1) function Y can be used Kintseva, uninterruptedі unambiguous;

2) weekend culpable uninterrupted;

3) the function may be integrated, then. integral buti is to blame kintsevim.

Rivnyannya (8) є to the hidden Rivnyannya of Schrödinger. Yogo is also called to the hourly tribute to Schrödinger The fragments will be placed according to the function Y for an hour. However, for most physical phenomena that are found in the microworld, equation (8) can be simplified by turning off the occurrence of Y at the hour, in order to know the Schrödinger equation for stationary stations – stations with fixed energy values. This, like a force field, in which a part collapses, is stationary, then. The function clearly does not lie in wait and has a sense of potential energy. In this case, Schrödinger's solution can be represented by the addition of two functions, one of which is a function without coordinates, the other - only an hour, and the time-period is expressed by a multiplier, so that

de E- The energy of the part is constant, it is constant when there is a stationary field. Substituting value in (8), omitting

Let's get to the point, which means the function y:

. (9)

Rivnyanna (9) is called Schrödinger's equations for stationary studies. To what extent is it possible to enter new energy? E parts. Theoretically, differential assessments are based on the fact that such assessments may result in an impersonal decision, in addition to the appearance of the overlap of borderline minds in selecting decisions that may result in a physical sense. For Schrödinger's adherence to such minds, the mind's regularity of bodily functions is of utmost importance. Thus, the real physical sense can only be achieved by decisions that are expressed by regular functions y. Ale regular decisions are made not for any parameter value E, especially when singing their set, attached to the given task. These energy values ​​are called powerful. Solutions as they suggest vlasnim energy values ​​are called power functions. Vlasna meaning E can be created as a continuous and discrete series. The first guy to talk about uninterrupted, or social, spectrum, for another – about discrete spectrum.

4. Nuclear model of the atom.

The currently accepted nuclear (planetary) model of the atom was introduced by E. Rutherford. It is clear from the model that around the positive nucleus that carries a charge Ze (Z- Ordinal number of the element in the Mendelev system, e- Elementary charge), size 10 -15 -10 -14 m that mass, practically equal to the mass of an atom, in a region with linear dimensions of the order of 10 -10 m Electrons collapse in closed orbits, destroying the electron envelope of the atom. The fragments of atoms are neutral, the charge of the nucleus is equal to the total charge of electrons, then. wraps around the core Z elektroniv.

Trying to figure out an atomic model within the boundaries of classical physics did not meet with success. The underworld of difficulties was thirsty for the creation of a clearly new thing - quantum- Theories of the atom. The first test of such a theory was made by Niels Bohr. Bohr based his theory on two postulates.

Bohr's first postulate (postulate of stationary states): in the atom there are stationary (not changing over the years) states, which do not have changing energies. The stationary state of an atom is illustrated by stationary orbits, in which electrons collapse. The flow of electrons beyond stationary orbits is not accompanied by changes in electromagnetic coils. In the stationary state of the atom, the electron, collapsing in a circular orbit, is responsible for the discrete quantization of the value of the moment of impulse, which satisfies the mind

de m e- Electron Masa, v- Yogo shvidkіst po n-th orbit radius r n.

Another Bohr postulate (frequency rule): when an electron moves from one stationary orbit to another, one photon with energy is dissipated (vanished)

equal difference in energy between the different stationary stations ( E nі E m– similar to the energy of the stationary states of the atom before and after the propagation (polishing)). At E n<E m photon propagation occurs (the transition of an atom from a higher-energy one to a lower-energy one, or the transition of an electron from a more distant orbital nucleus to a closer one), when E n>E m– its destruction (the transition of the atom from the station with greater energy, so that the transition of the electron is further removed from the nucleus orbit). Dial of possible discrete frequencies Quantum transitions are indicated by the linear spectrum of an atom.

The postulates laid down by Bohr allowed the spectrum of the water atom to be analyzed hydrogen-like systems– systems that are composed of nuclei and charge Ze and one electron (for example, He +, Li 2+ ions). Inheriting Bohr, let us look at the flow of the electron in such a system, interconnected by circular stationary orbits. The most common line, proponated by Rutherford, and the line (10), can be taken away for radius n-stationary orbit:

.

The signs show that the radii of the orbits grow proportionally to the squares of integers. For the atom water ( Z=1) radius of the first electron orbit at n=1, ranks first Borovsky radius (A), more expensive

,

which demonstrates the developments arising from the kinetic theory of gases.

Cream, medical quantization for radius n th stationary orbit value, it can be shown that the energy of the electron can take on only such permissible discrete values:

,

Where the minus sign means that the electron is in a connected state.

5. Atom water in quantum mechanics.

The related problem about the energy levels of the electron for the water atom (as well as water systems: helium ion He +, ionized lithium Li ++, etc.) is reduced to the problem about the electron collapse in the Coulomb field of the nucleus.

Potential energy of interaction between an electron and a nucleus that carries a charge Ze(for atom water Z=1),

,

de r– stand between the electron and the nucleus.

The state of an electron in an atom is described by the Hwyllian function y, which confirms the stationary Schrödinger equation (9), which is the front value of the potential energy:

, (12)

de m- Electron Masa, E- Full energy of an electron in an atom. If the fragment field in which the electron collapses is centrally symmetrical, then for the highest level (12) use a spherical coordinate system: r, q, j. Without getting caught up in the mathematical solution of this task, we will focus on looking at the most important results that emerge from it.

1. Energy. The theory of differential equations concludes that the equation of type (27) has solutions that satisfy the needs of unambiguity, endings, and continuity of the spine function. y, only at high energy values

, (13)

tobto. discrete set of negative energy values. Nainizhy Rhubarb E 1, which indicates minimal possible energy, - Main, all others ( E n >E 1, n=1, 2, 3, …) – awakened. At E<0 движение электрона является let's knit, and when E>0 – free; area of ​​uninterrupted spectrum E>0 confirms Ionized atom. Viraz (13) follows the formula derived by Bohr for the energy of the water atom. Since Bohr had the opportunity to introduce additional hypotheses (postulates), the quantum mechanics of discrete energy values, being an inheritance of the theory itself, flows directly from Schrödinger’s highest theory.

2. Quantum numbers. In quantum mechanics it happens that Schrödinger’s equation (12) satisfies the power functions, which are indicated by three quantum numbers: the head n, orbital l and magnetic m l.

Golovne quantum number n, obviously (13), means energy levels of the electron in an atom you can acquire any number of whole values ​​starting from one:

n=1, 2, 3, …

Schrödinger's determined jealousy is growing, so moment of impulse(mechanical orbital moment) electrons are quantized, then. cannot be sufficient, but takes discrete values, which are indicated by the formula

de l – orbital quantum number, for a given n accepts the value l=0, 1, …, (n-1), then. everything n meaning and means moment of electron impulse in atom.

Schrödinger's solution is the same as the vector L l the moment of electron impulse can no longer have such orientation in space, which has its projection Llz directly z the external magnetic field acquires quantized values ​​that are multiples of:

Rice. 1

de m l – magnetic quantum number, for a given l you can accept the value m l=0, ±1, ±2, …, ± l, then. total 2 l+1 value In such a manner magnetic quantum number m l means projection of the angular momentum of the electron onto direct tasks Moreover, the vector of the momentum of an electron in an atom can be found in space 2 l+1 orientation.

The diversity of electron detection in different parts of the atom varies. The electron in its own way is like “smearing” throughout the entire volume, creating an electronic cloud, the thickness of which characterizes the homogeneity of the electron’s presence at various points in the volume of the atom. Quantum numbers n and l characterize the size and shape of the electronic cloud, and the quantum number m l characterizes the orientation of the electronic cloud in space.

3. Spectrum. Gases that glow give a linear part of the spectrum of vibration. Consistent with Kirchhoff's law, the spectra of clay gases also exhibit a linear structure. All serial formulas for the spectrum of water can be expressed in a single formula, which is called formalized by Balmer's formula:

, (16)

de R=3.293×10 15 z -1 – Postina Rydberg, mі n– whole numbers, and for this series n=m+1, m+2, m+3 etc. This is divided into six series of spectral lines: the Lyman series ( m=1), Balmer series ( m=2), Paschen series ( m=3), Bracket series ( m=4), Pfund series ( m=5), Humphrey series ( m=6) (Fig. 1).

6. Electron spin. Pauli's principle. The principle of non-virtuousness

identical parts.

In 1922 It was discovered that a narrow beam of water atoms, which clearly exist near the s-state, splits into two beams in a non-uniform magnetic field. In this case, the entire moment of the electron impulse is equal to zero (14). The magnetic moment of the atom, which is with the orbital arm of the electron, is proportional to the mechanical moment, which is equal to zero and the magnetic field can flow water onto the arm of the atoms, which becomes important, then. splitting is not to blame buti.

To clarify this phenomenon, as well as a number of other difficulties in atomic physics, it was stated that the electron can power unimpaired mechanical moment to impulse, not bound by the flow of electrons in the open air, – spin. The spin of an electron (and all other particles) is a quantum quantity and has no classical analogue; This is the internal invisible power of the electron, similar to its charge and mass.

How the electron is assigned its own mechanical moment to the impulse (spin) L s then it is indicated by the power magnetic moment. Similar to the hidden concepts of quantum mechanics, spin is quantized according to the law

,

de s – spin quantum number.

In analogy with the orbital angular momentum, the projection L sz the spin is quantized so that the vector L s can take 2 s+1 orientation. The fragments in the traces were careful in only two orientations, then 2 s+1=2, stars s=1/2. The projection of the spin onto the direct line of the external magnetic field, with a quantized value similar to (15):

de m s – magnetic spin quantum number; there may be less than two meanings: .

The distribution of electrons in an atom is ordered by the quantum mechanical law, Pauli's principle or else principle of inclusion. In his simplest form, he can say: “Any atom cannot have two electrons that exist in two stationary states, which are indicated by a set of four quantum numbers: the head n, orbital l, magnetic m l that of spin m s", tobto. Z(n, l, ml, ms)=0 or 1, de Z(n, l, ml, ms)- The number of electrons present in a quantum state, which is described by a set of four quantum numbers: n, l, ml, ms. Thus, the Pauli principle states that two electrons bound in the same atom are divided by the values ​​of one quantum number.

The total number of electrons in an electron-rich atom that equals the same quantum number n, call electronic shell. In the membranes of the skin, electrons are distributed under the balls, which confirms this l. The fragments of the orbital quantum number increase in values ​​from 0 to n-1, the number of subshells is equal to the serial number n shells. The number of electrons in the ball of the stomach is indicated by magnetic and magnetic spin quantum numbers: the maximum number of electrons in the ball of the ball with data l one 2(2 l+1).

As soon as we go from looking at the influence of one microparticle (one electron) to rich elemental systems, then special powers emerge that have no analogue in classical physics. Let the quantum mechanical system be formed from new particles, such as electrons. All electronics have, however, physical properties - mass, electrical charge, spin and other internal characteristics. These parts are called identical.

The non-independent power of the system of new identical parts appears in fundamental principle of quantum mechanics - principle of non-dispersal of identical particles Therefore, it is impossible to experimentally separate the same parts. In a classical mechanism, however, new parts can be separated according to space and impulses, then. Classic pieces carry individuality.

Quantum mechanics is becoming different. This relationship of insignificances implies that for microparticles in the future the concept of trajectory is not stagnant; The location of a microparticle is described by a fork function, which makes it possible to calculate the excessiveness () of the presence of a microparticle on the outskirts of one or another point in space. Since the functions of two identical parts in space overlap, then Rozmova, in which part is in this galusa, in order to reduce the sense: we can also talk about the possibility of having one in this galusa. from the same parts. Thus, in quantum mechanics, the same parts completely lose their individuality and become inviolable.

7. Quantum statistics. Virogen gas.

The main task of statistical physics in quantum statistics lies in the known functions of the distribution of parts of the system for these and other parameters - coordinates, impulses, energies, etc., as well as the calculated average values ​​of these parameters that characterize There is a macroscopic structure of a system of particles. For systems of fermions and bosons, this situation holds true, but in a different way due to the fact that bosons do not obey the Pauli principle. Apparently, two quantum statistics are distinguished: Fermi-Dirac and Bose-Einstein, between which the type of function is determined by the distribution of the particles of the system by energy.

Guess what function of the energy division There is a part of the total number of particles that transmit energy in the range of values W before W+dW:

,

de N- a great number of particles, f(W)- Function of division according to energies.

For system n non-interacting fermions with energy W(ideal Fermi gas) or systems with n non-interacting bosons with energy W(Ideal Bose gas) were assigned similar functions to the subdivision:

, (17)

de k- Postin Boltzmann, T- Thermodynamic temperature, m- chemical potential, which changes the energy of the system when changing the number of particles of the system by one during an isochoric or isentropic process. Within the framework of the Fermi-Dirac statistics (32), take the “+” sign, then. in this situation. Suitable for Bose gas - the sign "-" i.

Gas called virogenim How do his powers conflict with the powers of the classic ideal gas. The fermented gas exhibits a mutual quantum-mechanical influx of particles into the gas, due to the non-dispersal of the same particles. The behavior of fermions and bosons is different during virility.

To characterize the gas generation stage, introduce parameter virogennya A:

The function of the subdivision for the additional parameter of the generation of both quantum statistics will be written in the form:

.

Yakshto parameter virogennya maliy A<<1, то и функция распределения превращается в the Maxwell-Boltzmann subdivision function, which underlies the classic statistics of ungenerated gas:

Virogen temperature is called the temperature, below which the quantum power of an ideal gas and the similarity of particles are clearly revealed. It is easy to roughly estimate the temperature criterion for the generation of gas. The generation of normal gases is indicated at low temperatures. This is not true for photonic and electron gases in metals. Electronic gas in metals is practically the beginning of its development. Only for temperatures greater than several tens of thousands of degrees of electrons and metals would follow the classical Maxwell-Boltzmann statistics. It is impossible to melt metals in a condensing plant at such temperatures. Therefore, the classic description of the behavior of electrons in metals is reduced to electrodynamics an hour before the laws, and it is very important to conclude. In conductors, the concentration of electron gas is significantly lower than in metals. In the minds, the temperature of degeneration becomes close to 10 -4 The electron gas in the conductors is non-generating and is in the order of classical statistics. The butt of the generated gas is photon gas. The fragments of the photon mass are equal to zero, then the temperature of the birth is indistinguishable. Photon gas is a product of any temperature. Atomic and molecular gases swell even at low temperatures. For example, for water, for normal people, the temperature of generation is close to 1 K. For other gases, the most important, lower water, it is even less. Gazis do not pretend to be normal minds. The virility associated with the quantum powers of gases manifests itself much less than the evolution of gases in the form of ideality, due to intermolecular interactions.

The maximum energy that can cause electron conductivity in a crystal at 0 K is called Fermi energy and is indicated E F. The highest energy source occupied by electrons is called equal to Fermi. p align="justify"> The Farm level is indicated by the energy of the Farm, which is where electrons are generated on this level. Rhubarb Fermi, obviously, will be the thing with the greater strength of the electron gas. The electron output from the metal must be restored from the Fermi level, then. from the upper energy level occupied by electrons.

8. Understanding the band theory of solids.

According to Schrödinger's theory, you can, in principle, look at the knowledge about the crystal, for example, find out the possible values ​​of its energy, as well as other energy levels. However, both in classical and in quantum mechanics there are daily methods for accurately achieving such a task for many parts. Therefore, the problem is approximately reduced to a problem of many particles to a one-electron problem about one electron that collapses in a given external field. A similar way to lead to band theory of solids.

Rice. 2

For now the atoms are isolated, then. There are one kind of one at a time on macroscopic scales, they smell like circuits of energy levels that are avoided. When illuminating the crystalline mountains, then. When atoms are brought close to interatomic regions, interactions between atoms result in the energy levels of atoms shifting, splitting and expanding into zones that create zone energy spectrum. In Fig. Figure 2 shows the splitting of energy levels directly between atoms. It can be seen that the equal parts of the external, valence electrons, which are weakest bound to the nucleus and have the greatest energy, are clearly split and expanded, as well as the other equals, which are mainly and the atoms will not be occupied by electrons. And the layers of internal electrons either do not split at all, or split weakly. Thus, in solids, internal electrons behave in the same way as in isolated atoms, and valence electrons are “collectivized” - they belong to every solid.

The energy of external electrons can increase the value at the boundaries marked in Fig. 2 regions, ranks permissible energy levels. The skin zone “contains” as many adjacent discrete atoms as a crystal: the more atoms there are in a crystal, the more atoms there are in the zone. The distance between the daily energy levels is very small (about 10 -22 eV), so that the zones can be operated practically without interruption, because the fact of the final number of levels in the zone plays an important role for the distribution of electrons and behind the camps. Allowed energy zones are separated by zones of protected energy values, which are called protected energy zones. The stench of electronics is overwhelming. The width of the zones (permitted and protected) does not lie with the size of the crystal. The zones allowed are wider, lower weak bonds of valence electrons with atoms.

The band theory of solids made it possible to see at a glance the origin of metals, dielectrics and conductors, explaining the importance of electrical authorities, first of all, to the unequal filling of permissible zones with electrons and, in other words, the width of the fenced zones. The level of filling of energy levels with electrons in a zone is determined by the filling of various atomic levels. In a zagalnym vipadka you can talk about valence band, which is completely filled with electrons and created from the energy levels of the internal electrons of free atoms; conductivity zone (free zone), Which is either often filled with electrons, or free and made from the energy levels of external “collectivized” electrons and isolated atoms. It depends on the stage of filling the zones with electrons and the width of the fenced zone, which may cause losses (Fig. 3).

In Fig. 3, A The main area for removing electronics is only partially filled, then. she has vacant positions. In this phase, electrons, having lost so many small energy “additions” (for example, for a change in thermal energy or electric field), can move to a higher energy level in the same zone,

The duration of the quantum part is proportional to the impulse.

One of the facts of subatomic light is that its objects - such as electrons and photons - are not at all similar to the primary objects of macrolight. They behave themselves not like particles, and not like hulks, but like all the special creations that reveal both khvilov’s and corpuscular power due to the surroundings. div. The principle of additionality. One on the right - this is to say, and completely different - to connect the whole and corpuscular aspects of the behavior of quantum particles, describing them exactly. The whole thing itself was broken down by de Broglie’s wife.

Louis de Broglie published his research as the author of his doctoral dissertation in 1924. De Broglie's discovery, which seemed at first like a divine idea, radically revolutionized the ideas of theoretical physicists about the microcosm and played an important role in the established quantum mechanics. From now on, de Broglie’s career was even more prosaic: before retiring, he worked as a professor of physics in Paris and never again rose to the foggy heights of revolutionary insights.

Now let us briefly describe the physical sense of de Broglie's relationship: one of the physical characteristics of any part - it fluidity. In this case, physicists, from a number of theoretical and practical considerations, pay more attention to talking not about the fluidity of a particle as such, but about it impulses(or How many rocs?), which is the old way to get the smoothness of the part on its mass. The peak is described by other fundamental characteristics - magnitude (the difference between two vessel peaks of the same sign of amplitude) and frequency (a value expressed in proportion to the peak, the number of peaks that pass through b through a fixed point in one hour). De Broglie was able to formulate the relationship that connects the impulse of a quantum part R From Dovzhnoy Hvilya λ, which she describes:

p = h/λ or else λ = h/p

It’s useful to say literally this: behind the scenes you can see a quantum object as a particle that makes a big difference to the roc R; From the other side, it can be seen as a joke, the dovzhina of which is ancient and is indicated by the corresponding equals. In other words, the physical and corpuscular powers of quantum parts are fundamentally interconnected.

De Broglie's research made it possible to clarify one of the greatest mysteries of quantum mechanics to emerge. When Niels Bohr proposed his model of the atom ( div. Bohr's atom), which included the concept permitted orbits electrons near the nucleus, which smells could wrap around for many years without wasting energy. With the help of de Broglie's interpretation, we can illustrate this concept. If you take in an electron frequently, then if an electron is lost in its orbit, it will have the same fluidity (or rather, momentum) at any distance from the nucleus.

To take into account electrons, in order for them to fit into the orbit of a given radius, it is necessary that the dovzhin number of this orbit is equal to the whole number of dozhni of its orbit. In other words, the orbit of an electron can account for at least one, two, three (and so on) dowzhins. In many cases, it is simply impossible to get an electron into the required orbit.

The main physical sense of de Broglie's work is that we can determine the permissibility of impulses (in the corpuscular manifestation) and the presence of electrons in orbits. For most orbits, however, de Broglie's correlation shows that an electron (seen as a fragment) with a specific impulse cannot produce a congeneric line (in the case of a particle) such that it fits into this orbit. And by the way, the electron, which looks like the death of a singing dowry, will not always receive a positive impulse that will allow the electron to be lost in orbit (in a corpuscular form). In other words, for most orbits with a specific radius, either a spinal or corpuscular description will show that an electron cannot travel at this distance from the nucleus.

However, it is clear that the number of orbits in which corpuscular phenomena about electrons occur is small. For these orbits, the impulse required for the electron to remain in the orbit (corpuscular description) exactly corresponds to the impulse required for the electron to fit into the circle (corpuscular description). These orbits themselves appear permissible In the model of the Bohr atom, the fragments only on them the corpuscular and biological power of electrons do not enter into supernaturality.

I like another interpretation of this principle - a philosophical one: Bohr's atomic model allows for such orbits of electrons, which are not important, since people stagnate for their description with two mental categories. That, in other words, is the real microworld of influences so that we have no idea what categories we are trying to understand!

Div. also:

Side 1

Chemical processes lead to the transformation of molecules, then. to the destruction and destruction of bonds between atoms. Therefore, the most important problem of chemistry has always been and is eliminated by the problem of chemical interaction, which is closely connected with the everyday power of speech. A current scientific interpretation of the nutrition of chemical substances and the nature of the chemical binder is given quantum

mechanics

– the theory of flow and interaction of microparticles (electrons, nuclei, etc.).

One of the hidden powers of matter is its duality. Pieces of matter are tossed around at the same time, both corpuscular and corporeal powers. The relationship between the kingdom and the part is such that with the changes in mass, the parts of the kingdom's power will become more powerful, and the corpuscular ones will weaken. If the part becomes equal to the atom, beware of typical wormholes. At the same time, it becomes impossible to describe the flow and the interaction of micro-particles with the laws of the flow of bodies and the great mass. The first story of the direct creation of Hwylov or quantum mechanics, the laws of which come from both Hwylov and the corpuscular power of particles, was created by de Broglie (1924). De Broglie came up with the hypothesis that the material part of the skin undergoes a periodic process. As a part collapses, this process appears to be expanding, as it is called hwileyu de Droyle

Abo phase hvilya

The fluidity of the particle V is related to the length of the needle λ de Broglie's narration

de m - Masa part (for example, electron);

h – Planck's stationary.

Rivnyanya (1) is brought to the free flow of particles. If a part collapses in a force field, then those associated with it can be described as so-called hvil function

The obscure appearance of this function is explained by Schrödinger (1926). We know the function of the advancing path. The level, which characterizes the field strength Ea of a flat monochromatic light wave, can be written in the form:

, (2)

de Ea0 - amplitude of the flue;

ν – kolivan frequency;

t – hour;

λ – dovzhina hvili;

x is the y coordinate of the direction of the width of the spine.

Fragments of other materials from the level of the flat spine (2), taken at the hour t and coordinate x, the levels are similar:

, (3)

, (4)

That

Substituting λ=с/ V (z – lightness of light), selectable level for flat light needle:

, (5)

The steps of the transformation are grounded on the sides, so that the widened de Broglie ridge is described as similar to the ridges, and that the ridges become stationary and spherical. It is immediately obvious that the values ​​of the new function of the coordinates (χ, y, z) change behind the equations (5), which affects the amplitude of the given colival process. Then, by replacing Ea with ψ, we take away the similarity of the form.

Few models of boru. Bohr's model of the atom is still being used in a number of cases. It can be used to interpret the distribution of elements in the periodic table and the patterns of change in the ionization energy of elements. Bohr's prote model has shortcomings. 1. This model does not allow us to explain the specific features of the spectra of important elements, even though they are 2. It is not experimentally confirmed that electrons in atoms wrap around the nucleus in circular orbits with a final moment.

The nature of the electron is unique. It is clear that electromagnetic vibrations tend to reveal both physical and corpuscular powers (similar to the powers of particles). Once in a while, you know it’s like a flow of particles – photons. The energy of a photon is associated with its frequency and frequency. E = hυ = h c/ λ ( h = λ · υ),

de h- Stationary Plank is 6.62517∙10 -34 J∙s, c- brightness of light.
Louis de Broglie noted that similar power could be attributed to the electron. Vіn ob'єdna vіnnyana Einstein ( E = m h 2) that Planck ( E = hυ) in one:

hυ = m·s 2 h · s/ λ = m·s 2 λ = h/m·s.

λ = h/m · ѵ,

de – ѵ electron fluidity. Ceremony ( de Broglie's Rive), which connects the dowzhin with his impulse ( mѵ), and formed the basis of Khvil’s theory of the electron state of the atom. De Broglie decided to consider the electron as a standing structure that must fit into an atomic orbit a number of times, which corresponds to the number of the electron level. Thus, an electron that is on the first electron level (n = 1) is indicated by one dozhni in the atom, and two or two in the other (n = 2).

The subversive nature of the electron leads to the fact that its flow cannot be described by a song trajectory, the trajectory blurs, it appears as a “mist of insignificance”, which is what it is. The more precisely we are able to determine the location of the electron, the less accurately we know about its fluidity. Another law of quantum mechanics sounds like this: “It is impossible to immediately, with any given accuracy, determine the coordinates and momentum (fluidity) of the electron that collapses” - this is Heisenberg’s principle of insignificance. This feasibility is assessed on the lines of Schrödinger (basically a line of quantum mechanics):

H · ψ = E · ψ,

where H is the Hamiltonian operator, which indicates the sequence of operations with the function. Zvidsi E = H · ψ/ψ. Rivne has a number of ties. The Wilian function, which is the solution to Schrödinger's equation, is atomic. orbital As a model of the state of an electron in an atom, the following statements about electron pollution are accepted: the density of similar sections is proportional to the number of electrons found there.

Regardless of the impossibility of accurately determining the position of the electron, one can show the certainty of the location of the electron at the exact position at any given time. Heisenberg's principle of non-significance has two important implications.

1. The collapse of an electron in an atom is a collapse without a trajectory. The replacement of the trajectory in quantum mechanics has a different concept -internationality the presence of an electron in the singing part of the atom, which correlates with the electronic strength when considering the electron as an electronic waste.

2. An electron cannot fall onto the nucleus. Bohr's theory did not explain this phenomenon. Quantum mechanics explained this phenomenon. An increase in the importance of the coordinates of the electron when it falls on the nucleus resulted from a sharp increase in the energy of the electron to 1011 kJ/mol and more. An electron with such energy instead of falling onto the nucleus is responsible for depriving the atom. It is obvious that the sound is necessary not in order to remove the electron from falling onto the nucleus, but in order to cause the electron to move between the atoms.

List of references:

Sinkevich O.A., Stakhanov I.R.; plasma physics; Publishing house MEI, 1991

Sinkevich O.A.; There is trouble and instability in the world; MEI branch, 2016

Sinkevich O.A.; Acoustic effects of solid state plasma; MEI Publishing House, 2007

Aretemov V.I., Levitan Yu.S., Sinkevich O.A.; Instability and turbulence in low-temperature plasma; MEI branch, 1994/2008

Ryder Y.P.; Physics of gas discharge 1992/2010

Ivanov A.A. Physics of highly unimportant plasma 1977

Plasma- The middle is made up of neutral particles (molecules, atoms, ions and electrons) due to the external interaction of the electromagnetic field with the main one.

Applications of plasma: Sun, electrics (blinkers), Pivnichne sіyannya, brewing, lasers.

Plasma booms

Gazoviy(9th semester). Thickness can be varied from 10 4 to 10 27 kg/m 3 temperature from 10 5 to 10 7 K

Solid(10th semester).

The plasma behind the aggregate mill is booming

Chastkova. If there are a lot of particles, some of them are ionized.

Povniy This means that all parts are ionized.

Method of applying plasma to acid. Starting at a temperature of 0 K, starting to heat up, the cob will be solid, after reaching a certain value, rare, and then gas-like. Starting at a low temperature, dissipation occurs and the acid molecule is divided into acid atoms. As soon as the kinetic energy of the electrons continues to heat up, it will be sufficient to displace the atom and thus the atom will transform into an ion (fractional plasma). If you continue heating, you simply won’t run out of atoms (all plasma)

Plasma physics is based on modern sciences:

Thermodynamics

Electrodynamics

Mechanics of charged bodies

1. Classic (Newton level)

   1. Nereviteliysk (U<

      Reviteliysk

Quantum

Kinetic theory (Boltzmann level)

Classical mechanics of external electromagnetic fields

Let's take a look at it in time, if B=0.

Let's take a look at the situation if E = 0, U = (Ux, 0,0); B=(0,0,Bz)

Let’s look at the situation if E = (0, Ey, 0) and B = (0,0, Bz). Let the unraveling of the heterogeneous rivalry appear

Classical mechanics of modern electromagnetic fields due to the power of construction

Hall effect- The flow does not flow to the vector of the electric field due to the presence of the magnetic field and the formation of particles.

Electrodynamics

Premise: 1 day of charge (q), significantE(r). The following assumptions are acceptable: the whole structure is stationary, there are no strums as part 1 and does not collapse. The fragments rot(B) and div(B) become 0, then the vector B=0. It can be assumed that this will be due to spherical symmetry, which means that the Ostrogradsky-Gauss theorem can be corrected.

Electromagnetic field near plasma

Zavdannya: є part of the charge (q), sharpened with neutral plasma. The assignments for the previous task have not changed, which means B=0. The plasma fragments are neutral, the concentration of negative and positive charges will be the same.

Plasma colivania

Let's look at this problem. Є 2 charge a proton and an electron. So, since the mass of a proton is much larger than the mass of an electron, the proton will not be crumbly. In an unknown way, the electron is introduced to a small level to become equal and let go, the approach of equalization is withdrawn.

Level of electromagnetic circuit

Let's look at the step, there is no flow, there is no power to the charge, then

If you put the solution on the level of the electromagnetic circuit, you will get

Level of electromagnetic flux with strum (in plasma)

In essence, there is nothing to change from the past task

Let the decision be taken to make this look like this, then

As the electromagnetic flux penetrates the plasma, it is not knocked out and melted.

Plasma thermodynamics

Thermodynamic system- this is a system in which there is no exchange of energy, impulse and information with the external medium.

Calculate the significance of thermodynamic potentials in this way

How to find the closest ideal gas for plasma

It is acceptable that all the charges are electrons, and the gap between them is very small, then

In an area of ​​weak lack of development, one can expect to see a sign of real rapport

The quantum internal energy zone has internal Faraday energy

In a zone of highly non-ideal plasma, the conductivity of the fluxes can change sharply, so that the flux becomes a dielectric and a conductor.

Rozrakhunok plasma warehouse

The basic principle of this design is taken to determine the concentration of chemical elements. Since this system is in constant control of temperature and pressure, then the equivalent Gibbs energy is equivalent to 0.

There are different types of ionization: quantum depletion, contact with an awakened atom, thermal etc. (the thermal itself can be seen from a distance). For her, this is a system of peerages.

The main problem lies in the fact that it is not clear how to store the chemical potential in the concentration, for which it is necessary to go to quantum physics.

For unknown reasons, the equation is equivalent to the one in which the concentration of the free energy is inverted. Remnants of De Broglie's thermal energy for the atom and for the ion, however, practically disappear. 2 fragments of electrons and 1 level of energy are generated, and this is the result.

Once the ion system is decoupled, the concentration of ions is determined by the following formula

The technique is mostly designed for ideal ionization, but it is expected that this will change if it is not ideal.

Since for the atom the ideality is not equal to 0, for the ion and the electron they are equal, no more changes are expected, so the ideality of Sakha looks like the coming order.

Umovi vinikneniya two temperature plasma

It is expected that the average thermal energy of the plasma itself is already dissipated by electrons, atoms and ions. And it turns out that the temperature for electrons reaches 10,000 K, while for atoms and ions it is more than 300 K.

Let's take a look at a simple loss of electrons in a stationary electric field, which gives rise to the thermoemy of electrons, then its fluidity can be determined by the onset of

Let's look at a similar situation, the electron coincides with the atoms, so we can say that the tension is removed

Kinetic theory of plasma in the transfer process

This theory was developed in order to solve the problem correctly in the event of a non-successful middle course, in which case a transition is possible in this theory.

The basis of this theory is laid in the assigned function of the division of particles in the singing relationship with the action of fluidity at the right moment. (This function was seen in TTSV, so there will be some repetition here + the writing data is so encrypted that I can’t recognize them).

Next, we will look at the relationship between the two pieces, which seem to be collapsing in space. This task can be solved simply by replacing that one part contains a liquid mass with a liquid liquid, which collapses in the same field at the same time, which is not dry. The purpose of this task is to what extent the part will recover from its primary direction. The smallest distance of the particle to the center of interaction is called the impact parameter.

Let's look at the function in thermodynamic equation, then

And the Maxwell function has been removed

The problem lies in the fact that in such a function it is not possible to calculate thermal conductivity and viscosity.

Let's move straight to plasma. Let the process that occurs be stationary, and the force F=qE, and the atoms also represent the Maxwellian branch.

When reversing the order, it became clear that what allows us to throw out a small member. Let the required function be designated as such