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6. MODEL OF ELECTRON AND PROTON

 

6.1. General Data on Electron

 

Let us pay attention to the fact that the interaction between electromagnetic structures of the atom takes place without resistance observation. If you ever held the magnets in your hands and tried to bring their like poles nearer each other, you felt resistance and complete lack of this resistance at the time when you displaced one magnet relatively to another. In that case you felt their free relative displacement. The same takes place when electromagnetic structures interact in the atom. It cannot be otherwise. In all other cases the law of conservation of angular momentum fails to operate.

In contrast to the photon, the electron  is at rest under the conditions when it is in space and when no external force influences it. But it spends greater part of its life in the atom. Here it works constantly supporting equilibrium between energy state of the atom and energy state of the environment. If surplus of some or other photons is available in the environment, it begins to absorb them immediately in order to support disturbed equilibrium. If there is a lack of some photons in the environment, the electron of the atom begins to radiate these photons intensively in order to support a new energy level of the environment. This process takes place in the Universe constantly; it is not stopped even for a second.

If the electron did not function in such a way, we’d never get warm in case we were cold. We can see the importance of the function performed by electrons! If you get warm, please, note that it is warmth from the electrons of your body, which have absorbed the photons from the environment. If you are cold, please, note that the electrons have deprived you of the photons and have radiated them into the environment. That’s why you dress warm when the weather is cold. You do it in order to reduce radiation of the photons.

It is very important to understand that after the electron has absorbed the photon, the electron moves away from the atomic nucleus. This is the main cause of expansion of gases and bodies when they are heated. After photon radiation it gets nearer to the atomic nucleus. This is the main cause of reduction of volumes of gases and sizes of solids during their cooling. Using this general information let us begin to find an electromagnetic model of the electron. For this purpose, let us analyse the existing notions concerning its orbital motion round the atomic nucleus.

 

 

6.2. Orbital Motion of the Electron in the Atom

 

It is supposed that when the electron moves in its orbit, it is influenced by two forces: Coulomb’s force  , which attracts it to the nucleus, and the centrifugal force of inertia , which withdraws it from the atom. It is considered that the electron  being the material point is kept on a definite orbit due to equality between the above-mentioned forces (Fig. 12).

 

Fig. 12. Diagram of planetary motion of the point model of the electron

 

                                                                                 (132)

 

It is not difficult to see that equality between potential   and kinetic   energies of the electron originates from equality of these forces.

.                                                                 (133)

Orbital velocity  of the electron depends on angular frequency  of its orbital rotation and radius  of the orbit (Fig. 12)

 

             .                                                                    (134)

 

Then the formula (133) will be written in such a way

 

,                                                    (135)

 

          where:  is Planck’s constant.

                                                 .                                                      (136)

 

As the equation (135) describes the bond between potential and kinetic energies of the electron in the hydrogen atom, it should correspond to the data of experimental spectroscopy. According to these data, when the electron passes from the first orbit to the second one, its binding energy with the nucleus is reduced from 13.6 eV to 3.4 eV, i.e. fourfold. The right part of the equation (135) shows that this reduction takes place due to the reduction of angular frequency  of rotation of the electron, because . The preservation of equality between the right and the left parts of the equation (135) is possible if orbital frequency  is reduced fourfold, radius  of the orbit is increased by the same magnitude.

Let us consider the expression of orbital angular momentum of the electron (136). As centrifugal force of inertia and Coulomb force of attraction of the electron to the nucleus are directed radially (Fig. 12), they change only its mechanical trajectory and cannot change rotation rate of the electron. That’s why in this case the law of conservation of angular momentum should operate (136). It is manifested in the following way.

When the electron passes from the first orbit to the second one, it absorbs the photon with the mass, which is almost 1000fold less than the mass of the electron itself. It means that the conservation of persistence of Planck’s constant in the expression (136) takes place mainly at the expense of the change of the values  and . But during the analysis of the formula (135) we have already shown that it appears from the experimental spectroscopy that the value  is reduced fourfold when the electron passes from the first orbit to the second orbit, and radius of the orbit R is increased by the same magnitude. It is clear that if  is reduced fourfold in the expression of Planck’s constant (136), value   should be increased fourfold as well in order to preserve this equality, but it is reduced sixteenfold, and it leads to the violation of persistence of Planck’s constant, i.e. to the violation of the law of conservation of orbital angular momentum (136). Such result points to the fact that the electron of the hydrogen atom has no orbital motion. Later on when we analyse the spectrum of the hydrogen atom, we’ll get additional proof of the absence of orbital motion of the electron in the atom.

Thus, if we take a material point as a model of the electron, the data of experimental spectroscopy show that such electron has no orbital motion.

 

 

6.3.  The model of electron is as a ring

 

It is known that the electron has its own energy which is usually determined according to the formula . But the meaning of such an assumption is deciphered not always. And the meaning is that   if the whole energy of the electron is transformed into energy of the  photon, its energy becomes equal to . This fact has a strong experimental confirmation. It is known the masses of electron and positron are equal. When they interact they form two – photons. That’s why the energy of the photon which has the corresponding mass can be attributed to the electron. Electron rest mass   is determined with great accuracy. Let us call electron energy  being equal to photon energy a photon energy of electron.

First of all, let us investigate the possibilities of the ring model of free electron. It is known that the electron has kinetic energy and potential energy which are equal to each other [168], [176].

 

                                                                 (137)

 

The calculation according to this formula gives the following value of photon energy of the electron:

 

                                         (138)

 

If free electron rotates only relatively to its axis, angular frequency  of rotation of ring model of free electron determined according to the formula (137) is equal to

 

                                             (139)

 

and radius of the ring is equal to

 

                                (140)

 

Velocity of  points of the rotating ring is equal to velocity of light:

 

                                           (141)

 

Let us try to memorize the obtained values  and . We shall get the same values, but with the help of other formulas, which contain electromagnetic characteristics of the electron.

We should pay attention to the following fact here. In classical mechanics the simplified models are often used instead of the actual objects. The same has taken place in this case as well. We have not found out the structure of the electron, but we have obtained its simplified model – the ring. This model helps us to analyze mechanical behavior of the electron, but it contains no information concerning its electromagnetic properties. Let us try to find such mathematical models which describe behavior of the ring model of the electron, which contain its charge , magnetic moment  and electron electromagnetic field strength   (magnetic induction of electron).

If we assume that the electron charge is distributed uniformly along the length of its ring model, each element of the ring  will have mass    and charge     (Fig. 13). In this case the rotating ring model of the electron will resemble ring current, and two forces which have equal values and opposite directions: inertial force      and Lorentz force  (Fig. 12).

 

 

 

Fig. 13. Diagram of ring model of the electron

 

                                                                    (142)

Let us pay attention to the fact that there are two notions for the magnetic field characteristic which are similar as far as physical sense is concerned: magnetic field induction  and magnetic field strength  which are connected by the dependence

where   is magnetic constant.

The analysis experience shows that it creates a certain confusion during the formation of the ideas concerning magnetic field, that’s why some authors refuse to use a clumsy term “magnetic induction” and preserve only one, more felicitous term “magnetic field strength” using symbol  for it. Cl. E. Suortz, the author of the book “Unusual physics of usual phenomena” [34], acted in this way, and we follow his example. Magnetic field will be characterized by vector , it will be called magnetic field strength measured in SI system in T (Tesla) [177].

Then the dimensions of left and right parts of formulae (142) will be:

 

 

If we write  for mass density of the ring and    for charge density, we shall have

 

                                                          (143)

 

 

                                                         (144)

As:

                                                                        (145)

                                                                        (146)

 

and  , the equation (142) assumes the form

 

                                                         (147)

 

or

                                                    (148)

 

Thus, we have got the mathematical relation which includes: mass  of free electron, its charge , magnetic field strength  inside the electron ring which is generated by rotating ring charge, angular frequency  and radius  of the electron ring. Magnetic moment of electron or, as it is called, Bohr magneton is missing in this relation which mathematical presentation is as follows

                                                   (149)

 

Let us pay attention to the fact that in the above-mentioned relation  is vector value; it gives vector properties to Bohr magneton  as well. It follows from the formula (149) that the directions of vectors  and  coincide. Let us convert the relation (148) in the following way

 

                                                      (150)

 

The result from it is as follows

 

                                                                           (151)

 

The left part of this relation can be considered as scalar  product of two vectors:  and . Energy value  is vector as well. We have come across vector  properties of single electron energy. Let us recollect that when we have considered the processes of radiation and absorption of the photons by the electrons we have found out that their energies are equal to vector products of two parallel vectors  and . Mathematical model of energy of the electron has the same dependence (151).

Now from the relations (151) we can determine magnetic field strength  inside the ring mode of the electron, angular velocity , rotations of the ring and its radius

 

                               (152)

 

Let us pay attention to rather large magnetic field strength in the centre of symmetry of the electron and let us remind  that it diminishes along the electron rotation axis directly proportional to the square of a distance from this centre [34]. We find from the relations (151)

 

                                (153)

 

As peripheral velocity of the ring points is equal to velocity of light, we have

 

                                                     (154)

 

The main parameters of the ring model of free electron: ring radius  (140), (154) and angular frequency of its rotation (139), (153) determined from the different relations  (137) and  (150) have turned out to be equal.

A drawback of the ring model is in the fact that it does not open a cause of positron birth, that’s why the intuition prompts that the ring should have some internal structure. Our next task is to find out this structure.

Before we begin to solve this task, let us pay attention to the diagram of the ring model of the electron which results from our calculations (Fig. 13). A coincidence of the directions of vectors  is the main peculiarity. The model of electron proves vector properties of Planck’s constant  and Bohr magneton . We see that these vectors play a decisive role in the formation of atoms, iones and molecules.

We’d like to draw the attention of the reader to the fact that in all cases of our electron behaviour analysis Planck’s constant in the integer form plays the role of its spin. In modern physics it is accepted to think that the photon spin is equal to , and the electron spin is equal to 0.5. But the electron spin value (0.5) is used only for the analysis of qualitative characteristics of electron behaviour [24], [111], [122]. Value  is used for quantitative calculations. In our investigations the integer of angular momentum  is the spin of the photon and the electron. It is used for quantitative calculations and qualitative characteristics of  behaviour of both photon and electron.

 

 

6.4. Toroidal model of the  electron

 

Torus is the nearest “relative” of the ring. For the beginning let us assume that torus is hollow. Let us write  for torus section circle radius (Fig. 14). The area of its surface is determined according to the formula

 

                                                   (155)

 

 

 

Fig. 14. Diagram of toroidal model of the  electron

 

 

Let us write  for surface density of electromagnetic substance of  the electron. Then

                                                                 (156)

 

Let us determine moment of inertia of hollow torus. We shall have the following equation from Fig. 14

 

                                                                 (157)

 

                                     (158)

 

                                                       (159)

 

As the electron demonstrates the electrical properties and the magnetic ones at the same time and has angular momentum, we have every reason to suppose that it has two rotations. Let us call the usual rotation relative to the axis of symmetry with angular frequency  kinetic rotation which forms its kinetic moment and kinetic energy. And secondly, let us call vortical rotation relative to the ring axis with angular frequency   (Fig. 14)  potential rotation which forms its potential energy and potential properties. It is natural to assume that the sum of kinetic energy   and potential energy  of free electron is equal to its photon energy . Let us consider the possibility of realization of our suppositions. Kinetic energy of hollow torus rotation is determined according to the formula (Fig. 14)

 

                                (160)

 

Frequency  of kinetic rotation of   torus is equal to

 

                                   (161)

 

We shall determine radius  of   torus from the formula (160)

 

                           (162)

 

As it is clear, and  (162), (161) coincide with the values of  and  in formulas (140), (154), (139) and (153) in this case as well. It is interesting to find out if there is an experimental confirmation of value  obtained by us. It turns out that there is such confirmation. In 1922 A. Compton, the American physicist  - experimenter, found that dissipated X-rays had larger wave-length that incidental ones. He calculated the shift of wave    according to the formula [3], [17], [24]

                                                                     (163)

 

The experimental value of magnitude  turned out to be equal to  [24]. Later on a theoretical value of this magnitude was obtained by means of complex mathematical conversions based on the ideas of  relativity  .

When we have studied Compton effect and have carried out its theoretical analysis, we have shown that the formula for the calculation of theoretical value of Compton wave-length   is obtained quite simple if we attach sense of the electron radius to the electron wave-length and consider the diagram of interaction of the ring model of electron with the ring model of roentgen photon [17], [24], [97].

The diagram of interaction of the ring model of roentgen photon with the ring model  of the atomic electron is shown in Fig. 15.

 

 

Fig. 15. Diagram of interaction of the  photon with the electron in Compton effect

 

 

The pulse   of the photon falling on the electron and the pulse  of the photon reflected from the electron are connected by simple dependence

                                                        (164)

 

After the interaction of the photon with the electron its pulse will be changed by the value

 

                                                     (165)

 

or

                                                            (166)

 

As

   и    ,

so

                                                               (167)  

or

                                                          (168)

The relation can be converted in the following way

 

                                                   (169)

 

       As     и   , the equation is as follows

 

                                       (170)

 

This is Compton formula of the calculation of the change of wave-length   of reflected roentgen photon. Value  being a constant is called Compton wave-length. In the formula (170) it is a coefficient determined experimentally and having the value [24,], [130]

 

                                                        (171)

 

which coincides completely with the value of radius  of  the electron which has been calculated by us theoretically according to the formula (140), (154) and (162)

 

                                                           (172)

 

 It should be noted that we have obtained the formula (170) without any relativity idea using only the classical notions concerning the interaction of the ring models of the photon and the electron.

Thus, the value of  of the ring model  of the electron obtained by us in the calculation with the help of several methods when a various set of characteristics of the electron has been used (140), (154) and (162) coincides completely with the experimental value of Compton wave-length of the electron (171).

As the analysis of the results of experimental spectroscopy has shown that electron wave-length is equal to radius of its ring model and as the results of various methods of the calculation of radius of electron coincide completely with Compton experimental result, the ring model of the electron is now the fact that is enough for the resolute advancement in our search.

It is desirable to know the value of radius  of  torus cross section circumference. Let us try to find this value from the analysis of potential rotation of electron with frequency  (Fig. 14).

We should pay attention to the fact that the pulse of both the photon and the electron is determined according to one and the same relation

                                                                              (173)

 

It means that both the photon and the electron display their pulse in the interval of one wave-length. This fact has been reflected in the models of the photon as an equality between wave-length  of the photon and its radius . As the photon is absorbed and radiated by the electron, the electron should have the same connection between the wave-length and radius. Besides, the models of the photon has six electromagnetic fields; the same quantity should be in the model of the electron when it radiates or absorbs the photon. The described conditions prove to be fulfilled if one assumes that angular frequency  of kinetic rotation is one-sixth of angular frequency   of  potential rotation of free electron, i.e.

                                                                             (174)

 

If we assume that velocity of the points of the axis ring of torus in kinetic rotation is equal to velocity of the points of the surface of torus in potential rotation, we shall have

 

                                                               (175)

From these relations we shall find out

 

                                                      (176)

 

and

                                            (177)

 

If we substitute the data being obtained into the formula (160), we shall find out the value of potential energy  of the electron

               (178)

 

If we double this result, we  shall obtain complete photon energy of free electron (138). Complete coincidence of photon energy of the electron obtained in different ways gives us the reason to suppose that the electron is a closed ring vortex which forms a toroidal structure which rotates relatively its axis of symmetry generating potential and kinetic energy.

It results from sixfold difference between angular velocities  and   that radius  is greater by sixfold than radius . We postulate this fact supposing that, as we have shown, the most economical mode of the photon movement is possible only at six electromagnetic fields. This principle is realized when the vortex moves in a closed helix of the torus. It results from the difference of radii and angular velocity that the vortex which moves along the surface of torus makes six rotations relative to the ring axis in a helix during one rotation of torus relatively its axis of rotation. A lead of a helix is equal to radius  of the axis ring and wave-length  of the electron (Fig. 16) [11], [15], [20], [29].

 

 

Fig. 16. Electron model diagram

 

 

Imagine now that external forces begin to rotate such torus opposite to helix motion. Six vorticity, radial directed fields are formed on the equatorial surface at once. External parts of these six vortexes are outside the toroidal surface. As their peripheral velocity is greater than velocity of light, this part is interrupted, and lagging behind the rotational movement of torus it forms six chord-arranged vorticity fields with unlike poles on their ends. They unite and form a hexagon; as they move, six magnetic vorticity fields connected with each other are formed. As the set of electrical field and magnetic field can exist only in motion, such structure of the fields begins to move in space as an electromagnetic formation which we call the photon.

The rest part of the electron restores its vorticity and ring movement again having changed angular velocities ,   and radii  ,  , respectively, in such a way that sixfold difference between them is preserved. Photon energy  will be reduced, respectively.

As energy of the electron  is equal to Planck’s constant product by angular frequency, energy of the electron will be reduced due to the reduction of its angular frequency  after photon radiation. In order that Planck’s constant can preserve its permanency, electron radius  should be increased. After the photon is absorbed, all its parameters are changed in the reverse order.

We can imagine the details of the processes of absorption and radiation of the photons by the electron and are ready to begin to analyse them, but the lack of time makes us settle other matters: to solve more important problems of the formation of the atoms, the molecules, and, possibly, the atomic nuclei.

Let us compare binding energy of hydrogen atom electron when it is on the first energy level (13.6 eV) with the full (photon) energy of free electron eV. It becomes clear at once that an insignificant reduction of energy (13.6 eV) of free electron will lead to almost inconspicuous increase of radius  when the bond is formed between it and the proton. This radius will remain almost unchangeable during the process of the transition.

Let us pay attention to one more fact. Ionization energy of hydrogen-type atoms is equal to the product of ionization energy of the hydrogen atom multiplied by the square of the number of the element in the periodic table. For example, ionization energy of the 46th electron of the 46th element (palladium) is as follows

 

                                                          (179)

 

Ionization energy of the 100th element (fermium) is as follows

 

                                                        (180)

 

Thus, when the palladium atom is formed in the moment when its nucleus has no electrons, the free electron forming a connection with such a nucleus radiates a photon or a series of photons with the total energy of  28777.6 eV. Later on when it has an opportunity to absorb the photons, this absorption will take place  in such a way that when the total energy of all absorbed photons becomes equal to energy 28777.6 eV, energy of its bond with the nucleus becomes equal to zero, and the full store of free electron energy will be restored.

Here it is appropriate to note an interesting peculiarity. Full energy of the electron is equal to  eV. When the 100th element is formed, the electron uses 136000 eV of its full energy in order to establish the connection with its nucleus. The question arises at once: which is the maximal ordinal number N of the chemical element for the formation of which full energy of the electron is enough? The following dependence gives the answer to this question:

 

                                                        (181)

 

Certainly, it is unattainable limit. In this case full energy of the electron will be spent for the bond with the nucleus. Probably, there is a limit minimal value of energy of the electron when it cannot be reduced anymore.

Free electron has potential (vortical) rotation relative its ring axis and kinetic rotation relative to the axis of symmetry. It radiates in the case when the external influence changes the balance between these rotations.

Besides the translational motion and rotary motion, in this case the electron has potential (vortical) rotation. We have noted that a sharp change of the relations between kinetic and potential rotations of the electron leads either to absorption or radiation of the photon depending on the direction of the change of this relation. If this change slows down kinetic rotation, the photon radiation process takes place; if this change accelerates it, the absorption process takes place.

         Modern relativists cannot withstand a flow of critic concerning their erroneous notions. Trying to defend them they give the results of some experiments, which, as they think, can be understood only on the grounds of relativistic ideas. They include an experimental fact of the increase of mass of the electron during the increase of velocity of its translational motion. They interpret the result of this experiment with the help of relativistic ratio

                                                                          (182)

 

       Actually, it follows from this ratio that with the increase of velocity of translational motion of the electron its mass m is increased as compared with rest mass . Ask them: why and due to what does it take place? You will get no answer, because their interpretation is based not on knowledge, but on faith in correctness of Einstein’s ideas of relativity. They affirm that this ratio can be obtained from the relativistic ideas only, not from other sources.

           It appears from the Newton’s law that mass m of the body is connected with force F influencing it and acceleration a with the dependence . It is clear from this dependence that mass can be increased due to two factors: increase of force  or reduction of acceleration . But due to unknown reasons this opportunity is not used for the analysis of this phenomenon and experimental check. One fails to measure these values in the experiments with the electrons directly. That’s why one tries to find indirect methods of explanation of this phenomenon.

           In order to show that there can be several variants of development of the formula (182) and the variants of its interpretation, we’ll try to find a new development of this formula and a new interpretation connected with the increase of rest mass of the electron during its accelerated motion. Motion of the model of the electron in the electric field is shown in Fig. 17. As the charge of the electron is formed on its toroidal surface, the direction of motion of the electron in the electric field will be formed, first of all, by the equatorial points of this surface. Both in free state and in motion the electron has moment of momentum (angular momentum) , its vector being directed along the axis of rotation of the torus [70].

 

 

 

Fig. 17. Diagram of motion of the electron in the electric field

 

 

       Taking into consideration the fact that the accelerated motion of the electron takes place under the predominance of the external influence, which changes the state of the medium (in which the electron moves) forming certain resistance to its motion, let us designate mass of the electron in its translational motion via . It will mean that we have included coefficient of resistance of medium, which is unknown to us, in symbol ; hereby it differs from symbol  in the expression of moment of momentum. In this case, the pulse of the electron will be written in the following way .

       Thus, during the forced translational motion two vectors  and , which are perpendicular to each other, are applied to the electron (if we do not take into consideration the direction of the magnetic field vector). The first one characterizes the rotation of the electron in relation to its axis of symmetry; the second one characterizes translational motion. A question arises: what total motion will the electron have in this case? It should be characterized by vector value, which is equal to the sum of the first two vectors. But we cannot add these vectors, because their numerical values have different dimensionalities. In order to do away with this drawback, it is necessary to change the numerical value of the second vector  in such a way that the dimensionalities of both vectors should be equal. For this purpose let us multiply it by value . It is natural that the sum of the first two vectors will be equal to the third vector, which should characterize two above-mentioned motions of the toroidal model of the electron immediately (Fig. 17). In order the third vector takes into account medium resistance as the second one, let us designate mass of the electron with symbol  in its expression. Besides, the third vector should have the same dimensionality as the first two. For this purpose let us multiply its numerical value by .

        After such preparation we have the right to find the geometrical sum of the first two vectors. From Fig. 17 we’ll get

 

                                                       (183)

or

Finally, we’ll determine

 

                                                                                           (184)

 

                      This is a famous relativistic ratio, which shows the increase of mass of the electron when velocity of  its translational motion is increased in the electric field. We should note that main thing. We have got this ratio not in the pseudo-Euclidean geometry by Minkovsky, but in Euclidean geometry and within the framework of the space-matter-time unity axiom.

          Now the kinematic sense of the ration  is clear. When the electron is influenced by none of the external forces, it rotates only in relation to its axis, and in this case the instantaneous centre of rotation  coincides with the geometrical centre of the electron (Fig. 17 b, c).

        As the electron receives translational notion, its instantaneous centre of rotation P begins to withdraw from the geometrical centre to the periphery of its toroidal structure (Fig. 17, d). When forward velocity  gets nearer to velocity , with which the ring axis of the torus rotates, the instantaneous centre will withdraw from the geometrical centre of the electron by value  (Fig. 17, d). All these changes take place in the reference system connected with the observer or the external source, which forms its accelerated translational motion forcibly.

        Let us recollect that in this case, except translational and rotational motions, the electron has potential (vortex) rotation. We have already noted that a sharp change of the relations between kinetic and potential rotations of the electron leads either to absorption or to emission of the photon depending on the direction of the change of this relation. If this change slows down kinetic rotation, the process of emission of the photon takes place; it the change accelerates it, the process of absorption takes place.

        It is easy to imagine that these both cases are possible during the alternating motion of the electron in the electric field. In one of the cases emission of the photons should be observed, it is called deceleration emission; in another case absorption takes place, but not of the photons, but a substance of  the medium formed by the electromagnetic field, in which the electron moves. Roughly speaking, toroid of the electron will wind lines of force of the field on itself and due to this fact it will increase its mass at   (Fig. 17, a).

          Thus, we have every reason to suppose that energy and consequently mass of the electron will be increased at the expense of absorption of the material base of the medium, which increases its motion. We can call this medium the ether. Even a cursory analysis of motion of the toroidal model of the electron in the electric field gives the answers to the questions: why and at what expense is the mass of the electron increased? These answers have all the features, which give the opportunity to consider them as hypothetical ones at the  first stage. This is a way to the truth, not to the faith.

         A question arises: what development of the relation (182) and what variant of its interpretation is nearer to the truth, the relativistic one or the one considered by us?

           Let us recollect that in this case, except translational and rotational motions, the electron has potential (vortex) rotation. We have already noted that a sharp change of the relations between kinetic and potential rotations of the electron leads either to absorption or to emission of the photon depending on the direction of the change of this relation. If this change slows down kinetic rotation, the process of emission of the photon takes place; it the change accelerates it, the process of absorption takes place.

          When we have substantiated the model of the electron, we have used the existing Coulomb’s law and Newton’s law, spectrum formation law formulated by us, Lorentz electromagnetic force and the following constants: velocity of light , Planck’s constant , electron rest mass , its charge , electron rest energy, Bohr magneton , electrical constant , Compton wavelength of the electron, which should be called Compton radius of the electron and the ionization of the hydrogen atom.

        Thus, the electron has the from of the rotating hollow torus (Fig. 16). Its structure proves to be stable due to availability of two rotations. The first rotation takes place about an axis, which goes through the geometrical centre of torus perpendicular to the plane of rotation. The second rotation is a vortical one about the ring axis, which goes through the torus cross section circumference centre.

Several methods of torus radius calculation which include its various energy and electromagnetic properties give the same result which completely coincides with the experimental value of Compton wave-length of the electron, i.e. [17], [70], [97].

Electron spin is its another important characteristic. It is equal to Planck’s constant and is vector quantity .  Its vector properties originate from the main dimensionality  – moment of momentum or angular momentum.

 

 

 

Fig. 18. Diagram of electromagnetic model of the electron

 (only a part of electric and magnetic lines of force is given in the figure)

 

 

The third important characteristic of the electron – magnetic moment or Bohr magneton which generates strength  of magnetic field of the electron (Fig. 18). In its geometrical centre it is equal to . It is a significant value, but it is reduced with the increase of the distance from the geometrical centre of the electron along the axis of rotation according to dependence  . Here  is the distance from the geometrical centre of the electron along its axis of rotation [34].

Only a part of magnetic lines of force and the lines which characterize electric field of the electron is shown in Fig. 18. If the whole set of these lines is shown, the model of the electron will assume the form which resembles of the form of an apple. As the lines of force of the electric field are perpendicular to the lines of force of the magnetic field, the electric field in this model will become almost spherical, and the form of the magnetic field  will resemble the magnetic field of  a bar magnet.

 

 




       
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The Foundations of Physchemistry of Microworld

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