" xml:lang="en-EN" lang="en-EN">14. Explain how to determine the elementary charge based on the experimental data.

;font-family:'Arial'" xml:lang="en-EN" lang="en-EN">15. Choose a system of units for processing the received data and recalculate all the values of the necessary constants in this system.

;font-family:'Arial'" xml:lang="en-EN" lang="en-EN">16. Use formula (5) to estimate the amount of voltage needed to lift droplets carrying a charge equal to 3 electron charges?

;font-family:'Arial'" xml:lang="en-EN" lang="en-EN">17. Using the Millikan method, you can determine the charge of an electron. What other methods for determining the charge of an electron do you know?

Literature

;font-family:'Arial'" xml:lang="en-EN" lang="en-EN">1;font-family:'Arial'" xml:lang="en-EN" lang="en-EN">. Ioffe A.F. Meetings with physicists. My memories of foreign

;font-family:'Arial'" xml:lang="en-EN" lang="en-EN">physicists. L., Nauka, 1983.

;font-family:'Arial'" xml:lang="en-EN" lang="en-EN">2;font-family:'Arial'" xml:lang="en-EN" lang="en-EN">. Mitchel W. American scientists and inventors. M., Znanie, 1975.

;font-family:'Arial'" xml:lang="en-EN" lang="en-EN">3;font-family:'Arial'" xml:lang="en-EN" lang="en-EN">.;font-family:'Arial'" xml:lang="en-RU" lang="en-RU">http://www.phywe.de

;font-family:'Arial'" xml:lang="en-EN" lang="en-EN">4;font-family:'Arial'" xml:lang="en-EN" lang="en-EN">. Sivukhin D.V.;font-family:'Arial'" xml:lang="en-EN" lang="en-EN">General course of physics: V 5 v. M., 1979. T.3, “Electricity”.

;font-family:'Arial'" xml:lang="en-EN" lang="en-EN">5.;font-family:'Arial';color:#000000" xml:lang="en-EN" lang="en-EN">Rules for formalizing the results of experimental vimirovanie at the vikonannі laboratory work from the course “Gas Physics”. Vorobyova N. V., Gorchinsky O.D., Kovalenko V.F., 2004.;font-family:'Arial';color:#000000" xml:lang="en-EN" lang="en-EN">

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DEFINITION OF ELEMENTARY

ELECTRIC CHARGE BY ELECTROLYSIS METHOD

Equipment: direct current source, cuvette with electrodes from the “Electrolyte” set, laboratory voltmeter, resistor, scales with weights or electronic, key, connecting wires, copper sulphate solution, stopwatch (or clock with a second hand).

EXPLANATION TO WORK. To determine the charge of an electron, one can use the Faraday law of electrolysis, where m is the mass of the substance released at the cathode; M is the molar mass of the substance; n is the valency of the substance; e is the electron charge; Na is Avogadro's constant; I - current strength in the electrolyte; ∆t is the time of passage of current through the electrolyte.

It can be seen from this formula that in order to achieve the goal of the work, it is necessary to know the molar mass of the substance released at the cathode, its valency and the Avogadro constant. In addition, during the experiment, it is necessary to measure the current strength and the time of its flow, and after the end of electrolysis, the mass of the substance released on the cathode.

For the experiment, a saturated aqueous solution of copper sulphate is used, which is poured into a cuvette with two copper electrodes. One electrode is rigidly fixed in the center of the cuvette, and the other (removable) - on its wall.

In an aqueous solution, not only copper sulphate molecules (CuSO4 = Cu2+ + ), but also water (H20 = H+ + OH -) molecules dissociate, although to a weak degree. Thus, an aqueous solution of CuSO4 contains both positive Cu2+ and H+ ions and negative SO2- and OH- ions. If an electric field is created between the electrodes, then positive ions will begin to move towards the cathode, and negative ions - towards the anode. Cu2+ and H+ ions approach the cathode, but not all of them are discharged. This is explained by the fact that copper and hydrogen atoms easily transform into positively charged ions, losing their outer electrons. But a copper ion can more easily attach an electron than a hydrogen ion. Therefore, copper ions are discharged at the cathode.

Negative ions and OH- will move towards the anode, but none of them will be discharged. In this case, copper will begin to dissolve. This is explained by the fact that copper atoms more easily give electrons to the external section of the electrical circuit than ions and OH - and, having become positive ions, will go into solution: Cu = Cu2+ + 2e-.

Thus, when the electrodes are connected to a direct current source in a solution of copper sulphate, a directed movement of ions will occur, which will result in the release of pure copper on the cathode.

In order for the layer of released copper to be dense and well retained on the cathode, electrolysis is recommended to be carried out at a low current strength in the solution. And since this will lead to a large measurement error, instead of a laboratory ammeter, a resistor and a voltmeter are used in the work. According to the reading of the voltmeter U and the resistance of the resistor R (it is indicated on its case), the current strength I is determined. The schematic diagram of the experimental setup is shown in Figure 12.

The strength of the current in the electrolyte during the experiment can change, therefore, its average value 1sr is substituted into the formula for determining the charge. The average value of the current strength is determined by recording every 30 s the readings of the voltmeter throughout the entire observation time, then they are summed up and the resulting value is divided by the number of measurements. This is how Ucp is found. Then, according to Ohm's law, Icp is found for the circuit section. It is more convenient to record the results of voltage measurements in an auxiliary table.

The current flow time is measured with a stopwatch.

PROCEDURE FOR PREPARATION FOR WORK

1. Indicate what physical quantities are subject to direct measurement to determine the electron charge by the method used in this work. What measuring instruments will be used to measure? Determine and write down the limits of the absolute errors of these instruments.

2. Determine and write down the limits of absolute reading errors when using a mechanical stopwatch, voltmeter and scales.

3. Write down the formula for determining the absolute error limit ∆е.

4. Prepare a spreadsheet to record measurement results, errors, and calculations.

Prepare an auxiliary table for recording voltmeter readings.

ANSWER THE QUESTIONS

Why does the time of current flow in the electrolyte affect the error in the result of measuring the electron charge?

How does the concentration of the solution affect the result of measuring the electron charge?

What is the valency of copper?

What is the molar mass of copper?

What is the Avogadro constant?

WORK PROCEDURE

1. Determine the mass of the removable electrode m1 on the balance.

2. Attach the electrode to the cuvette and assemble the electrical circuit shown in Figure 12. Make sure that the removable electrode is connected to the negative pole of the voltage source.

3. Fill the cuvette with a solution of copper sulphate, close the key and record the voltmeter readings every 30 s for 15 minutes.

4. After 15 minutes, open the key, disassemble the circuit, remove the electrode, dry it and determine its mass m2 together with the copper deposited on it.

5. Calculate the mass of released copper: m- and the limit of the absolute error of its measurement ∆m.

6. Calculate the average value of the voltage across the resistor Uav and the average value of the current in the electrolyte I cf.

7. Calculate the electron charge e.

8. Calculate the limit of the absolute error in determining the electron charge ∆е.

9. Write down the result of determining the charge, taking into account the limit of absolute error.

10. Compare the electron charge, determined from the results of the experiment, with the table value.

Ministry of Education of the Russian Federation

Amur State Pedagogical University

Methods for determining the elementary electric charge

Completed by student 151g.

Venzelev A.A.

Checked by: Cheraneva T.G.

Introduction.

1. Prehistory of the discovery of the electron

2. History of the discovery of the electron

3. Experiments and methods for discovering the electron

3.1 Thomson experience

3.2 Rutherford's experience

3.3. Millikan method

3.3.1. short biography

3.3.2. Installation description

3.3.3. Calculation of the elementary charge

3.3.4. Conclusions from the method

3.4. Compton Imaging Method

Conclusion.

Introduction:

ELECTRON - the first elementary particle in terms of discovery time; the material carrier of the smallest mass and the smallest electric charge in nature; constituent part of the atom.

The charge of an electron is 1.6021892. 10 -19 C

4.803242. 10 -10 units SGSE

The electron mass is 9.109534. 10 -31 kg

Specific charge e/m e 1.7588047 . 10 11 Cl. kg -1

The electron spin is 1/2 (in units of h) and has two projections ±1/2; electrons obey Fermi-Dirac statistics, fermions. They are subject to the Pauli exclusion principle.

The magnetic moment of the electron is - 1.00116 m b, where m b is the Bohr magneton.

The electron is a stable particle. According to experimental data, the lifetime is t e > 2 . 10 22 years old.

Not involved in the strong interaction, lepton. Modern physics considers the electron as a truly elementary particle that does not have structure and dimensions. If the latter and are nonzero, then the electron radius r e< 10 -18 м

1. Background of discovery

Uncertainty was at a fundamentally important point. First, the electron appeared as a result of an atomistic interpretation of the laws of electrolysis, then it was discovered in a gas discharge. It was not clear whether physics is really dealing with the same object. A large group of skeptical naturalists believed that the elementary charge is the statistical average of charges of the most varied magnitude. Moreover, none of the experiments on measuring the charge of an electron gave strictly repeating values.
There were skeptics who generally ignored the discovery of the electron. Academician A.F. Ioffe in his memoirs about his teacher V.K. Roentgene wrote: “Until 1906 - 1907. the word electron was not to be spoken at the Physics Institute of the University of Munich. Roentgen considered it an unproven hypothesis, often applied without sufficient grounds and without need.

The electron has not yet left the framework of "pure" science. Recall that the first electron tube appeared only in 1907. To move from faith to conviction, it was necessary first of all to isolate the electron, to invent a method for directly and accurately measuring the elementary charge.

The solution to this problem was not long in coming. In 1752, the idea of the discreteness of the electric charge was first expressed by B. Franklin. Experimentally, the discreteness of charges was substantiated by the laws of electrolysis discovered by M. Faraday in 1834. The numerical value of the elementary charge (the smallest electric charge found in nature) was theoretically calculated on the basis of the laws of electrolysis using the Avogadro number. Direct experimental measurement of the elementary charge was carried out by R. Millikan in classical experiments carried out in 1908 - 1916. These experiments also gave irrefutable proof of the atomism of electricity. According to the basic concepts of electronic theory, the charge of a body arises as a result of a change in the number of electrons contained in it (or positive ions, the charge of which is a multiple of the charge of the electron). Therefore, the charge of any body must change abruptly and in such portions that contain an integer number of electron charges. Having established by experience the discrete nature of the change in electric charge, R. Milliken was able to confirm the existence of electrons and determine the charge of one electron (elementary charge) using the oil drop method. The method is based on the study of the movement of charged oil droplets in a uniform electric field of known strength E.

2.Discovery of the electron:

If we ignore what preceded the discovery of the first elementary particle - the electron, and what accompanied this outstanding event, we can say briefly: in 1897, the famous English physicist Thomson Joseph John (1856-1940) measured the specific charge q / m cathode-ray particles - "corpuscles", as he called them, according to the deflection of cathode rays *) in electric and magnetic fields.

From a comparison of the obtained number with the specific charge of the monovalent hydrogen ion known at that time, by indirect reasoning, he came to the conclusion that the mass of these particles, later called "electrons", is much less (more than a thousand times) than the mass of the lightest hydrogen ion.

In the same year, 1897, he put forward the hypothesis that electrons are an integral part of atoms, and cathode rays are not atoms or electromagnetic radiation, as some researchers of the properties of rays believed. Thomson wrote: "Thus, cathode rays represent a new state of matter, essentially different from the usual gaseous state ...; in this new state, matter is the substance from which all elements are built."

Since 1897, the corpuscular model of cathode rays began to gain general recognition, although there were a variety of judgments about the nature of electricity. So, the German physicist E. Wiechert believed that "electricity is something imaginary, existing really only in thoughts", and the famous English physicist Lord Kelvin in the same year, 1897, wrote about electricity as a kind of "continuous fluid".

Thomson's idea of cathode ray corpuscles as the main components of the atom was not met with great enthusiasm. Some of his colleagues thought he had mystified them when he suggested that cathode ray particles should be considered as possible components of the atom. The true role of Thomson corpuscles in the structure of the atom could be understood in combination with the results of other studies, in particular, with the results of the analysis of spectra and the study of radioactivity.

On April 29, 1897, Thomson delivered his famous message at a meeting of the Royal Society of London. The exact time of the discovery of the electron - day and hour - cannot be named in view of its originality. This event was the result of many years of work by Thomson and his staff. Neither Thomson nor anyone else has ever observed an electron in the literal sense, no one has been able to isolate a single particle from a beam of cathode rays and measure its specific charge. The author of the discovery is J.J. Thomson because his ideas about the electron were close to modern ones. In 1903, he proposed one of the first models of the atom - "raisin pudding", and in 1904 suggested that the electrons in the atom are divided into groups, forming various configurations that determine the periodicity of chemical elements.

The place of discovery is precisely known - the Cavendish Laboratory (Cambridge, UK). Created in 1870 by J.K. Maxwell, in the next hundred years it became the "cradle" of a whole chain of brilliant discoveries in various fields of physics, especially in atomic and nuclear. Its directors were: Maxwell J.K. - from 1871 to 1879, Lord Rayleigh - from 1879 to 1884, Thomson J.J. - from 1884 to 1919, Rutherford E. - from 1919 to 1937, Bragg L. - from 1938 to 1953; deputy director in 1923-1935 - Chadwick J.

Scientific experimental research was carried out by one scientist or a small group in an atmosphere of creative search. Lawrence Bragg later recalled his work in 1913 with his father, Henry Bragg: “It was a wonderful time when new exciting results were obtained almost every week, like the discovery of new gold-bearing areas where nuggets can be picked up directly from the ground. This continued until the beginning of the war *), which terminated our joint work ".

3. Electron discovery methods:

3.1 Thomson experience

Joseph John Thomson Joseph John Thomson, 1856–1940

English physicist, better known simply as J. J. Thomson. Born in Cheetham Hill, a suburb of Manchester, in the family of a second-hand antique dealer. In 1876 he won a scholarship to study at Cambridge. In 1884-1919, he was a professor at the Department of Experimental Physics at the University of Cambridge and part-time head of the Cavendish Laboratory, which, thanks to Thomson's efforts, became one of the most famous research centers in the world. At the same time, in 1905-1918, he was a professor at the Royal Institute in London. Winner of the Nobel Prize in Physics in 1906 with the wording "for research on the passage of electricity through gases", which, of course, includes the discovery of the electron. Thomson's son George Paget Thomson (1892-1975) also eventually became a Nobel laureate in physics - in 1937 for the experimental discovery of electron diffraction by crystals.