Discovered electrons measured their charge and mass. Determination of the specific charge of an electron. Josephson effect and von Klitzing constant

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The structure of matter.

The structure of the atom.

An atom is the smallest particle of a chemical element, the carrier of all its chemical properties. The atom is chemically indivisible. Atoms can exist both in a free state and in conjunction with atoms of the same element or of another element.
At present, 1/12 of the mass of a carbon atom with an atomic mass equal to 12 (isotope) is taken as a unit of atomic and molecular masses. This unit is called a carbon unit.

Mass and dimensions of atoms. Avogadro's number.

A gram-atom, like a gram-molecule of any substance, contains 6.023 10 ^ 23 atoms or molecules, respectively. This number is called Avogadro's number (N0). So, in 55.85 g of iron, 63.54 g of copper, 29.98 g of aluminum, etc., there is a number of atoms equal to Avogadro's number.
Knowing Avogadro's number, it is easy to calculate the mass of one atom of any element. For this, the gram-atomic mass of one atom must be divided by 6.023 10 ^ 23. So, the mass of a hydrogen atom (1) and the mass of a carbon atom (2) are respectively equal:

Based on Avogadro's number, the volume of an atom can also be estimated. For example, the density of copper is 8.92 g / cm ^ 3, and the gram-atomic mass is 63.54 g. Hence, one gram-atom of copper occupies a volume , and one copper atom has a volume .

The structure of atoms.

The atom is a complex entity and consists of a series of smaller particles. The atoms of all elements are composed of a positively charged nucleus and electrons - negatively charged particles of very small mass. The nucleus occupies a negligible part of the entire volume of an atom. The diameter of the atom is cm, and the diameter of the nucleus is cm.
Although the diameter of the nucleus of an atom is 100,000 times less than the diameter of the atom itself, practically all the mass of an atom is concentrated in its nucleus. Hence it follows that the density of atomic nuclei is very high. If it was possible to collect 1 cm3 of atomic nuclei, then its mass would be about 116 million tons.
The nucleus is made up of protons and neutrons. These particles have a common name - nucleons.
Proton- - a stable elementary particle with a mass close to a carbon unit. The proton charge is equal to the electrode charge, but with the opposite sign. If the charge of the electron is taken equal to -1, then the charge of the proton is equal to +1. A proton is a hydrogen atom devoid of an electron.
Neutron- an atomic shell, the negative charge of which compensates for the positive charge of the nucleus due to the presence of protons in it.
Thus, the number of electrons in an atom is equal to the number of protons in its nucleus.
The relationship between the number of protons, the number of neutrons and the mass number of an atom is expressed by the equation: N = A-Z
Hence, the number of neutrons in the nucleus of an atom of any element is equal to the difference between its mass number and the number of protons.
So the number of neutrons in the nucleus of a radium atom with a mass of 226 N = A-Z = 226-88 = 138

Mass and charge of an electron.

All chemical processes of the formation and destruction of chemical compounds occur without changing the nuclei of the atoms of the elements that make up these compounds. Only the electronic shells undergo changes. Chemical energy is thus related to the energy of the electrons. To understand the processes of formation and destruction of chemical compounds, one should have an idea about the properties of the electron in general and especially about the properties and behavior of the electron in the atom.
Electron is an elementary particle with an elementary negative electric charge, that is, the smallest amount of electricity that can exist. The electron charge is equal to e. Art. units or a pendant. The rest mass of an electron is g, i.e. 1837.14 times less than the mass of a hydrogen atom. The mass of an electron is a carbon unit.

Bohr's model of the atom.

At the beginning of the 20th century, M. Planck A. Einstein created the quantum theory of light, according to which light is a flux of individual quanta of energy, which is not present in a particle of light - photons.
Quantity of energy(E) is different for different emissions and is proportional to the vibration frequency:
,
where h is Planck's constant.
M. Planck showed that atoms absorb or emit radiant energy only in separate, well-defined portions - quanta.
Trying to link the law of classical mechanics with quantum theory, the Danish scientist N. Bohr believed that an electron in a hydrogen atom can be located only in certain - constant orbits, the radii of which relate to each other as squares of integers These orbits were named stationary by N. Bohr.
Radiation of energy occurs only when an electron passes from a farther orbit to an orbit closer to the nucleus. When the electron passes from the pains of a close orbit to a more distant one, the energy is absorbed by the atom.
, where are the energies of electrons in stationary states.
When Ei> Ek, energy is released.
For Ei< Ек энергия поглощается.
The solution to the problem of the distribution of electrons in the atom is based on the study of the line spectra of the elements and their chemical properties. The spectrum of the hydrogen atom almost completely confirmed the theory of N. Bohr. However, the observed splitting of spectral lines in multielectron atoms and the enhancement of this splitting in magnetic and - electric fields could not be explained by Bohr's theory.

Wave properties of the electron.

The laws of classical physics oppose the concepts of "particle" and "wave" to each other. Modern physical theory, called quantum, or wave mechanics, showed that the movement and interaction of particles of small mass - microparticles occur according to laws different from the laws of classical mechanics. A microparticle simultaneously has some properties of corpuscles (particles) and some properties of waves. On the one hand, an electron, proton or other microparticle moves and acts like a corpuscle, for example, when it collides with another microparticle. On the other hand, when a microparticle moves, interference and diffraction phenomena typical of electromagnetic waves are detected.
Thus, in the properties of the electron (as well as in other microparticles), in the laws of its motion, the indissolubility and interconnection of two qualitatively different forms of existence of matter, matter and field are manifested. A microparticle cannot be considered either as an ordinary particle or as an ordinary wave. A microparticle has a particle-wave dualism.
Speaking about the relationship of matter and field, one can come to the conclusion that if a certain mass is inherent in each material particle, then, apparently, the same particle must correspond to a certain length, a wave. The question arises about the relationship between mass and wave. In 1924, the French physicist Louis de Broglie suggested that a wave process is associated with each moving electron (and in general with each moving material particle), the wavelength of which, where is the wavelength in cm (m), h is Planck's constant equal to erg. sec (), m is the mass of the particle in g (kg), is the speed of the particle, in cm / sec.
It can be seen from this equation that a particle at rest must have an infinitely large wavelength and that the wavelength decreases with increasing particle velocity. The wavelength of a moving particle of large mass is very small and cannot yet be determined experimentally. Therefore, we are talking about the wave properties of only microparticles. An electron has wave properties. This means that its motion in an atom can be described by a wave equation.
The planetary model of the structure of the hydrogen atom, created by N. Bohr, who proceeded from the concept of the electron only as a classical particle, cannot explain a number of properties of the electron. Quantum mechanics has shown that the idea of the motion of an electron around the nucleus in certain orbits, similar to the motion of planets around the Sun, should be considered untenable.
An electron, possessing the properties of a wave, moves throughout its volume, forming an electron cloud, which for electrons in one atom can have a different shape. the density of this electron cloud in one or another part of the atomic volume is not the same.

Characterization of an electron by four quantum numbers.

The main characteristic that determines the motion of an electron in the field of a nucleus is its energy. The energy of an electron, like the energy of a particle of a light flux - a photon, takes not any, but only certain discrete, discontinuous, or, as they say, quantized values.
A moving electron has three degrees of freedom of movement in space (respectively, three coordinate axes) and one additional degree of freedom due to the presence of the electron's own mechanical and magnetic moments, which take into account the rotation of the electron around its axis. Consequently, for the complete energy characteristic of the state of an electron in an atom, it is necessary and sufficient to have four parameters. These parameters are named quantum numbers... Quantum numbers, like the energy of an electron, can not penetrate all, but only certain values. Adjacent values of quantum numbers differ by one.

Principal Quantum Number n characterizes the total energy storage of an electron or its energy level. The principal quantum number can take on integer values from 1 to. For an electron in the field of a nucleus, the principal quantum number can take values from 1 to 7 (corresponding to the number of the period in the periodic system in which the element is located). Energy levels are denoted either by numbers in accordance with the values of the main quantum number, or by letters:

NS
Level designation

If, for example, n = 4, then the electron is at the fourth, counting from the nucleus of the atom, the energy level, or at the N level.

Orbital quantum number l, which is sometimes called a side quantum number, characterizes the different energy state of an electron of a given level. The fine structure of the spectral lines suggests that the electrons of each energy level are grouped into sublevels. The orbital quantum number is associated with the angular momentum of the electron when it moves relative to the nucleus of the atom. The orbital quantum number also determines the shape of the electron cloud. The quantum number l can take all integer values from 0 to (n-1). For example, for n = 4, l = 0, 1, 2, 3. Each value of l corresponds to a certain sublevel. For sublevels, letter designations are used. So, at l = 0, 1, 2, 3 the electrons are located on the s-, p-, d-, f- sublevels, respectively. Electrons of different sublevels are respectively called s-, p-, d-, f - electrons. The possible number of sublevels for each energy level is equal to the number of this level, but does not exceed four. The first energy level (n = 1) consists of one s-sublevel, the second (n = 2), the third (n = 3) and fourth (n = 4) energy levels, respectively, consist of two (s, p), three (s , p, d) and four (s, p, d, f) sublevels. There cannot be more than four sublevels, since the values l = 0, 1, 2, 3 describe the electrons of the atoms of all 104 currently known elements.
If l = 0 (s-electrons), then the angular momentum of the electron relative to the atomic nucleus is zero. This can only be when the electron is moving translationally not around the nucleus, but from the nucleus to the periphery and back. The s-electron cloud has the shape of a ball.

Magnetic quantum number- with the moment of the electron's momentum, its magnetic moment is also associated. The magnetic quantum number characterizes the magnetic moment of the electron. the magnetic quantum number characterizes the magnetic moment of the electron and indicates the orientation of the electron cloud relative to the chosen direction or relative to the direction of the magnetic field. The magnetic quantum number can take any positive and negative integers, including zero in the range from - l to + l. For example, if l = 2, then it has 2 l + 1 = 5 values (-2, -1, 0, +1, +2). For l = 3, the number of values is 2 l + 1 = 7 (-3, -2, -1, 0, +1, +2, +3). The number of values of the magnetic quantum number, which is equal to 2 l + 1, is the number of energy states in which the electrons of a given sublevel can be. Thus, s-electrons have only one state (2 l + 1 = 1), p-electrons - 3 states (2 l + 1 = 3), d-, f-electrons - 5 and 7 states, respectively. Energy states are usually denoted schematically by energy cells, depicting them in the form of rectangles, and electrons in the form of arrows in these cells.

Spin quantum number- characterizes the internal motion of an electron - spin. It is associated with the intrinsic magnetic moment of the electron, due to its movement around its axis. This quantum number can take only two values: + 1/2 and -1/2, depending on whether the magnetic field of the electron spin is oriented parallel or antiparallel to the magnetic field caused by the motion of the electron around the nucleus.
Two electrons (pair) with the same values of quantum numbers: n, I, but with oppositely directed spins (↓) are called paired or lone pair of electrons. Electrons with unsaturated spins () are called unpaired.

Pauli's principle, principle of least energy, Gund's rule.
The distribution of electrons in the atoms of elements is determined by three main provisions: Pauli's principle, the principle of least energy and Gund's rule.

Pauli's principle. Studying the numerous spectra of atoms, the Swiss physicist W. Pauli in 1925 came to the conclusion, which was called the Pauli principle or prohibition: there may even be two electrons with the same values for all four quantum numbers. " The energy states of electrons, characterized by the same values of three quantum numbers: n, I and m1, are usually denoted as an energy cell.
According to Pauli's principle, there can be only two electrons in an energy cell, and with opposite spins
The presence of a third electron in one energy cell would mean that two of them have all four quantum numbers the same. The number of possible states of electrons (Fig. 4) on a given sublevel is equal to the number of values of the magnetic quantum number for this sublevel, ie, 21+ 1. The maximum number of electrons on this sublevel, according to Pauli's principle, will be 2 (21+ 1). Thus, 2 electrons are possible at the s-sublevel; there are 6 electrons on the p-sublevel; 10 electrons on the d-sublevel; there are 14 electrons at the f-sublevel. The number of possible states of electrons at any level is equal to the square of the principal quantum number, and the maximum number of electrons at this level is

Least Energy Principle.

The sequence of placement of electrons in an atom must correspond to their greatest connection with the nucleus, that is, the electron must have the lowest energy. Therefore, it is not necessary for an electron to occupy an overlying energy level if there are places in the lower level where the electron will have less energy.

Since the energy of an electron is mainly determined by the values of the principal n and the orbital / quantum numbers, then those sublevels for which the sum of the values of the quantum numbers n and / is smaller are first filled. For example, the energy store at the 4s sublevel (n + / = 4 +0 = 4) is less than at 3d (n + / = 3 + 2 = 5); 5s (n + / = 5 + 0 = 5) less than 4d (n + / = 4 + 2 = 6); 5p (n + / = 5 +1 = 6) less than 4f (n + 1 = 4 + 3 = 7). If for two levels the sums of the values of n and / are equal, then first the filling of the sublevel with a smaller value of n takes place. n, that is, in the following sequence: 3d-4p-5s.
When the energies of close sublevels differ very little from each other, there are some exceptions to this rule. Thus, the 5d sublevel is filled with one 5dl electron before 4f; 6d1-2 before 5f.
Energy levels and sublevels are filled in the following sequence: ls → 2s → 2p → 3s → 3p → 4s → 3d → 4p → 5s → 4d → 5p → 6s → (5dl) → 4f → 5d → 6p → 7s → (6d1-2 ) → 5f → 6d → 7p

Gund's rule.
The electrons within a given sublevel are at first located in a separate cell in the form of unpaired "blank" electrons. In other words, at a given value of I. electron, then each of them will be located in a separate cell in this way:

Electronic formulas of atoms and schemes.

Taking into account the considered provisions, it is easy to imagine the distribution of electrons by energy levels and sublevels in the atoms of any element. This distribution of electrons in an atom is written in the form of so-called electronic formulas. In electronic formulas, the letters s, p, d, f denote the energy sublevels of electrons; the numbers in front of the letters indicate the energy level in which the given electron is located, and the subscript at the top right indicates the number of electrons in the given sublevel. For example, the record 5p3 means that 3 electrons are located on the p-sublevel of the fifth energy level.
To compose the electronic formula of an atom of any element, it is enough to know the number of this element in the periodic table and fulfill the basic provisions that govern the distribution of electrons in the atom.
Suppose, for example, you need to compose electronic formulas for the atoms of sulfur, calcium, scandium, iron and lanthanum. From the periodic table, we determine the numbers of these elements, which are respectively equal to 16, 20, 21, 26,. This means that at the energy levels and sublevels of the atoms of these elements, respectively, 16, 20, 21, 26, 57 electrons are contained. Observing the Pauli principle and the principle of least energy, i.e., the sequence of filling the energy levels and sublevels, it is possible to compose the electronic formulas of the atoms of these elements:

The structure of the electron shell of an atom can also be depicted as a diagram of the distribution of electrons in energy cells.
For iron atoms, such a scheme is as follows:

This diagram clearly shows the fulfillment of the Gund rule. At the 3d-sublevel, the maximum number of cells (four) is filled with unpaired electrons. The image of the structure of the electron shell in the atom in the form of electronic formulas and in the form of diagrams does not clearly reflect the wave properties of the electron. However, it should be remembered that each s-, p-, d-, f-electron is characterized by its own electron cloud. The different shape of the electron cloud indicates that the electron has a different probability of finding an atom in a given region of space. Depending on the value of the magnetic quantum number m1, the orientation of the electron cloud in space will also be different.

The electron is a fundamental particle, one of those that are the structural units of matter. According to the classification, it is a fermion (a particle with a half-integer spin, named after the physicist E. Fermi) and a lepton (a particle with a half-integer spin that does not participate in strong interactions, one of the four main in physics). Baryonic is zero, like other leptons.

Until recently, it was believed that the electron is an elementary, that is, indivisible, structureless particle, but now scientists have a different opinion. What does an electron consist of, according to modern physicists?

History of the name

Even in Ancient Greece, naturalists noticed that amber, previously rubbed with wool, attracts small objects to itself, that is, it exhibits electromagnetic properties. The electron got its name from the Greek ἤλεκτρον, which means "amber". The term was proposed by J. Stoney in 1894, although the particle itself was discovered by J. Thompson in 1897. It was difficult to detect it, the reason for this is the small mass, and the electron charge became decisive in the experiment for finding. The first images of the particle were obtained by Charles Wilson using a special camera, which is used even in modern experiments and is named after him.

An interesting fact is that one of the prerequisites for the discovery of the electron is the statement of Benjamin Franklin. In 1749, he developed a hypothesis according to which electricity is a material substance. It was in his works that terms such as positive and negative charges, capacitor, discharge, battery and a particle of electricity were first used. The specific charge of the electron is considered to be negative, and of the proton - positive.

Discovery of the electron

In 1846 the German physicist Wilhelm Weber began to use the concept of "electricity atom" in his works. Michael Faraday discovered the term "ion", which is now, perhaps, still known from school. Many eminent scientists, such as the German physicist and mathematician Julius Plücker, Jean Perrin, the English physicist William Crookes, Ernst Rutherford and others, were engaged in the question of the nature of electricity.

Thus, before Joseph Thompson successfully completed his famous experiment and proved the existence of a particle smaller than an atom, many scientists worked in this field, and the discovery would not have been possible if they had not done this colossal work.

In 1906, Joseph Thompson received the Nobel Prize. The experiment consisted in the following: beams of cathode rays were passed through parallel metal plates that created an electric field. Then they had to go the same way, but this time through a system of coils that created a magnetic field. Thompson found that under the action of an electric field, the rays were deflected, and the same was observed under a magnetic action, but the beams of cathode rays did not change their trajectories if both of these fields acted on them in certain ratios that depended on the speed of the particles.

After the calculations, Thompson learned that the speed of these particles was significantly lower than the speed of light, which meant that they had mass. From that moment, physicists began to believe that open particles of matter are part of the atom, which was later confirmed. He called it the "planetary model of the atom."

Paradoxes of the quantum world

The question of what an electron consists of is rather complicated, at least at this stage of the development of science. Before considering it, you need to turn to one of the paradoxes of quantum physics, which even scientists themselves cannot explain. This is the famous double-slit experiment that explains the dual nature of the electron.

Its essence is that a frame with a vertical rectangular opening is installed in front of the "cannon" that shoots particles. Behind her there is a wall, on which traces of hits will be observed. So, first you need to figure out how matter behaves. The easiest way to imagine how tennis balls are launched by a machine. Some of the balls fall into the hole, and the traces of hits on the wall add up to one vertical line. If at some distance you add one more hole of the same type, the traces will form, respectively, two stripes.

Waves behave differently in such a situation. If traces from a collision with a wave are displayed on the wall, then in the case of one hole, there will also be one strip. However, everything changes in the case of two slots. The wave, passing through the holes, is divided in half. If the top of one of the waves meets the bottom of the other, they cancel each other out, and an interference pattern (several vertical stripes) will appear on the wall. The places at the intersection of the waves will leave a trace, but the places where mutual suppression has occurred will not.

Amazing discovery

Using the experiment described above, scientists can clearly demonstrate to the world the difference between quantum and classical physics. When they began to bombard the wall with electrons, the usual vertical trail appeared on it: some particles, just like tennis balls, fell into the gap, and some did not. But that all changed when the second hole appeared. It appeared on the wall. At first, physicists decided that electrons were interfering with each other, and decided to let them in one by one. However, after a couple of hours (the speed of moving electrons is still much lower than the speed of light), the interference pattern began to appear again.

Unexpected turn

The electron, along with some other particles such as photons, exhibits wave-particle duality (the term "quantum-wave duality" is also used). Similarly, both alive and dead, the state of the electron can be both corpuscular and wave.

However, the next step in this experiment created even more mysteries: a fundamental particle that everyone seemed to know about, presented an incredible surprise. Physicists decided to install an observing device at the holes in order to record exactly which slit the particles pass through, and how they manifest themselves as a wave. But as soon as the observation mechanism was installed, only two stripes appeared on the wall, corresponding to the two holes, and no interference pattern! As soon as the "surveillance" was removed, the particle again began to exhibit wave properties, as if it knew that no one was watching it anymore.

Another theory

Physicist Born suggested that the particle does not turn into a wave in the literal sense of the word. The electron "contains" a wave of probability, it is this wave that gives the interference picture. These particles have the property of superposition, that is, they can be anywhere with a certain degree of probability, so they can be accompanied by such a "wave".

Nevertheless, the result is obvious: the very fact of the presence of an observer affects the result of the experiment. It seems incredible, but this is not the only example of this kind. Physicists carried out experiments on larger parts of matter, once the object was the thinnest piece of aluminum foil. Scientists noted that the mere fact of some measurements influenced the temperature of the object. They are still unable to explain the nature of such phenomena.

Structure

But what does an electron consist of? At the moment, modern science cannot answer this question. Until recently, it was considered an indivisible fundamental particle, but now scientists are inclined to believe that it consists of even smaller structures.

The specific charge of an electron was also considered elementary, but now quarks have been discovered that have a fractional charge. There are several theories as to what constitutes an electron.

Today, you can see articles that claim that scientists have managed to split an electron. However, this is only partly true.

New experiments

Back in the eighties of the last century, Soviet scientists suggested that the electron could be divided into three quasiparticles. In 1996, they managed to split it into spinon and holon, and recently physicist Van den Brink and his team split the particle into spinon and orbiton. However, splitting can be achieved only under special conditions. The experiment can be carried out at extremely low temperatures.

When electrons “cool down” to absolute zero, which is about -275 degrees Celsius, they practically stop and form between themselves something like matter, as if merging into one particle. Under such conditions, physicists manage to observe the quasiparticles that make up the electron.

Carriers of information

The radius of the electron is very small, it is 2.81794. 10 -13 cm, however, it turns out that its components are much smaller. Each of the three parts into which it was possible to "divide" an electron carries information about it. Orbiton, as the name suggests, contains data about a particle's orbital wave. The spinon is responsible for the spin of the electron, and the holon tells us about the charge. Thus, physicists can observe separately the different states of electrons in highly cooled matter. They managed to trace the pairs "holon-spinon" and "spinon-orbiton", but not all three together.

New technologies

The physicists who discovered the electron had to wait several decades until their discovery was put into practice. Nowadays, technologies are being used after a few years, just remember graphene - an amazing material consisting of carbon atoms in one layer. How will electron splitting be useful? Scientists predict the creation of the speed of which, in their opinion, is several tens of times higher than that of the most powerful modern computers.

What is the secret of quantum computer technology? This can be called a simple optimization. In a familiar computer, the smallest, indivisible piece of information is a bit. And if we consider data to be something visual, then there are only two options for a machine. A bit can contain either zero or one, that is, parts of a binary code.

New method

Now, let's imagine that a bit contains both zero and one is a "quantum bit" or "cubit". The role of simple variables will be played by the spin of the electron (it can rotate either clockwise or counterclockwise). Unlike a simple bit, a cubit can perform several functions at the same time, due to this, the speed of work will increase, the small mass and charge of the electron do not matter here.

This can be explained using the example of the labyrinth. To get out of it, you need to try many different options, of which only one will be correct. Although a traditional computer solves problems quickly, it can still work on only one problem at a time. He will go through all the options one by one, and eventually find a way out. A quantum computer, thanks to the duality of the cube, can solve many problems at the same time. He will revise all possible options not in turn, but at a single point in time, and he will also solve the problem. The difficulty so far is only in getting many quanta to work on one problem - this will be the basis of a new generation computer.

Application

Most people use a computer at a household level. So far, ordinary PCs do an excellent job with this, but to predict events that depend on thousands, maybe hundreds of thousands of variables, the machine must be simply huge. it can easily handle things like forecasting monthly weather, processing and predicting disaster data, and performing complex mathematical calculations with many variables in a fraction of a second, all with a processor the size of a few atoms. So it may very soon be that our most powerful computers will be as thin as a sheet of paper.

Maintaining health

Quantum computer technology will make a huge contribution to medicine. Humanity will be able to create nanomechanisms with powerful potential, with their help it will be possible not only to diagnose diseases by simply looking at the whole body from the inside, but also to provide medical care without surgery: the smallest robots with the "brains" of an excellent computer will be able to perform all operations.

A revolution in the field of computer games is inevitable. Powerful machines capable of instantly solving problems will be able to play games with incredibly realistic graphics, and fully immersive computer worlds are just around the corner.

An electron is an elementary particle, which is one of the main units in the structure of matter. The electron charge is negative. The most accurate measurements were made in the early twentieth century by Milliken and Joffe.

The electron charge is equal to minus 1.602176487 (40) * 10 -1 9 C.

Through this value, the electric charge of other smallest particles is measured.

General concept of the electron

In particle physics, it is said that an electron is indivisible and has no structure. It is involved in electromagnetic and gravitational processes, belongs to the lepton group, just like its antiparticle - the positron. Among other leptons, it has the lightest weight. If electrons and positrons collide, this leads to their annihilation. Such a pair can arise from the gamma-ray quantum of particles.

Before neutrinos were measured, it was the electron that was considered the lightest particle. In quantum mechanics, it is referred to as fermions. Also, the electron has a magnetic moment. If a positron is also referred to it, then the positron is divided as a positively charged particle, and the electron is called a negatron, as a particle with a negative charge.

«>

Selected properties of electrons

Electrons belong to the first generation of leptons, with the properties of particles and waves. Each of them is endowed with a quantum state, which is determined by measuring energy, spin orientation, and other parameters. His belonging to fermions is revealed through the impossibility of finding two electrons simultaneously in one state of a quantum (according to the Pauli principle).

It is studied in the same way as a quasiparticle in a periodic crystal potential, in which the effective mass can differ significantly from the mass at rest.

Electric current, magnetism and thermo EMF occur through the movement of electrons. The charge of an electron in motion forms a magnetic field. However, the external magnetic field deflects the particle from the forward direction. When accelerated, an electron acquires the ability to absorb or emit energy as a photon. Its set consists of electronic atomic shells, the number and position of which determine the chemical properties.

The atomic mass is mainly composed of nuclear protons and neutrons, while the mass of electrons is on the order of 0.06% of the total atomic weight. Coulomb's electrical force is one of the main forces capable of keeping an electron close to the nucleus. But when molecules are created from atoms and chemical bonds arise, electrons are redistributed in the newly formed space.

Nucleons and hadrons are involved in the appearance of electrons. Isotopes with radioactive properties are capable of emitting electrons. In laboratory conditions, these particles can be studied in special devices, and for example, telescopes can detect radiation from them in plasma clouds.

Opening

The electron was discovered by German physicists in the nineteenth century, when they studied the cathodic properties of rays. Then other scientists began to study it in more detail, bringing it to the rank of a separate particle. Radiation and other related physical phenomena were studied.

For example, a group led by Thomson estimated the electron charge and the mass of the cathode rays, the ratios of which, as they found, did not depend on the material source.
And Becquerel found out that minerals emit radiation by themselves, and their beta rays are able to be deflected by the action of an electric field, and the mass and charge retained the same ratio as the cathode rays.

Atomic theory

According to this theory, an atom consists of a nucleus and electrons around it, arranged in the form of a cloud. They are in certain quantized states of energy, the change of which is accompanied by the process of absorption or emission of photons.

Quantum mechanics

At the beginning of the twentieth century, a hypothesis was formulated according to which material particles have the properties of both particles proper and waves. Also, light is able to manifest itself in the form of a wave (it is called a de Broglie wave) and particles (photons).

As a result, the famous Schrödinger equation was formulated, which described the propagation of electron waves. This approach is called quantum mechanics. It was used to calculate the electronic states of energy in the hydrogen atom.

Fundamental and quantum properties of the electron

The particle exhibits fundamental and quantum properties.

The fundamental ones include mass (9.109 * 10 -31 kilograms), an elementary electric charge (that is, the minimum portion of the charge). According to the measurements that have been carried out so far, no elements are found in the electron that can reveal its substructure. But some scientists are of the opinion that it is a point charged particle. As indicated at the beginning of the article, an electronic electric charge is -1,602 * 10 -19 C.

«> Being a particle, an electron can simultaneously be a wave. The experiment with two slits confirms the possibility of its simultaneous passage through both of them. This contradicts the properties of the particle, where it is possible to pass through only one slit each time.

It is believed that electrons have the same physical properties. Therefore, their rearrangement, from the point of view of quantum mechanics, does not lead to a change in the system state. The wave function of electrons is antisymmetric. Therefore, its solutions vanish when identical electrons enter the same quantum state (Pauli's principle).

Electron. Formation and structure of the electron. Electron magnetic monopole.

(continuation)

Part 4. The structure of the electron.

4.1. An electron is a two-component particle, which consists of only two superdensified (condensed, concentrated) fields - electric field-minus and magnetic field-N. Wherein:

a) the density of an electron is the maximum possible in Nature;

b) the size of the electron (D = 10 -17 cm and less) - minimal in Nature;

c) in accordance with the requirement to minimize energy, all particles - electrons, positrons, particles with fractional charges, protons, neutrons, etc. must have (and have) a spherical shape;

d) for unknown reasons, regardless of the energy of the "parent" photon, absolutely all electrons (and positrons) are born absolutely identical in their parameters (for example, the mass of absolutely all electrons and positrons is 0.511 MeV).

4.2. “It has been reliably established that the magnetic field of an electron is the same inherent property as its mass and charge. The magnetic fields of all electrons are the same, just as their masses and charges are the same. ”(C) This automatically makes it possible to make an unambiguous conclusion about the equivalence of the mass and charge of the electron, that is: the mass of the electron is the equivalent of the charge, and vice versa - the charge of the electron is the equivalent of the mass (for positron - similarly).

4.3. The specified property of equivalence also applies to particles with fractional charges (+2/3) and (-1/3), which are the basis of quarks. That is: the mass of a positron, electron and all fractional particles is the equivalent of their charge, and vice versa - the charges of these particles are the equivalent of mass. Therefore, the specific charge of an electron, positron and all fractional particles is the same (const) and is equal to 1.76 * 10 11 Cl / kg.

4.4. Since an elementary quantum of energy is automatically an elementary quantum of mass, the mass of an electron (taking into account the presence of fractional particles 1/3 and 2/3) should have values that are multiples of the masses of three negative semi-quanta. (See also "Photon. The structure of a photon. The principle of movement. Section 3.4.)

4.5. It is very difficult to determine the internal structure of an electron for many reasons; nevertheless, it is of considerable interest, at least in the first approximation, to consider the influence of two components (electrical and magnetic) on the internal structure of an electron. See fig. 7.

Fig. 7. The internal structure of the electron, options:

Option number 1. Each pair of negative semi-quanta petals forms "microelectrons", which then form an electron. In this case, the number of "microelectrons" should be a multiple of three.

Option number 2. An electron is a two-component particle, which consists of two docked independent hemispherical monopoles - electric (-) and magnetic (N).

Option number 3. An electron is a two-component particle, which consists of two monopoles - electric and magnetic. In this case, a spherical magnetic monopole is located in the center of the electron.

Option number 4. Other options.

Apparently, the option can be considered when the electric (-) and magnetic fields (N) can exist inside the electron not only in the form of compact monopoles, but also in the form of a homogeneous substance, that is, they form an almost structureless? crystalline? homogeneous? particle. However, this is highly questionable.

4.6. Each of the options proposed for consideration has its own advantages and disadvantages, for example:

a) Options # 1. Electrons of this design make it possible to calmly form fractional particles with a mass and charge multiple of 1/3, but at the same time make it difficult to explain the electron's own magnetic field.

b) Option number 2. This electron, when moving around the nucleus of an atom, is constantly oriented towards the nucleus by its electric monopole and therefore can have only two variants of rotation around its axis - clockwise or counterclockwise (Pauli ban?), Etc.

4.7. When considering these (or newly proposed) options, it is imperative to take into account the real properties and characteristics of the electron, as well as take into account a number of mandatory requirements, for example:

- the presence of an electric field (charge);

- presence of a magnetic field;

- the equivalence of some parameters, for example: the mass of an electron is equivalent to its charge and vice versa;

- the ability to form fractional particles with mass and charge multiples of 1/3;

- the presence of a set of quantum numbers, spin, etc.

4.8. The electron appeared as a two-component particle, in which one half (1/2) is a condensed electric field-minus (electric monopole-minus), and the other half (1/2) is a condensed magnetic field (magnetic monopole-N). However, it should be borne in mind that:

- electric and magnetic fields under certain conditions can generate each other (transform into each other);

- an electron cannot be a one-component particle and consist of 100% of the minus field, since a single-charged minus field will decay due to repulsive forces. That is why the presence of a magnetic component is necessary inside the electron.

4.9. Unfortunately, it is not possible to carry out a complete analysis of all the advantages and disadvantages of the proposed options and to choose the only correct option for the internal structure of the electron in this work.

Part 5. “Wave properties of the electron”.

5.1. “By the end of 1924. the point of view, according to which electromagnetic radiation behaves partly like waves, and partly like particles, became generally accepted ... And it was at this time that the Frenchman Louis de Broglie, who was a graduate student at that time, dawned on a brilliant thought: why the same could not be for substances? Louis de Broglie did the opposite work on particles that Einstein did on waves of light. Einstein associated electromagnetic waves with particles of light; de Broglie connected the movement of particles with the propagation of waves, which he called waves of matter. De Broglie's hypothesis was based on the similarity of equations describing the behavior of rays of light and particles of matter, and was purely theoretical. Experimental facts were required to confirm or refute it. ”(C)

5.2. “In 1927, American physicists K. Davisson and K. Jermer discovered that when electrons are“ reflected ”from the surface of a nickel crystal at certain angles of reflection, maxima appear. Similar data (the appearance of maxima) were already available from the observation of the diffraction of X-ray waves of rays by crystal structures. Therefore, the appearance of these maxima in reflected electron beams could not be explained in any other way, except on the basis of the concept of waves and their diffraction. Thus, the wave properties of particles - electrons (and de Broglie's hypothesis) have been proven experimentally. ”(C)

5.3. However, consideration of the process of the appearance of corpuscular properties in a photon described in this work (see Fig. 5.) allows us to draw quite unambiguous conclusions:

a) as the wavelength decreases from 10 -4 to 10 - 10 (C) (C) (C) (C) (C) see the electric and magnetic fields of the photon are condensed

(C) (C) (C) (C) (C) (C) (C) (C) (C) (C) b) when the electric and magnetic fields become more dense, the “dividing line” begins to rapidly increase the “density” of fields and already in the X-ray range, the field density is commensurate with the density of an "ordinary" particle.

c) therefore, the X-ray photon, when interacting with an obstacle, is no longer reflected from the obstacle as a wave, but begins to bounce off it as a particle.

5.4. That is:

a) already in the range of soft X-rays, the electromagnetic fields of photons have become so dense that it is very difficult to detect wave properties in them. Quote: "The shorter the wavelength of a photon, the more difficult it is to detect the properties of a wave in it, and the more strongly the properties of a particle are manifested in it."

b) in the hard X-ray and gamma range, photons behave like one hundred percent particles, and it is almost impossible to detect wave properties in them. That is: the X-ray and gamma-photon completely loses the properties of the wave and turns into a one hundred percent particle. Quote: "The energy of quanta in the X-ray and gamma range is so great that the radiation behaves almost one hundred percent like a stream of particles" (c).

c) therefore, in experiments on the scattering of an X-ray photon from the surface of the crystal, it was no longer a wave that was observed, but an ordinary particle, which bounced off the surface of the crystal and repeated the structure of the crystal lattice.

5.5. Before the experiments of K. Davisson and K. Dzhermer, there were already experimental data on the observation of the diffraction of X-ray waves of rays on crystal structures. Therefore, having obtained similar results in experiments with electron scattering on a nickel crystal, they automatically attributed wave properties to the electron. However, an electron is a "solid" particle, which has a real rest mass, dimensions, etc. It is not an electron-particle that behaves like a photon-wave, but an X-ray photon has (and exhibits) all the properties of a particle. The electron is not reflected from the obstacle as a photon, but the X-ray photon is reflected from the obstacle as a particle.

5.6. Therefore: the electron (and other particles) did not have any "wave properties", and cannot and cannot. And there are no prerequisites, let alone opportunities for changing this situation.

Part 6. Conclusions.

6.1 The electron and positron are the first and fundamental particles, the presence of which determined the appearance of quarks, protons, hydrogen and all other elements of the periodic table.

6.2. Historically, one particle was called an electron and assigned a minus sign (matter) to it, while another was called a positron and was assigned a plus sign (antimatter). "The electric charge of an electron was agreed to be considered negative in accordance with an earlier agreement to call the charge of electrified amber negative" (c).

6.3. An electron can appear (appear = be born) only in a pair with a positron (an electron is a positron pair). The appearance in Nature of at least one "unpaired" (single) electron or positron is a violation of the law of conservation of charge, the general electroneutrality of matter and is technically impossible.

6.4. The formation of an electron-positron pair in the Coulomb field of a charged particle occurs after the division of elementary quanta of a photon in the longitudinal direction into two components: negative - from which a minus particle (electron) is formed and positive - from which a plus-particle (positron) is formed. The division of an electrically neutral photon in the longitudinal direction into two parts, absolutely equal in mass, but different in charges (and magnetic fields), is a natural property of a photon arising from the laws of conservation of charge, etc. The presence of "inside" an electron of even insignificant amounts of "plus-particles" , and "inside" the positron - "particles-minus" - is excluded. It also excludes the presence of electrically neutral "particles" (scraps, pieces, scraps, etc.) of the parent photon inside the electron and proton.

6.5. For unknown reasons, absolutely all electrons and positrons are born by reference "maximum-minimum" particles (ie, they cannot be larger and cannot be smaller in mass, charge, dimensions and other characteristics). The formation of any smaller or larger particles - plus (positrons) and minus particles (electrons) from electromagnetic photons - is excluded.

6.6. The internal structure of an electron is unambiguously predetermined by the sequence of its appearance: an electron is formed as a two-component particle, which is 50% a densified electric field-minus (electric monopole-minus), and 50% is a densified magnetic field (magnetic monopole-N). These two monopoles can be regarded as particles of different charges, between which forces of mutual attraction (cohesion) arise.

6.7. Magnetic monopoles exist, but not in a free form, but only as components of an electron and a positron. In this case, the magnetic monopole (N) is an integral part of the electron, and the magnetic monopole (S) is an integral part of the positron. The presence of a magnetic component "inside" an electron is necessary, since only a magnetic monopole (N) can form a strong (and unprecedented in strength) connection with a single-charged electric monopole-minus.

6.8. Electrons and positrons have the greatest stability and are particles whose decay is theoretically and practically impossible. They are indivisible (by charge and mass), that is: spontaneous (or forced) division of an electron or positron into several calibrated or "different-sized" parts is excluded.

6.9. An electron is eternal and it cannot "disappear" until it encounters another particle that has electric and magnetic charges of equal magnitude, but opposite in sign (positron).

6.10. Since only two standard (calibrated) particles can appear from electromagnetic waves: an electron and a positron, only standard quarks, protons and neutrons can appear on their basis. Therefore, all the visible (baryonic) matter of our and all other universes consists of the same chemical elements (periodic table) and uniform physical constants and fundamental laws, analogous to "our" laws, operate everywhere. The appearance at any point of infinite space of "other" elementary particles and "other" chemical elements is excluded.

6.11. All visible matter in our Universe was formed from photons (presumably in the microwave range) according to the only possible scheme: photon → electron-positron pair → fractional particles → quarks, gluon → proton (hydrogen). Therefore, all the "solid" matter of our Universe (including Homo sapiens) is condensed electric and magnetic fields of photons. There were no other "matters" for its formation in the Cosmos, and cannot be.

P.S. Is the electron inexhaustible?

Properties

The electron charge is indivisible and is equal to −1.602176565 (35) 10 −19 C (or −4.80320427 (13) 10 −10 units of the CGSE charge in the CGSE system or −1.602176565 (35) . СГСМ in the СГСМ system); it was first directly measured in experiments ( English) A.F. Ioffe (1911) and R. Milliken (1912). This value serves as a unit for measuring the electric charge of other elementary particles (unlike the electron charge, the elementary charge is usually taken with a positive sign). The mass of an electron is 9.10938291 (40) · 10 −31 kg.

Kg is the mass of an electron.

Cl is the electron charge.

C / kg is the specific charge of an electron.

Spin of an electron in units

According to modern concepts of elementary particle physics, the electron is indivisible and structureless (at least up to distances of 10 −17 cm). The electron participates in weak, electromagnetic and gravitational interactions. It belongs to the group of leptons and is (together with its antiparticle, the positron) the lightest of the charged leptons. Before the discovery of the neutrino mass, the electron was considered the lightest of the massive particles - its mass is about 1836 times less than the mass of the proton. The electron spin is 1/2, and thus the electron belongs to fermions. Like any charged particle with spin, an electron has a magnetic moment, and the magnetic moment is divided into a normal part and an anomalous magnetic moment. Sometimes both electrons themselves and positrons are referred to as electrons (for example, considering them as a common electron-positron field, a solution to the Dirac equation). In this case, a negatively charged electron is called a negatron, and a positively charged one is called a positron. [ source not specified 120 days]

Being in the periodic potential of the crystal, the electron is considered as a quasiparticle, the effective mass of which can differ significantly from the electron mass.

A free electron cannot absorb a photon, although it can scatter it (see the Compton effect).

Etymology and history of discovery

The name "electron" comes from the Greek word ἤλεκτρον, meaning "amber": even in ancient Greece, naturalists conducted experiments - pieces of amber were rubbed with wool, after which they began to attract small objects to themselves. The term "electron" as the name of the fundamental indivisible unit of charge in electrochemistry was proposed by J. J. Stoney ( English) in 1894 (the unit itself was introduced by him in 1874). The discovery of the electron as a particle belongs to E. Wichert and J.J. Thomson, who in 1897 established that the ratio of charge to mass for cathode rays does not depend on the material of the source. (see Discovery of the electron)

Discovery of wave properties... According to the hypothesis of de Broglie (1924), the electron (like all other material micro-objects) has not only corpuscular, but also wave properties. The de Broglie wavelength of a nonrelativistic electron is equal to, where is the speed of the electron. Accordingly, electrons, like light, can experience interference and diffraction. The wave properties of electrons were experimentally discovered in 1927 by the American physicists K. Davisson and L. Jermer (Davisson-Jermer experiment) and independently by the English physicist J.P. Thomson.

Usage

Most low-energy electron sources use the phenomena of thermionic emission and photoelectron emission. High-energy, with energies ranging from a few keV to several MeV, electrons are emitted in the processes of beta decay and internal conversion of radioactive nuclei. The electrons emitted in beta decay are sometimes called beta particles or beta rays. Accelerators serve as sources of higher energy electrons.

The movement of electrons in metals and semiconductors makes it easy to transfer and control energy; it is one of the foundations of modern civilization and is used almost everywhere in industry, communications, computer science, electronics, and in everyday life. The drift speed of electrons in conductors is very low (~ 0.1-1 mm / s), but the electric field propagates at the speed of light. In this regard, the current in the entire circuit is established almost instantly.

Electron beams accelerated to high energies, for example, in linear accelerators, are one of the main tools for studying the structure of atomic nuclei and the nature of elementary particles. More prosaic applications of electron beams are televisions and monitors with cathode ray tubes (CRTs). The electron microscope also exploits the ability of electron beams to obey the laws of electronic optics. Before the invention of transistors, almost all radio engineering and electronics were based on vacuum electronic tubes, where the movement of electrons in a vacuum is controlled by electric (sometimes magnetic) fields. Electrovacuum devices (EVP) continue to be used to a limited extent in our time; the most common applications are magnetrons in microwave generators and the aforementioned cathode ray tubes (CRTs) in televisions and monitors.

Electron as a quasiparticle

If an electron is in a periodic potential, its motion is considered as the motion of a quasiparticle. Its states are described by a quasi-wave vector. The main dynamic characteristic in the case of a quadratic dispersion law is the effective mass, which can differ significantly from the mass of a free electron and, in the general case, is a tensor.

Electron and the Universe

It is known that out of every 100 nucleons in the Universe, 87 are protons and 13 are neutrons (the latter are mainly part of helium nuclei). To ensure the general neutrality of the substance, the number of protons and electrons must be the same. The density of the baryonic mass (observed by optical methods), which consists mainly of nucleons, is well known (one nucleon per 0.4 cubic meter). Taking into account the radius of the observable Universe (13.7 billion light years), it can be calculated that the number of electrons in this volume is ~ 10 80, which is comparable to the large Dirac numbers.

Determination of the specific charge of an electron

Teaching aid for laboratory work No. 3.10

in the discipline "Physics"

Vladivostok

Far Eastern Federal University

UDC 53.082.1; 531.76

Determination of the specific charge of an electron: educational and methodical. manual for laboratory work No. 3.10k in the discipline "Physics" / Far Eastern Federal University, School of Natural Sciences / Comp. N.P. Dymchenko, O. V. Plotnikova ,. - Vladivostok: Far East. federal un-t, 2014 .-- 13 p.

The manual, prepared at the Department of General Physics of the School of Natural Sciences of the FEFU, contains a brief theoretical material on the topic "The movement of charged particles in electric and magnetic fields" and guidelines for the laboratory work "Determination of the specific charge of an electron" in the discipline "Physics". The manual is intended for students of the FEFU engineering school.

UDC 53.082.1; 531.76

Laboratory work No. 3.10k Determination of the specific charge of an electron

Purpose of work: study the laws of motion of charged particles in electric and magnetic fields, determine the specific charge of an electron e / m, using Helmholtz coils.

Devices: installation for demonstrating the Lorentz force and determining the ratio of the electron charge to its mass, right-angled triangle.

Brief theory.

Specific charge of an electron e / m is one of the fundamental constants such as the speed of light with, Planck's constant h, Boltzmann's constant k other. When an electron moves in electric and magnetic fields, the trajectory of the electron is determined by the configuration of these fields and the ratio of the electron's charge to its mass.

If a moving charged particle is under the action of a uniform electric and magnetic field, then the force acting on the particle is:

where is the particle velocity, q- its electric charge, - the strength of the electric field, - the induction of the magnetic field.

This force is called the Lorentz force. The formula shows that it is equal to the vector sum of the forces acting from the electric and magnetic fields.

Consider the motion of a charged particle at constant speed in a uniform magnetic field, provided that there is no electric field. In this case, only the magnetic component of the Lorentz force acts on the particle:

The direction of this force depends on the sign of the charge and can be determined by the right screw rule (left hand rule), Fig. 1.

The modulus of the Lorentz force is equal to:

where α is the angle between the vectors of the particle velocity and the magnetic induction.

If the particle moves with a speed directed along the lines of force of magnetic induction, then the force does not act on it (F = 0), the particle acceleration will be equal to 0 and the motion will be uniform.

If the speed of the particle is directed perpendicular to the lines of force of magnetic induction, then the particle will be under the action of a force constant in magnitude: directed perpendicular to the speed, and imparting only normal (centripetal) acceleration to the particle. The speed module does not change in this case. Explain why? As a result, the particle will move in a circle, the radius of which can be found on the basis of Newton's second law:

Particle orbital period:

It can be seen from the obtained expression that the period of revolution of a particle in a uniform magnetic field does not depend on the speed of the particle and is inverse to its specific charge.

With a known radius of the trajectory of the particle, from expression (4), one can find the velocity of the particle:

If the velocity of a charged particle is directed at an angle α to the vector of magnetic induction, then its motion can be represented as a superposition of two motions:

As a result of the addition of the two movements, a spiral motion occurs, the axis of which is parallel to the lines of force of the magnetic field (Fig. 2).

Distance h between the two nearest turns of a helix is called a pitch. The helix pitch is:

In this laboratory work, the motion of an electron in a magnetic field is considered, and all the relations obtained are used to describe this motion.

Rice. 2. The trajectory of motion of a charged particle that has flown in at an angle α to the lines of force of a uniform magnetic field. R - radius, h - helix pitch.

Having passed the accelerating potential difference U, the electron acquires a speed, the value of which can be found from the equality of the work of the electric field and the kinetic energy of the electron (the law of conservation of energy is written for the nonrelativistic case):

where is the electron charge (modulo), is the electron mass.

Using expression (6), we find the speed of the electron:

Substituting (9) into (8) and expressing the specific charge of an electron, we get:

Experimental setup

The determination of the specific charge of an electron is carried out on the installation shown in Fig. 3. The main elements of the installation are: a cathode-ray tube 7, a system of Helmholtz coils 11, which creates a uniform magnetic field in the entire volume covered by the coils, and the control elements shown in Fig. 3.

Rice. 3. Installation for determining the specific charge of an electron.

1 - On-off button of the device: 2 - three position switch, serves to change the direction of the magnetizing current in the Helmholtz coils 11 "clockwise", "off", "counterclockwise"; 3 - knob for adjusting the magnetizing current, the current is measured using an ammeter located on the front panel of the unit; 4 - knob for adjusting the accelerating voltage, it is read using a voltmeter located on the front panel of the unit; 5 - switch, has three positions, in in this experiment, it should be in the "off" position, 6 - handle for adjusting the electrostatic field, not used in this experiment and should be in the extreme left position; 7 - cathode ray tube; 8, 10 devices for measuring the diameter of the electron beam; 9 - trail of an electron beam.

Helmholtz coils are a system of two thin coils located coaxially at a distance between the cents of the coils equal to their radius. The thickness of the coils is significantly less than their average diameter. With this geometry of the arrangement of the coils, the magnetic field induction in the entire volume between the coils is practically the same. The induction vector of the magnetic field of the Helmholtz coils is directed along the axis of both coils towards the observer or away from the observer, depending on the direction of the current in the Helmholtz coils. Switching the direction of the current is made by toggle switch 2, Fig. 3. The cathode-ray tube 7 is located in the central region of the field created by these coils, fig. 3.

Magnetic field induction B inside the ring system can be calculated based on the Biot - Savard - Laplace law and the principle of superposition of fields created by two Helmholtz rings. This calculation gives the expression for the magnetic field induction:

where is the magnetic constant, N = the total number of turns of the two coils, R is the average radius of the coils, I is the current in the Helmholtz coils.

Taking into account (11), formula (10) takes the form:

where k stands for the expression:. Substituting into this formula the value of the constant μ O and the values of the parameters N and R of the Helmholtz coils of this installation, we obtain the final expression for formula (12):

Work order

The unit is ready for operation, it is not allowed to rotate the cathode ray tube, and also to rotate or toggle other buttons than specified in this manual. Continuous experiment time should not exceed 45 minutes.Switch 5, Fig. 3, must be in the "off" position and in this experiment its positionshouldn't change. The magnetizing current is selected within 1 - 2 A, y the accelerating voltage is set in the range of 150 - 200 V. Before turning off the device, the handle for adjusting the current 2 and the accelerating voltage 4, Fig. 3 turn to the extreme left position.

Rice. 4 Electron beam in the absence of a magnetic field. To visualize the electron beam, a small amount of inert gas is terminated in the cathode ray tube previously evacuated from air. Due to the collisions between the electrons and the inert gas atoms, the gas atoms are excited and then emit a greenish light, thereby indicating the trajectory of the electrons.

Rice. 5. View of an electron beam in a magnetic field created by the magnetic field of the Helmholtz coils.

Measurement procedure

As can be seen from the working formula (12), for the experimental determination of the specific charge of an electron, the accelerating voltage should be measured U, magnetizing current I and the radius of the electron ring r... Measurement of the accelerating voltage and magnetizing current is carried out using a voltmeter and an ammeter located on the front panel of the installation. The measurement of the radius of the ring is carried out by measuring the diameter of the ring using a measuring ruler 10, Fig. 3. To improve the accuracy of measuring the radius of the electronic ring, we recommend the following sequence of actions. To measuring ruler 3, Fig. 6, attach a right-angled triangle 2 with one leg. Then, move the sight 4 and triangle 2 and observe with the eye the position of the right edge of the ring along the other leg. As soon as the edge of the electronic ring, the sighting device and the observer's eye are on the same line, we count the coordinates of this edge of the ring. Then, in the same way, we count the left edge of the electron beam. The difference between these coordinates will give the value of the diameter of the electron ring, corresponding to the given values of the accelerating voltage and magnetizing current in the Helmholtz rings. Such a procedure reduces the error in measuring the diameter of the ring associated with parallax, a change in the position of the sight when the observer's eyes are displaced in the direction perpendicular to the line of sight.

After mastering the technique of the necessary readings, one should proceed to the main experiment. We set the magnetizing current to 1.50 A, measure the diameters of the rings at 3 different accelerating voltages: 150, 175, 200 V. Then we set the accelerating voltage to 175 V and measure the diameters of the rings at three values of the magnetizing current: 1.00 A, 1.50 A, 2.00 A. The measurement results are entered into a prepared table. The indicated readings should be made with an accuracy of half the scale division of the measuring instruments.

Table # 1

Experimental data table

№ p / p	Current strength(I ± ∆I)	Accelerating voltage(U±∆ U)	Ring diameter(d±∆ d)	Ring radius(r±∆ r)	Specific chargee / m e
				m ∙ 10 -3	Cl / kg

Processing the results of the experiment.

where. is the absolute error i-th measurement of the specific charge, is the Student's coefficient, n is the number of measurements, in our case 6 measurements are selected, α is the Student's reliability factor. In laboratory measurements, it is recommended to choose it equal to 95%.

Calculate the relative error ε of the specific charge of an electron using the formula:

Write down the final result and compare it with the table value for the specific charge of the electron.

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