“Determination of the charge of an electron. Determination of elementary electric charge by electrolysis Laboratory work in physics measurement of elementary charge

10.01.2022

DEFINITION OF ELEMENTARY

ELECTRIC CHARGE BY ELECTROLYSIS METHOD

Equipment: DC source, cuvette with electrodes from the Electrolyte set, laboratory voltmeter, resistor, scales with weights or electronic, key, connecting wires, copper sulfate solution, stopwatch (or watch with a second hand).

EXPLANATIONS FOR THE WORK. To determine the charge of an electron, you can use Faraday's 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 - electron charge; Na is Avogadro's constant; I is the current strength in the electrolyte; ∆t is the time it takes for current to pass through the electrolyte.

From this formula it is clear 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 Avogadro’s constant. In addition, during the experiment it is necessary to measure the strength of the current and the time it flows, and after the end of electrolysis, the mass of the substance released at the cathode.

To conduct the experiment, a saturated aqueous solution of copper sulfate 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) is on its wall.

In an aqueous solution, dissociation of molecules not only of copper sulfate (CuS04 = Cu2+ +), but also of water (H20 = H+ + OH -) occurs, although to a weak extent. Thus, an aqueous solution of CuS04 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 the copper ion attaches an electron more easily than the 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, the copper will begin to dissolve. This is explained by the fact that copper atoms more easily give up electrons to the external part 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, a directed movement of ions will occur in the copper sulfate solution, which will result in the release of pure copper at 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 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. Based on the reading of the voltmeter U and the resistance of the resistor R (it is indicated on its body), the current strength I is determined. The schematic diagram of the experimental setup is shown in Figure 12.

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

The time of current flow is measured with a stopwatch.

PREPARATION PROCEDURE FOR WORK

1. Indicate which physical quantities are subject to direct measurement to determine the charge of an electron by the method used in this work. What measuring instruments will be used to take measurements? 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 table to record your measurements, errors, and calculations.

Prepare a help table to record the 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 a solution affect the result of measuring the charge of an electron?

What is the valence of copper?

What is the molar mass of copper?

What is Avogadro's constant?

PROCEDURE FOR PERFORMANCE OF THE WORK

1. Determine the mass of the removable electrode t1 on the scale.

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 copper sulfate solution, close the key and record the voltmeter readings every 30 seconds for 15 minutes.

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

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

6. Calculate the average voltage across the resistor Uav and the average current in the electrolyte I Wed

7. Calculate the charge of the electron e.

8. Calculate the absolute error limit for determining the electron charge ∆e.

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

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

Parshina Anna, Sevalnikov Alexey, Luzyanin Roman.

Purpose of the work: learn to determine the value of the elementary charge by electrolysis; study charge determination methods electron.

Equipment: cylindrical vessel with copper sulfate solution, lamp, electrodes, scales, ammeter, constant voltage source, rheostat, clock, key, connecting wires.

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Slide captions:

Laboratory work Determination of the elementary charge by electrolysis Performed by students of the Chuchkovskaya secondary school of the 10th grade: Parshina Anna, Sevalnikov Alexey, Luzyanin Roman. Head: physics teacher Chekalina O.Yu.

Purpose of the work: learn to determine the value of the elementary charge by electrolysis; study methods for determining the charge of an electron. Equipment: cylindrical vessel with copper sulfate solution, lamp, electrodes, scales, ammeter, constant voltage source, rheostat, clock, key, connecting wires.

We have assembled the chain: Work progress:

The result of our work

We learned how to determine the value of the elementary charge by electrolysis, and studied methods for determining the charge of an electron. Conclusion:

V. Ya. Bryusov "The World of the Electron" Perhaps these electrons are Worlds where there are five continents, Arts, knowledge, wars, thrones And the memory of forty centuries! Also, perhaps, each atom is a Universe with a hundred planets; Everything that is here is there, in a compressed volume, But also what is not here. Their measures are small, but Their infinity is still the same, as here; There is sorrow and passion, just like here, and even there there is the same worldly arrogance. Their sages, having placed their boundless world at the center of existence, Hasten to penetrate into the sparks of mystery And think, as I do now; And at the moment when currents of new forces are created from destruction, They shout, in the dreams of self-hypnosis, That God has extinguished his torch!

Ministry of Education of the Russian Federation

Amur State Pedagogical University

Methods for determining elementary electric charge

Completed by student 151g.

Venzelev A.A.

Checked by: Cheraneva T.G.

Introduction.

1. Background to the discovery of the electron

2. History of the discovery of the electron

3. Experiments and methods for discovering the electron

3.1.Thomson's experiment

3.2.Rutherford's experience

3.3. Millikan method

3.3.1. Brief biography

3.3.2. Description of installation

3.3.3. Elementary Charge Calculation

3.3.4. Conclusions from the method

3.4. Compton imaging method

Conclusion.

Introduction:

ELECTRON - the first elementary particle to be discovered; the material carrier of the smallest mass and the smallest electrical charge in nature; component of an atom.

The electron charge is 1.6021892. 10 -19 Cl

4.803242. 10 -10 units SSSE

The mass of the electron is 9.109534. 10 -31 kg

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

The electron spin is equal to 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 an electron is equal to - 1.00116 m b, where m b is the Bohr magneton.

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

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

1.Background of the opening

The discovery of the electron was the result of numerous experiments. By the beginning of the 20th century. the existence of the electron was 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. In reality, the “discovery” of the electron took more than half a century and did not end in 1897; Many scientists and inventors took part in it.

First of all, there was not a single experiment that involved individual electrons. The elementary charge was calculated based on measurements of the microscopic charge, assuming the validity of a number of hypotheses.

There was uncertainty at a fundamentally important point. The electron first appeared as a result of an atomic interpretation of the laws of electrolysis, then it was discovered in a gas discharge. It was not clear whether physics was actually dealing with the same object. A large group of skeptical natural scientists believed that the elementary charge is a statistical average of charges of the most varied sizes. Moreover, none of the experiments measuring the electron charge gave strictly repeatable values.
There were skeptics who generally ignored the discovery of the electron. Academician A.F. Ioffe in his memories of his teacher V.K. Roentgene wrote: “Until 1906 - 1907. the word electron should not have been uttered at the Physics Institute of the University of Munich. Roentgen considered it an unproven hypothesis, often applied without sufficient grounds and needlessly.”

The question of the mass of the electron has not been resolved, and it has not been proven that charges on both conductors and dielectrics 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 into theoretical constructions. Lorentz's electronic theory featured a continuously distributed charge density. The theory of metallic conductivity, developed by Drude, dealt with 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. Let us 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 and invent a method for direct and accurate measurement of the elementary charge.

The solution to this problem was not long in coming. In 1752, the idea of discreteness of electric charge was first expressed by B. Franklin. Experimentally, the discreteness of charges was justified by the laws of electrolysis, discovered by M. Faraday in 1834. The numerical value of the elementary charge (the smallest electrical charge found in nature) was theoretically calculated based on the laws of electrolysis using Avogadro's number. Direct experimental measurement of the elementary charge was carried out by R. Millikan in classical experiments performed in 1908 - 1916. These experiments also provided 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 value 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 experimentally established the discrete nature of the change in electric charge, R. Millikan was able to obtain confirmation of the existence of electrons and determine the value of 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, based on the deflection of cathode rays *) in electric and magnetic fields.

By comparing the obtained number with the specific charge of the monovalent hydrogen ion known at that time, through indirect reasoning, he came to the conclusion that the mass of these particles, which later received the name “electrons,” is significantly less (more than a thousand times) than the mass of the lightest hydrogen ion.

In the same year, 1897, he hypothesized 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 the cathode rays represent a new state of matter, essentially different from the ordinary gaseous state...; in this new state matter is the substance from which all the elements are constructed."

Since 1897, the corpuscular model of cathode rays began to gain general acceptance, although there were a wide variety of opinions about the nature of electricity. Thus, the German physicist E. Wichert 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 basic components of the atom was not met with much enthusiasm. Some of his colleagues thought that 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 made his famous message at a meeting of the Royal Society of London. The exact time of discovery of the electron - day and hour - cannot be named due to its uniqueness. This event was the result of many years of work by Thomson and his employees. Neither Thomson nor anyone else had ever actually observed an electron, nor had anyone 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 he proposed that the electrons in an atom are divided into groups, forming different configurations that determine the periodicity of chemical elements.

The location of the discovery is precisely known - the Cavendish Laboratory (Cambridge, UK). Created in 1870 by J.C. Maxwell, over 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 physics. 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 1923-1935 - Chadwick J.

Scientific experimental research was carried out by one scientist or a small group in an atmosphere of creative exploration. 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 stopped our joint work."

3.Methods for opening an electron:

3.1.Thomson's experiment

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 Cambridge. In 1884-1919, he was a professor at the Department of Experimental Physics at the University of Cambridge and, concurrently, the head of the Cavendish Laboratory, which, through 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 Institution in London. Winner of the Nobel Prize in Physics in 1906 with the wording “for his studies of the passage of electricity through gases,” which, naturally, 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.

Details Category: Electricity and magnetism Published 06/08/2015 05:51 Views: 6694

One of the fundamental constants in physics is the elementary electric charge. This is a scalar quantity that characterizes the ability of physical bodies to take part in electromagnetic interaction.

The elementary electric charge is considered to be the smallest positive or negative charge that cannot be divided. Its value is equal to the electron charge.

The fact that any electric charge found in nature is always equal to a whole number of elementary charges was suggested in 1752 by the famous political figure Benjamin Franklin, a politician and diplomat who was also engaged in scientific and inventive activities, the first American to become a member of the Russian Academy of Sciences.

Benjamin Franklin

If Franklin's assumption is correct, and the electric charge of any charged body or system of bodies consists of an integer number of elementary charges, then this charge can change abruptly by an amount containing an integer number of electron charges.

For the first time, this was confirmed and quite accurately determined experimentally by the American scientist, professor at the University of Chicago, Robert Millikan.

Millikan experience

Millikan experiment diagram

Millikan conducted his first famous experiment with oil drops in 1909 together with his assistant Harvey Fletcher. They say that at first they planned to do the experiment using drops of water, but they evaporated in a few seconds, which was clearly not enough to get the result. Then Milliken sent Fletcher to the pharmacy, where he bought a spray bottle and a bottle of watch oil. This was enough for the experiment to be a success. Subsequently, Millikan received the Nobel Prize for it, and Fletcher received his doctorate.

Robert Milliken

Harvey Fletcher

What was Millikan's experiment?

An electrified drop of oil falls down under the influence of gravity between two metal plates. But if an electric field is created between them, it will keep the droplet from falling. By measuring the strength of the electric field, the charge of the drop can be determined.

The experimenters placed two metal capacitor plates inside the vessel. There, using a spray bottle, tiny droplets of oil were introduced, which became negatively charged during spraying as a result of their friction with the air.

In the absence of an electric field, the droplet falls

Under the influence of gravity F w = mg, the droplets began to fall down. But since they were not in a vacuum, but in an environment, the force of air resistance prevented them from falling freely Fras = 6πη rv 0 , Where η – air viscosity. When Fw And Fras balanced, the fall became uniform with speed v 0 . By measuring this speed, the scientist determined the radius of the drop.

A droplet “floats” under the influence of an electric field

If, at the moment the droplet fell, voltage was applied to the plates in such a way that the upper plate received a positive charge and the lower one a negative one, the fall stopped. He was prevented by the emerging electric field. The droplets seemed to hover. This happened when the force F r balanced by the force acting from the electric field F r = eE ,

Where F r – the resultant of gravity and Archimedes' force.

F r = 4/3 πr 3 ( ρ – ρ 0) g

ρ - density of an oil drop;

ρ 0 – air density.

r is the radius of the drop.

Knowing F r And E , we can determine the value e .

Since it was very difficult to ensure that a droplet remained stationary for a long time, Millikan and Fletcher created a field in which the droplet, after stopping, began to move upward at a very low speed v . In this case

The experiments were repeated many times. Charges were imparted to the droplets by irradiating them with an X-ray or ultraviolet installation. But each time, the total charge of the drop was always equal to several elementary charges.

In 1911, Millikan established that the charge on an electron is 1.5924(17) x 10 -19 C. The scientist was wrong by only 1%. Its modern value is 1.602176487(10) x 10 -19 C.

Ioffe's experiment

Abram Fedorovich Ioffe

It must be said that almost simultaneously with Millikan, but independently of him, similar experiments were carried out by the Russian physicist Abram Fedorovich Ioffe. And his experimental setup was similar to Millikan's. But the air was pumped out of the vessel, and a vacuum was created in it. And instead of droplets of oil, Ioffe used small charged particles of zinc. Their movement was observed through a microscope.

Ioffe installation

1- tube

2-camera

3 - metal plates

4 - microscope

5 - ultraviolet emitter

Under the influence of an electrostatic field, a speck of zinc dust fell. As soon as the gravity of the dust grain became equal to the force acting on it from the electric field, the fall stopped. As long as the charge of the dust particle did not change, it continued to hang motionless. But if it was exposed to ultraviolet light, then its charge decreased and the balance was disrupted. She was starting to fall again. Then the amount of charge on the plates was increased. Accordingly, the electric field increased, and the fall stopped again. This was done several times. As a result, it was found that each time the charge of the dust grain changed by an amount that was a multiple of the charge of the elementary particle.

Ioffe did not calculate the charge of this particle. But, having carried out a similar experiment in 1925 together with physicist N.I. Dobronravov, slightly modifying the experimental setup and using bismuth dust particles instead of zinc, he confirmed the theory

Ministry of Education of the Russian Federation

Amur State Pedagogical University

Methods for determining elementary electric charge

Completed by student 151g.

Venzelev A.A.

Checked by: Cheraneva T.G.

Introduction.

1. Background to the discovery of the electron

2. History of the discovery of the electron

3. Experiments and methods for discovering the electron

3.1.Thomson's experiment

3.2.Rutherford's experience

3.3. Millikan method

3.3.1. Brief biography

3.3.2. Description of installation

3.3.3. Elementary Charge Calculation

3.3.4. Conclusions from the method

3.4. Compton imaging method

Conclusion.

Introduction:

ELECTRON - the first elementary particle to be discovered; the material carrier of the smallest mass and the smallest electrical charge in nature; component of an atom.

The electron charge is 1.6021892. 10 -19 Cl

4.803242. 10 -10 units SSSE

The mass of the electron is 9.109534. 10 -31 kg

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

The electron spin is equal to 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 an electron is equal to - 1.00116 m b, where m b is the Bohr magneton.

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

1.Background of the opening

2.Discovery of the electron:

3.Methods for opening an electron:

3.1.Thomson's experiment

Joseph John Thomson Joseph John Thomson, 1856–1940

In 1897, the young English physicist J. J. Thomson became famous throughout the centuries as the discoverer of the electron. In his experiment, Thomson used an improved cathode ray tube, the design of which was supplemented by electric coils that created (according to Ampere's law) a magnetic field inside the tube, and a set of parallel electric capacitor plates that created an electric field inside the tube. Thanks to this, it became possible to study the behavior of cathode rays under the influence of both magnetic and electric fields.

Using a new tube design, Thomson showed successively that: (1) cathode rays are deflected in a magnetic field in the absence of an electric one; (2) cathode rays are deflected in an electric field in the absence of a magnetic field; and (3) under the simultaneous action of electric and magnetic fields of balanced intensity, oriented in directions that separately cause deflections in opposite directions, the cathode rays propagate rectilinearly, that is, the action of the two fields is mutually balanced.

Thomson found that the relationship between the electric and magnetic fields at which their effects are balanced depends on the speed at which the particles move. After conducting a series of measurements, Thomson was able to determine the speed of movement of the cathode rays. It turned out that they move much slower than the speed of light, which meant that cathode rays could only be particles, since any electromagnetic radiation, including light itself, travels at the speed of light (see Spectrum of electromagnetic radiation). These unknown particles. Thomson called them “corpuscles,” but they soon became known as “electrons.”

It immediately became clear that electrons must exist as part of atoms - otherwise, where would they come from? April 30, 1897 - the date of Thomson's report of his results at a meeting of the Royal Society of London - is considered the birthday of the electron. And on this day the idea of the “indivisibility” of atoms became a thing of the past (see Atomic theory of the structure of matter). Together with the discovery of the atomic nucleus that followed a little over ten years later (see Rutherford's experiment), the discovery of the electron laid the foundation for the modern model of the atom.

The “cathode” tubes described above, or more precisely, cathode ray tubes, became the simplest predecessors of modern television picture tubes and computer monitors, in which strictly controlled quantities of electrons are knocked out from the surface of a hot cathode, under the influence of alternating magnetic fields they are deflected at strictly specified angles and bombard the phosphorescent cells of the screens , forming on them a clear image resulting from the photoelectric effect, the discovery of which would also be impossible without our knowledge of the true nature of the cathode rays.

3.2.Rutherford's experience

Ernest Rutherford, First Baron Rutherford of Nelson, 1871–1937

New Zealand physicist. Born in Nelson, the son of an artisan farmer. Won a scholarship to study at the University of Cambridge in England. After graduation, he was appointed to the Canadian McGill University, where, together with Frederick Soddy (1877–1966), he established the basic laws of the phenomenon of radioactivity, for which he was awarded the Nobel Prize in Chemistry in 1908. Soon the scientist moved to the University of Manchester, where, under his leadership, Hans Geiger (1882–1945) invented his famous Geiger counter, began researching the structure of the atom, and in 1911 discovered the existence of the atomic nucleus. During the First World War, he was involved in the development of sonars (acoustic radars) to detect enemy submarines. In 1919 he was appointed professor of physics and director of the Cavendish Laboratory at the University of Cambridge and in the same year discovered nuclear decay as a result of bombardment by high-energy heavy particles. Rutherford remained in this position until the end of his life, at the same time being for many years president of the Royal Scientific Society. He was buried in Westminster Abbey next to Newton, Darwin and Faraday.

Ernest Rutherford is a unique scientist in the sense that he made his main discoveries after receiving the Nobel Prize. In 1911, he succeeded in an experiment that not only allowed scientists to peer deep into the atom and gain insight into its structure, but also became a model of grace and depth of design.

Using a natural source of radioactive radiation, Rutherford built a cannon that produced a directed and focused stream of particles. The gun was a lead box with a narrow slot, inside of which radioactive material was placed. Due to this, particles (in this case alpha particles, consisting of two protons and two neutrons) emitted by the radioactive substance in all directions except one were absorbed by the lead screen, and only a directed beam of alpha particles was released through the slot.

Experience scheme

Further along the path of the beam there were several more lead screens with narrow slits that cut off particles deviating from strictly

given direction. As a result, a perfectly focused beam of alpha particles flew towards the target, and the target itself was a thin sheet of gold foil. It was the alpha ray that hit her. After colliding with the foil atoms, the alpha particles continued their path and hit a luminescent screen installed behind the target, on which flashes were recorded when the alpha particles hit it. From them, the experimenter could judge in what quantity and how much alpha particles deviate from the direction of rectilinear motion as a result of collisions with foil atoms.

Rutherford, however, noted that none of his predecessors had even tried to test experimentally whether some alpha particles were deflected at very large angles. The raisin grid model simply did not allow for the existence of structural elements in the atom so dense and heavy that they could deflect fast alpha particles at significant angles, so no one bothered to test this possibility. Rutherford asked one of his students to re-equip the installation in such a way that it was possible to observe the scattering of alpha particles at large deflection angles - just to clear his conscience, to finally exclude this possibility. The detector was a screen coated with sodium sulfide, a material that produces a fluorescent flash when an alpha particle hits it. Imagine the surprise not only of the student who directly carried out the experiment, but also of Rutherford himself when it turned out that some particles were deflected at angles of up to 180°!

The picture of the atom drawn by Rutherford based on the results of his experiment is well known to us today. An atom consists of a super-dense, compact nucleus that carries a positive charge, and negatively charged light electrons around it. Later, scientists provided a reliable theoretical basis for this picture (see Bohr's Atom), but it all started with a simple experiment with a small sample of radioactive material and a piece of gold foil.

3.2.Method Milliken

3.2.1. Brief biography:

Robert Milliken was born in 1868 in Illinois into a poor priest's family. He spent his childhood in the provincial town of Maquoketa, where a lot of attention was paid to sports and poor teaching. A high school principal who taught physics said, for example, to his young listeners: “How is it possible to make sound out of waves? Nonsense, boys, it’s all nonsense!”

Oberdeen College was no better, but Milliken, who had no financial support, had to teach high school physics 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 teaching them successfully. In 1893 he entered Columbia University, then went to study in Germany.

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

3.2.2. First experiences and solutions to problems:

The first experiments boiled down to the following. Between the plates of a flat capacitor, to which a voltage of 4000 V was applied, a cloud was created, consisting of droplets of water deposited on the ions. First, the cloud top was observed to fall in the absence of an electric field. Then a cloud was created while the voltage was turned on. The fall of the cloud occurred under the influence 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 υ 1 in the second υ 2, then

Knowing the dependence of the cloud falling speed υ on the air viscosity, we can calculate the required charge q. However, this method did not provide the desired accuracy because it contained hypothetical assumptions beyond the control of the experimenter.

To increase the accuracy of measurements, it was necessary first of all to find a way to take into account the evaporation of the cloud, 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. We’ll let the author himself tell the story of the invention:
“Realizing that the rate of evaporation of the droplets remained unknown, I tried to come up with 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 cloud top falling under the influence of gravity. Now I wanted to strengthen this field so much that the upper surface of the cloud remained at a constant height. In this case, it became possible to accurately determine the rate of cloud evaporation and take it into account in calculations.”

To implement this idea, Millikan designed a small-sized rechargeable battery that produced a voltage of up to 10 4 V (for that time this was an outstanding achievement of an experimenter). It had to create a field strong enough to keep the cloud suspended, like the “coffin of Mohammed.” “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 at that moment it melted before my eyes, in other words, not even a small piece remained of the whole cloud that could be observed with the help of a control optical instrument, 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 often happened in the history of science, failure gave rise to a new idea. It led to the famous drop method. “Repeated experiments,” writes Millikan, “showed that after a cloud dissipates in a powerful electric field, in its place several individual water drops could be distinguished"(emphasis added by me - V.D.). The “unsuccessful” experiment led to the discovery of the possibility of keeping individual droplets in equilibrium and observing them for quite a long time.

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

The experimental procedure turned out to be simple. Adiabatic expansion forms a cloud between the capacitor plates. It consists of droplets with charges of different magnitude and sign. When the electric field is turned on, drops with charges identical to the charge of the upper plate of the capacitor quickly fall, and 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 electrical 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 indicated 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 field force, they begin to fall slowly, but since they gradually evaporate, their downward movement soon stops, and they become motionless for quite a long time.” . Then the field begins to dominate and the drops begin to slowly rise. At 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.”

3.2.3. Installation description:

A diagram of Millikan's installation, with which decisive results were obtained in 1909, is shown in Figure 17.

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) was placed in chamber C. A small hole p was made in the center of the top plate, through which drops of oil passed. The latter were formed by injecting a stream of oil using a sprayer. The air was previously cleared of dust by passing it through a pipe with glass wool. The oil droplets had a diameter of about 10 -4 cm.

A voltage of 10 4 V was supplied from battery B to the capacitor plates. Using a switch, it was possible to short-circuit the plates and this would destroy the electric field.

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

The ions necessary for droplet condensation 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.

Using a special device, lowering the piston expanded the gas. 1 - 2 s after expansion, the radium was removed or obscured by a lead screen. Then the electric field was turned on and the observation of drops into the telescope began. The pipe had a scale on which it was possible to count the path traveled by the drop over a certain period of time. Time was recorded using an accurate clock with a lock.

During his observations, Millikan discovered a phenomenon that served as the key to the entire series of subsequent precise measurements of individual elementary charges.

“While working on suspended drops,” writes Millikan, “I forgot several times to shield them from the 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, apparently capturing in the first case a positive, and in the second case a negative ion. This opened up the possibility of reliably measuring not only the charges of individual drops, as I had done until then, but also the charge of an individual atmospheric ion.

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

3.2.4. Elementary charge calculation:

The elementary charge was calculated by Millikan based on the following considerations. The speed of movement of a drop is proportional to the force acting on it and does not depend on the charge of the drop.
If a drop fell between the plates of a capacitor under the influence of gravity alone with a speed v, then

When a 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 speed of the drop will be equal to:

υ 2 =k(qE-mg) (2)

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

From here

Let the drop capture an ion and its charge become equal to q", and the speed of movement υ 2. Let us denote the charge of this captured ion by e.

Then e= q"- q.

Using (3), we get

The value is constant for a given drop.

3.2.5. Conclusions from the Millikan method

Consequently, any charge captured by a drop will be proportional to the difference in speed (υ " 2 - υ 2), in other words, proportional to the change in the speed of the drop due to the capture of an ion! So, the measurement of the elementary charge was reduced to measuring the path traveled by the drop and the time during which this the path was passed. Numerous observations showed 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,” writes Millikan, “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 have observed the capture of many thousands of ions in this way, and in all cases the charge captured... was either exactly equal to the smallest of all the charges captured, or it was equal to a small integer multiple of this value. This is direct and irrefutable proof that the electron is not a “statistical average,” but that all the electrical charges on the ions are either exactly equal to the charge of the electron or represent small integer multiples of that charge.”

So, the atomicity, discreteness or, in modern language, quantization of the 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, charges were created by ionization of neutral gas molecules by a stream of radioactive radiation. The charge of ions captured by the droplets was measured.

When a liquid is sprayed with a spray bottle, the droplets become electrified due to friction. This was well known back in the 19th century. Are these charges also quantized, like the ion charges? Millikan "weighs" the droplets after spraying and measures the charges 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 charges on bodies of any physical nature consist in all cases, without exception, of individual elementary portions of strictly constant magnitude. In 1913, Millikan summarized the results of numerous experiments and gave the following value for the elementary charge: e = 4.774. 10 -10 units SGSE charge. This was how one of the most important constants of modern physics was established. Determining electric charge became a simple arithmetic problem.

3.4 Compton imaging method:

The discovery of C.T.R. played a major role in strengthening the idea of the reality of the electron. Wilson, the effect of condensation of water vapor on ions, which led to the possibility of photographing particle tracks.

They say that A. Compton at a lecture could not convince a skeptical listener of the reality of the existence of microparticles. He insisted that he would believe only after seeing them with his own eyes.
Then Compton showed a photograph with an alpha particle track, next to which was a fingerprint. “Do you know what this is?” - asked Compton. “Finger,” answered the listener. “In that case,” Compton said solemnly, “this luminous stripe is the particle.”
Photographs of electron tracks not only testified to the reality of electrons. They confirmed the assumption of the small size of electrons and made it possible to compare the results of theoretical calculations, which included the electron radius, with experiment. Experiments, which began with Lenard's study of the penetrating power of cathode rays, showed that very fast electrons emitted by radioactive substances produce tracks in the gas in the form of straight lines. The track length is proportional to the electron energy. Photographs of tracks of high-energy α-particles show that the tracks consist of a large number of points. Each dot is a water droplet 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 its 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 alpha particle must travel approximately 300 atoms before it encounters one of the electrons that make up the shell of the atom on its 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, the slow electron is deflected by the intra-atomic field. It produces more ionization events along its path.

From scattering theory one can obtain data for estimating the deflection angles depending on 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.

Conclusion:

The measurement of 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 - Avogadro's constant. Before Millikan's experiments, there were only rough estimates of Avogadro's 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 over a fairly wide range from 2. 10 23 to 20 . 10 23 1/mol.

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

If the mass of the deposited substance is equal to one mole,

then Q = F- Faraday constant, and F = N 0 e, from which:

Obviously, the accuracy of determining Avogadro's constant is determined by the accuracy with which the electron charge is measured. Practice has required an increase in the accuracy of determining the fundamental constants, and this was one of the incentives to continue improving the methodology for measuring the quantum of electric charge. This work, which is now purely metrological in nature, continues to this day.

The most accurate values currently are:

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

N 0 = (6.0230±0.0005) 10 23 1/mol.

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

Knowing 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 a molecule. Finally, from the charge of the electron one can determine the Planck constant and the Stefan-Boltzmann constant in the law of thermal radiation.