In solid state physics, the effective mass of a particle is the dynamic mass that appears when the particle moves in the periodic potential of the crystal. It can be shown that electrons and holes in a crystal react to an electric field as if they were moving freely in vacuum, but with some effective mass, which is usually defined in units of the electron rest mass me (9.11×10−31 kg). It is different from the rest mass of the electron. The effective mass is determined by analogy with Newton's second law using quantum mechanics to show that for an electron in an external electric field E: 
de a - acceleration, - Planck's constant, k - wave vector, which is determined from momentum as k =, ε(k) - dispersion law, which relates energy to wave vector k. In the presence of an electric field, a force acts on the electron, where the charge is denoted by q. From here we can get an expression for the effective mass m * : 
For a free particle, the dispersion law is quadratic, and thus the effective mass is constant and equal to the rest mass. In a crystal, the situation is more complicated and the dispersion law differs from a quadratic one. In this case, only in the extrema of the dispersion law curve, where it can be approximated by a parabola, can the concept of mass be used. The effective mass depends on the direction in the crystal and is generally a tensor. The effective mass tensor is a term in solid state physics that characterizes the complex nature of the effective mass of a quasiparticle (electron, hole) in a solid. The tensor nature of the effective mass illustrates the fact that in a crystal lattice an electron moves not as a particle with a rest mass, but as a quasi-particle whose mass depends on the direction of motion relative to the crystallographic axes of the crystal. The effective mass is introduced when there is a parabolic dispersion law, otherwise the mass begins to depend on energy. As a result, a negative effective mass is possible. By definition, the effective mass is found from the dispersion law Where is the wave vector, is the Kronecker symbol, is Planck's constant. Electron. An electron is a stable, negatively charged elementary particle, one of the basic structural units of matter. Is a fermion (i.e. has a half-integer spin). Refers to leptons (the only stable particle among charged leptons). The electron shells of atoms consist of electrons, where their number and position determines almost all chemical properties of substances. The movement of free electrons causes such phenomena as electric current in conductors and vacuum. The electron as a quasiparticle. If the 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. Properties The charge of an electron is indivisible and is equal to −1.602176487(40)×10−19 Kkg - the mass of the electron. Kl - the charge of the electron. 
C/kg - specific electron charge. 
electron spin 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 spin of an electron is 1/2, and thus the electron is a fermion. 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 of the Dirac equation). In this case, a negatively charged electron is called a negatron, a positively charged one is called a positron. Being in the periodic potential of the crystal, the electron is considered as a quasi-particle, the effective mass of which can differ significantly from the mass of the electron. A free electron cannot absorb a photon, although it can scatter it (see the Compton effect). Hole. A hole is a quasiparticle, a carrier of a positive charge equal to the elementary charge in semiconductors. Definition according to GOST 22622-77: An unfilled valence bond, which manifests itself as a positive charge, numerically equal to the electron charge. The concept of a hole is introduced in band theory to describe electronic phenomena in a valence band not completely filled with electrons. In the electronic spectrum of the valence band, several bands often appear that differ in the effective mass and energy position (the bands of light and heavy holes, the band of spin-orbitally split-off holes).
V. N. Guskov.
Properties characterize the content of a physical object (FO) in its interactions with the outside world.
It follows from this that the properties themselves cannot be considered directly as the material content of the object. The properties are real only because the content of the OP is real. They are completely dependent on the content of objects and manifest themselves in their interactions with the outside world. Therefore, all kinds of physical constants of specific properties of OP are, in essence, indicators of the invariance of the material content of the object.
Mass of an electron.
Mass, according to Newton, is an internal characteristic of the FD, a measure of its inertia (inertia).
In physics, it is believed that the inertia of an object is manifested in its ability to resist changes, external influences. However, from the point of view of the concept of direct short-range action (CNB), the ability to resist changes is possessed by all FDs involved in transforming interactions, regardless of whether they have mass properties.
Any FD will resist changes in its own content, its internal movement. This is also characteristic of energy objects - photons, which do not have mass (at least in the form of a scalar quantity).
From the point of view of the National Security Committee, the presence of mass in the FD is determined by its ability not to resist changes at all or to maintain its structure, its internal organization, but resist a change in one's connection with a particular material substance in which this structure is realized as a FD.
This ability to have mass is opposite to the ability of energy FDs retain their individuality only through the continuous change of the material substrate with which its structure and content are related.
It is the combination of these opposite abilities in one whole (in the system) that leads the SP having mass to spatial movement, and the SP having energy to braking, slowing down its movement in the material space. Such a combined FD (EPSM) consisting of ESM and SPM can never and under no circumstances be spatially at rest or move in it at the speed of light.
Naturally, both the ability to have mass and the ability to have energy are strictly related to the structural organization of the FD.
As soon as the structure of the PO having mass, for example, the electron and positron, is destroyed during annihilation, the newly formed structures lose their ability to have mass. They become structurally different objects - photons. Which, losing connection with a specific material substance in their existence, acquire energy characteristics.
It would seem that from this we can conclude that all changes that do not lead to irreversible consequences for an object that has mass and, in particular, for an electron, are of secondary importance. However, it is not.
Any transformative interactions with the external world lead to the transformation of the charge motion in the structure of the electron. (Actually speaking, there is nothing else in the content of the electron except this motion.).
But the structure of the electron, despite its simplicity, is such that the transformations of structure-forming movements are always reversible. As a result of this, the total amount of charge motion in the electron is also conserved.
And this ensures not only the preservation of its structure, but also the constancy of its properties, including mass.
On the other hand, the constancy of the content allows the electron, even if it enters the composition of a more complex formation, to retain (partly) its individuality and always become the same FD after leaving the system.
The ability to have a mass is possessed exclusively by the SSM (including the electron), as well as by the increasingly complex FDs that they are part of. Matter that is in the ground state or in the energy state does not have this property.
However, the constancy of the mass does not provide the electron with the ability to display this property in full measure at any moment of its existence.
It can be seen from the previous article that the content of an electron from phase to phase changes the direction of manifestation of its content (its internal momentum). And since the structure-forming interactions occurring in the electron proceed at the speed of light, then the electron, which is in the phase of "converging" semiquanta, will be a kind of " outgoing" an object.
This means that any attempts to enter into a transformative interaction with him at this moment will not lead to anything. It will be unavailable for interaction, as it will move away from any confrontations with the outside world. (Similarly, the photon is not available, but only always (!), for positively accelerating interactions in the propagation plane.)
The incompatibility of an electron with something external, and, consequently, a transformation, is impossible in this phase of existence. The question is - can an electron in such a state manifest its mass property in relations with the surrounding world? Obviously not.
And this is when the electron has a full-fledged content, which quantitatively does not differ in any way from its content in the phase of "divergent" half-quanta.
Electric charge of an electron.
The external manifestation of the electric charge of an electron is more diverse than the manifestation of its mass property. Indeed, in some interactions with objects that are identical in sign of charge, the electron is “repelled” from them, and in others with objects that have the opposite sign of charge, on the contrary, it is “attracted”.
This ambiguity of the external manifestation of the electron charge allows us to assert that the result always depends on the content and properties of both interacting objects.
However, in itself, the statement of the visual facts of "attraction" or "repulsion" of objects, depending on their sign affiliation, allows us to determine only the external signs of the internal laws of the process and derive the corresponding mathematical laws (Coulomb's law, for example). But in order to understand why the manifestation of the charge property of an electron is so different, and what are principles its implementation will obviously not be enough.
To understand the essence of what is happening in the interactions of objects with electric charges, we are forced to deviate somewhat from the topic of conversation. The structure of an electron, like the structure of any other FD, exists in the “environment” of the OSM. Therefore, it is very important to know how the OSM element works.
In the previous article, it was already noted that semi-quanta of different signs, which are part of the OSM element, must compensate for the manifestation of each other in order for the object to acquire true (including electrical) neutrality. This means that not only counter-directed half-quanta of the same type, but also unidirectional semi-quanta of different types “balance” each other in their opposition. This means that the relationship between semiquanta in the OSM element is diverse and multifaceted.
In essence, it will not work here to separate semiquanta in the OSM element according to the sign feature as we did (significantly simplifying the reality) when analyzing the structure of an electron. The real connection between the semiquanta in OSM is such that they literally cannot exist without each other. They represent one whole, sides of one reality. At the same time, none of these cumulative interactions, in which OSM semiquanta participate, can be unambiguously considered as, of course, internal or external. (Which is quite acceptable in the case of the electron structure.). They are absolutely identical. Therefore, the definition of their status is absolutely subjective, since the position of the observer (subject) will play a decisive role.
Any interaction can be considered as central and structure-forming and, at the same time, as external with other elements of the OCM.
Therefore, there is every reason to consider the OSM structure as continuous, consisting of a kind of "knots", which are interactions. These interactions of matter in the ground state are of the same type in terms of the principles of internal organization, material content, and therefore do not have distinctive features.
Of course, all of the above about the proposed structure of the OSM may be of interest to the reader. But for us now, only one detail is important - the dependence of the intensity of the manifestation of one type of OSM semiquanta on the presence of semiquanta of another type, which neutralize this manifestation, unidirectional with them. What does all of this mean? Only one thing - if different-sign unidirectional semi-quanta are equal, then they completely neutralize each other. If one type of semi-quanta begins to dominate, then a charge motion is formed, which is what we observe in an electron.
"Repulsion" of electrons.
The factor of dominance of one type of semi-quantum over another is very important for explaining the principle of organization of internal motion in an electron.
It is equally important for explaining mechanism of interaction between ZSM. For example, between two electrons. Knowing the organization of the internal motion in an electron, it is not difficult to understand what will happen to it when its neutral interaction with the OSM is replaced by an interaction with an identical in sign GSM.
Their incompatibility will lead to exactly the same transformative interaction that they had before with OSM. And its result will be the same - the transformation of the momentum of the interacting semi-quanta.
The only difference will be that this interaction will be "premature" and it will occur at a smaller distance from the location of the previous central interactions in the GMS.
Consequently, in the contact zone of electrons, the transformation of the charge motion will occur earlier than on the opposite side (in the zone of their interactions with the OSM). As a result, there will be bias subsequent central transformation interaction in each of the electrons.
It is not difficult to guess in which direction this shift will occur - in the direction of each other. from friend. It is also not difficult to understand that this the displacement of the centers of electrons is equivalent to their displacement from each other in space.
Such mechanism of "repulsion" of identical ZSM,
in this case two electrons. As you can see, it is simple and does not require the introduction of any additional entities into the content of the AP for its implementation.
Of course, here is a simplified interpretation of the process of "repulsion" without taking into account the energy component. But most importantly - without taking into account the interaction with the OSM.
"Attraction" of the electron and positron.
Now let's see if the electrically opposite ZSMs (electron and positron) need any connecting "strings" for the implementation of "attraction" or transmission of energy impulses.
As already noted, unidirectional half-quanta of different signs in OSM almost completely neutralize each other. The coupling between the half-quanta is also retained during the transition of the OSM to the charge state.
Only as a result of violation of the quantitative balance between semi-quanta does the neutrality inherent in them in OSM also disappear. One kind of semi-quantum becomes dominant, but what happens to the other? Obviously his neutralization even more intensifies.
Naturally, these changes cannot but manifest themselves in the interaction of different-sign ZSMs. And if in the interaction of identical ZSM transformation the predominant type of semiquanta comes earlier than in the case of a similar interaction of these SCs with the OSM, then in the interaction of SCs with different signs, there will be observed reverse effect.
transformative interaction in the zone of their contact will be delayed regarding similar interaction with OSM. Accordingly, there will be bias subsequent central interactions in each of the GSM in the direction of each other to friend. And this means that the objects must move spatially towards each other.
The objects will actually move, but not towards each other, but each other! This clarification is based on the provision of the KNB on the inevitability of direct contact in the event of interaction between the FD.
Therefore, if already interacting objects move in opposite directions, then this can only mean one thing - their spatial combination, not a formal approximation.
It would be wrong to assume that due to the combination of objects with different signs, some kind of “doubling” of reality can occur. Nothing of the kind - the combined objects perfectly complement each other, but the material basis of their existence (OSM) will remain the same. Spatially compatible structures of the ZSM, but not matter. And the deeper will be their interpenetration, the less will be the opposition of structures (up to the moment of their possible annihilation).
Thus, we see that for the implementation of "attraction" there is no need for connecting threads, through which objects could attract each other. There is also no need for an unnatural (reverse in terms of transformation essence “repulsion”) and, therefore, illogical transmission of energy movement through virtual photons. The attraction process is based on the same mechanism of transformative interaction(more precisely, a set of interactions) which is the basis of "repulsion".
However, the explanation of the mechanisms of both "repulsion" and "attraction" will be incomplete without taking into account the interactions of objects not only among themselves, but also with the OSM in opposite directions. These interactions are always present, but only in the presence of charge interactions does their role as driving factors begin to manifest itself.
So, in the case of "repulsion", the value of the opposition in these interactions turns out to be less than the value of the opposition of electrons, and in the case of "attraction", the same value will be greater than the opposition of the electron and the positron. As a result, the FD begin to shift along the line of least resistance in the first case from each other, in the second - into each other.
Result relative the weakening of the opposition of different-sign FDs in their interaction can be visually represented as a process of “falling through” them into each other or “pressing” into each other by external interaction with the surrounding OSM. But these visual images do not quite correctly reflect the essence of what is happening. They do not reflect the diversity of the causes of what is happening. After all, in fact, the "attraction" of objects (as well as "repulsion" for that matter) is the result of not one or even two specific interactions, but a complex of all-round interactions of the PhD with the matter surrounding them.
Preliminary results.
Due to the almost complete mutual and comprehensive compensation of semiquanta, the OSM medium is electrically neutral. However, it is enough to strengthen or weaken one of the meaningful components (one type of semi-quanta) of the OSM through the transformation, as the balance is disturbed, and it passes into the GSM.
Naturally, this is expressed not only in the strengthening of the manifestation of the predominant type of semiquanta, but also in the weakening of the opposite type of semiquanta that is unidirectional with it.
In the electric charge of an electron, its ability to enter into external transforming interactions with varying degrees of activity finds expression.
The manifestation of this property is directly related to the properties of another FD interacting with it. At the same time, the content of the interacting parties can manifest itself in different ways. That's why the charge property can be defined as a mutual change in the intensity of the manifestation of individual aspects of the content of the PhD during their interaction.
There is nothing mysterious in the implementation of "repulsion" and "attraction" of electrically charged elementary FDs.
In nature, at the elementary level, these phenomena themselves are absent as such - this is only an external manifestation of deep processes. Which are based on the transformative interaction of incompatible parties. Therefore, in principle, the mechanism for implementing "repulsion" and "attraction" is indistinguishable. The only difference lies in the degree of opposition of objects, in the magnitude of their incompatibility.
"Spin" of an electron.
If we proceed from the position of the identity of all electrons, then, arguing strictly logically, it should be recognized that there can be no property that would allow dividing all electrons into two types.
Indeed, since the properties characterize the content of the object, the difference in some properties of electrons will indicate their substantial difference. This contradicts the position on the complete identity of all electrons.
From the point of view of the KNB, the structure of an electron is absolutely transparent and it will not be possible to detect “something” in it that could serve as a basis for an assumption about the structural or content difference of electrons (at least at this level of development of our ideas about it).
Therefore, there is every reason to assert that electrons have no properties, which would allow them to be divided into separate groups. Therefore, "spin" as a property All electrons must have the same
On the other hand, the identity of the structures of all electrons does not prevent them from interacting with each other while in different phases of their internal existence. It is the presence of an internal "pulsation" of the GL content that makes it possible to resolve a seemingly insoluble dilemma with different "spins" of electrons.
The presence of two phases in the internal transformation processes of the SL introduces diversity into their relationship. Summarizing the possible scenarios for the development of events in the interaction of APs, we single out two opposite situations.
The first one is that the phases of existence of the interacting ZPs coincide.
The second one is that structure-forming motions in interacting SLs are in antiphase.
Both variants of interactions will lead to the same result - "repulsion", but in details they will differ. The least controversial (up to a certain point) will be the relationship between the SCs, whose internal charge motions are in antiphase. Therefore, the convergence of such objects will be as possible as possible.
If the phases of the existence of interacting electrons coincide, their opposition will, on the contrary, be maximum. Therefore, other things being equal, their convergence in comparison with the first situation will be minimal.
Obviously, this difference in the results of interactions between electrons allows us to assert that they have different spins.
Conclusion - "spin" is a comparative characteristic of interacting objects. The spin of an individual electron loses its certainty.
It is impossible to say in advance before the interaction what specific "spin" the electron has. It can be assumed that it simply does not exist.
Failure to understand the dependence factor, the subordination of properties to the material content of the object, can lead to serious difficulties in forming ideas about FD. The presence of any characteristics (mass, energy, charge) of a FD, especially if they have a constant value, is often associated in the mind of the subject with the very material content of the object. Allegedly properties are present in it.
Properties are perceived as additional entities that an object has Besides its material content or included in its material content as separate elements.
However, this is not the case, properties can manifest themselves with different intensity (depending on the nature of the interaction), and sometimes completely disappear with the termination of the corresponding interactions. The content of the object in this case, at least quantitatively, can remain unchanged.
The conclusion is “habitat”, the area of existence of properties is always a process of interaction, outside of it, properties cannot manifest themselves in anything and in anything. In fact, the properties that we consider a characteristic of an individual object are an indicator of the process of interaction, and sometimes of the whole set of interactions.
Dualism of electron properties.
Before proceeding directly to the "dualism" of the properties of the electron, let us consider some aspects of the relationship between the electron and the photon.
In the previous article, the absence of energy motion in the structure of the electron was already noted. This gives grounds for asserting that the electron does not have the ability to possess energy. (Here energy is considered as property inherent exclusively energy objects - photons).
In general, the concept of energy in physics has a double meaning.
On the one hand, it is identified with the energy content the object itself. On the other hand, energy is considered as property the same object.
There is no doubt that such a union cannot be justified by anything. Here it is necessary to determine: either the energy is the content of the FD, or its property - the third is not given.
From the author's point of view energy is a property of an energy object, not its content. That's why DO cannot emit or absorb energy directly. He can only exercise your energy.
Of course, energy, like any other property, can be lost or gained, but only through the transformation of the material content of the object, its quantitative change.
Without a physical process, the movement of the "energy" property is impossible. Therefore, when one speaks of the radiation or absorption of energy, one usually means a quantitative change in the material content of an object, which is characterized by energy movement.
Essentially there is no need for energy to organize the internal motion of an electron. But for manifestations properties of the electron energy movement and, therefore, energy are needed.
This is not difficult to achieve - it is enough for an electron to unite with a photon. However, there is one subtlety here - by “acquiring” energy motion, the electron ceases to be itself and, therefore, loses its original properties.
Despite the fact that in physics a spatially moving electron is considered as an electron "possessing" energy, in fact it is not an electron, but a new FD.
The electron is included in this object as an element. Therefore, in fact an electron, having united with a photon, not only does not acquire new properties, but also loses the properties inherent in it initially. This always happens with all FDs, which through interaction form a new whole - a system. Neither the content of the elements of the system, nor their properties retain autonomy.
It means that the combined properties are not summed up, but are transformed into new cumulative properties inherent in the system as a whole. Thus, the new FD acquires not only the energy inherent in the photon, but also the mass and charge of the electron. A new FD is formed, which can be conditionally called a "photon-electron" or an energy-charge state (ECS). This FD will have the combined properties corresponding to it (and only to it!) "energy mass".
Conclusion - when the system is formed: electron + photon, the former properties of the elements of the system are not preserved. Therefore, the expression "moving electron" is as illiterate as the expression "photon at rest".
Such objects do not exist in nature, unless we mean by them a system (ESS) with the property “energy mass” inherent in this system.
Analyzing the structure and properties of the electron, we considered the electron, so to speak, in a "pure" form. An electron is like a FD that participates in external interactions (without this, it cannot exist!), but is not part of a larger physical organization, system.
This approach is caused by the need to consider not the properties of some system, but the properties of a specific elementary object - an electron. It is clear that for the interaction of an electron with any object (except OSM) and, therefore, for the manifestation of properties, spatial displacement of at least one of them is necessary. This means that the presence of energy movement in interacting objects is mandatory. However, simplifying the situation, we ignore this fact, we abstract from it.
Let's pass to consideration directly of "dualism" of properties of an electron.
An analysis of the organization of the intra-charge motion of an electron showed that during one period of its existence, it experiences amazing metamorphoses. It would seem that the properties of the electron should change accordingly.
However, despite the peculiar “two-facedness” of the electron content, it does not possess any mutually exclusive properties. The opposition of an electron as a "particle" and as a "wave" is purely arbitrary. At least, because its content qualitatively and quantitatively at the moments of manifestation of these "properties" remains unchanged, and the changes in the electron content themselves are consistent in time.
Therefore, in what follows, we will only talk about variability properties of an electron in the course of its existence, and not about their duality.
As noted in the previous article, the electron is not a wave in nature - it is a natural harmonic oscillator. Therefore, the property of a “wave” observed in experiments on “diffraction” and “interference” of an electron is actually manifested not by an electron, but by a system: electron + photon. Only due to the constant connection with the photon, the electron, in the composition new FD acquires wave properties. Therefore, strictly speaking, it must be admitted that The "corpuscular-wave dualism" of properties as such is not inherent in the electron.
In what follows, we will talk about photon-electron» - a system consisting of the energy and charge states of matter, i.e. about energy-charging state of matter (ECSM).
Of course, when analyzing experiments with EPSM confirming their "wave" nature, it would be necessary to take into account all the real circumstances of what is happening. In particular, the fact that not a “single-phase” abstract copy of an electron participates in the process, but an objectively existing “two-phase” electron. It would not hurt to have real ideas about the structure of the photon with which the electron forms a system, as well as to have clearer ideas about the structure of the target. But, unfortunately, on the basis of existing knowledge, it will not be possible to present in its entirety what is happening in the experiments. Therefore, we confine ourselves to general considerations based on elementary logic.
Let's start by passing the EPSM through two slits. Since no mysticism is inappropriate in science, we immediately recognize this fact. Of course, it does not follow from this that the EZS at this moment consists of two halves. Both the electron and the photon in this system always retain their integrity.
So, at the initial moment of passage of the EPM in the form of a moving electron through the target, obviously, the FD is in the phase of external charge-forming interaction.
This, by the way, allows us to draw certain conclusions about the size of the EZS at the moment of the greatest "expansion" of the electron. They will be comparable to the distance between the holes in the target. In the further advancement of the object through the target, their structures must be in a state of antiphase. This will allow the EZS to reach the other end of the target with the least changes.
The result that will be observed on the screen depends entirely on the distance from the target to the screen. If the FD interacts with the screen in the state of coinciding phases, then a peak in the manifestation of the "energy-mass" properties of a moving electron will be observed exactly in the center of the screen relative to the location of the holes in the target. There will be a reflection of the EZS from the screen.
If they come into contact in a state of antiphase, then the DO will penetrate deep into the screen, and we will not see anything.
If the direction of movement of the FD deviates from a straight line, the distance to the screen will change. The result of interactions will also change, because The DOF will reach the screen in different phases.
Thus, a pattern similar to that observed in wave interference will be created. However, let the reader think for himself whether this effect from the interactions of a moving electron with a screen can be considered as an interference of it with itself.
In other words, you need to find out - can a single wave interfere? Given that, according to the provisions of classical physics, to obtain this effect, it is necessary to superimpose waves on each other.
To explain the "diffraction" of a moving electron when it passes through one hole, there is little that can be added to what has been said.
Reasoning logically, it should be assumed that at the initial moment of passage of the target, the FD must be in the “particle” state, or simply in antiphase with the state of the target.
When leaving the target, in case of deviation of the movement from the rectilinear FD, it is not at all necessary to have the ability to “go around” the obstacle. It is enough for him to be in antiphase with the content of the target in order to pass through it almost unhindered. Of course, the structure and dimensions of the obstacle must be appropriate to the frequency of oscillations in the structure of the FD.
Results.
The mass and charge of an electron, observed during a time significantly exceeding the frequency of its own oscillations, look like conserved, constant values. But during one period of oscillatory movements in the GL structure, the intensity of manifestation of properties can vary from a maximum, almost to zero.
An electron in the phase of "converging" half-quanta is practically not observed and does not show any properties (with the possible exception of a charge).
All properties of an electron known to physics can be attributed to the phase of "divergent" semiquanta. As a result a separate phase of the period of existence of an electron is perceived by the subject as a full-fledged physical object. Therefore, when analyzing the properties of an electron, we are forced to subdivide its existence in the phase of "divergent" half-quanta into two sorts of "subphases". In one of them (at the initial stage of expansion), the electron will have an almost “monolithic” structure, representing a “particle”. In the other (at the maximum stage of expansion), due to the uncertainty in size and the "scattering" of the content in the OSM space, the electron will appear in the form of a "wave".
In other words an electron in the initial stage of expansion appears for an external observer in the form of a point emitter of moving matter, which produces "divergent" semiquanta of the same kind.
Due to the practical unobservability of the external transforming interaction the boundaries of the electron in the stage of maximum "expansion" become ghostly.
The differences between the electron and the OSM spatial deformation field, as well as with the OSM content itself, are erased. As a result, it becomes absolutely unclear where the "single-phase" electron "draws" the charge motion to implement the process of "radiation" of its material content.
All the more inexplicable is the appearance of energy, which a “resting” electron does not have (and cannot have in principle), but which, according to the existing physical theory, the electron must irrevocably radiate into the surrounding space. (Here, "energy" refers to the energy content of a photon.)
In connection with such a one-sided perception of the electron structure, a number of problems arise in modern theoretical physics.
In particular, ideas about the nature of an electron based on mathematical models that appear as a result of generalizing only a visual, external manifestation of one side of the electron content are illogical in nature.
They demand to abandon the norms of formal logic, to think not just in an original way, but "unconventionally".
This can lead to nothing but an increase in the number of patients in psychiatric clinics. Since no sane subject is able to present a FD that is both a wave and a particle.
In the mathematical models themselves, designed to describe natural phenomena in accordance with the original, disproportions and infinities appear in a number of quantities (including mass, charge, size and energy). In the fight against these "divergences", ingenious methods are used (in particular, the theory of renormalizations), designed to fit theory to experimental data.
This is somewhat reminiscent of an attempt by a primary school student to solve a mathematical problem. in any way, after he learned the answer at the end of the textbook.
All these "difficulties" are quite understandable. theoretical physics is forced to explain phenomena that are in principle inexplicable from the standpoint of modern theory.
Most likely, the physical reality is richer and more diverse than our wildest fantasies, and the properties of matter even at the elementary level (especially OSM) are multifaceted and inexhaustible.
Probably not only the electron in its entirety of its structural content, but also many other realities of the physical world elude our attention. But even now we can say that there is nothing mystical or exclusively unknowable in the phenomena of the microworld.
An electron is an elementary particle, which is one of the main units in the structure of matter. The charge of an electron is negative. The most accurate measurements were made in the early twentieth century by Millikan and Ioffe.
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 the 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-quantum of particles.
Before the neutrino was measured, it was the electron that was considered the lightest particle. In quantum mechanics, it is referred to as fermions. The electron also has a magnetic moment. If a positron is also referred to it, then the positron is separated as a positively charged particle, and the electron is called a negatron, as a particle with a negative charge.
Individual 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 the energy, spin orientation, and other parameters. He reveals his belonging to fermions through the impossibility of having two electrons in the same quantum state at the same time (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.
Through the movement of electrons, an electric current, magnetism and thermo EMF occur. The charge of an electron in motion forms a magnetic field. However, an external magnetic field deflects the particle from a straight direction. When accelerated, the electron acquires the ability to absorb or emit energy as a photon. Its set consists of electron atomic shells, the number and position of which determine the chemical properties.
The atomic mass mainly consists of nuclear protons and neutrons, while the mass of electrons is about 0.06% of the total atomic weight. The Coulomb electric force is one of the main forces that can keep an electron close to the nucleus. But when molecules are created from atoms and chemical bonds arise, electrons are redistributed in the new space formed.
Nucleons and hadrons are involved in the appearance of electrons. Isotopes with radioactive properties are capable of emitting electrons. Under laboratory conditions, these particles can be studied in special instruments, 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 charge of an electron and the mass of cathode rays, the ratios of which, as they found out, do not depend on a material source.
And Becquerel found that minerals emit radiation by themselves, and their beta rays can be deflected by the action of an electric field, while 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 some 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 proper particles and waves. Also, light can manifest itself in the form of a wave (it is called the 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), 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, the 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 conflicts with the properties of the particle, where it is only possible to pass through one slit each time.
Electrons are considered to have the same physical properties. Therefore, their permutation, 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. Magnetic monopole of an electron.
(continuation)
Part 4. The structure of the electron.
4.1. The electron is a two-component particle, which consists of only two super-condensed (condensed, concentrated) fields - the electric field-minus and the magnetic field-N. Wherein:
a) electron density - the maximum possible in Nature;
b) electron dimensions (D = 10 -17 cm and less) - minimal in Nature;
c) in accordance with the requirement of energy minimization, all particles - electrons, positrons, particles with a fractional charge, protons, neutrons, etc. must have (and have) a spherical shape;
d) for unknown reasons, regardless of the energy value 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 is reliably established that the magnetic field of an electron is the same integral 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 allows us to draw 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. This equivalence property also applies to particles with fractional charges (+2/3) and (-1/3), which are the basis of quarks. That is: the mass of the positron, electron and all fractional particles is the equivalent of their charge, and vice versa - the charges of these particles are the equivalent of the mass. Therefore, the specific charge of the electron, positron and all fractional particles is the same (const) and is equal to 1.76 * 10 11 C/kg.
4.4. Because the elementary quantum of energy is automatically an elementary quantum of mass, then the electron mass (taking into account the presence of fractional particles 1/3 and 2/3) must have values , multiples of the masses of three negative semiquanta. (See also "Photon. The structure of the photon. The principle of movement. paragraph 3.4.)
4.5. It is very difficult to determine the internal structure of an electron for many reasons, however, it is of considerable interest, at least in the first approximation, to consider the influence of two components (electric 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 leaves of the negative half-quantum forms "microelectrons", which then form an electron. In this case, the number of "microelectrons" must be a multiple of three.
Option number 2. The electron is a two-component particle, which consists of two joined independent hemispherical monopoles - electric (-) and magnetic (N).
Option number 3. The electron is a two-component particle, which consists of two monopoles - electric and magnetic. In this case, the spherical magnetic monopole is located at the center of the electron.
Option number 4. Other options.
Apparently, a variant can be considered when electric (-) and magnetic fields (N) can exist inside an electron not only in the form of compact monopoles, but also in the form of a homogeneous substance, that is, they form a practically structureless? crystalline? homogeneous? particle. However, this is highly doubtful.
4.6. Each of the proposed options has its own advantages and disadvantages, for example:
a) Options #1. Electrons of this design make it possible to easily form fractional particles with a mass and charge that is a 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 to the nucleus with its electric monopole and therefore can have only two options for rotation around its axis - clockwise or counterclockwise (Pauli's prohibition?), etc.
4.7. When considering these (or newly proposed) options, it is imperative to take into account the actual 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);
The presence of a magnetic field;
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 a mass and charge that is a multiple 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 compacted electric field-minus (electric monopole-minus), and the second half (1/2) is a compacted magnetic field (magnetic monopole-N). However, it should be borne in mind that:
Electric and magnetic fields under certain conditions can give rise to each other (turn into each other);
An electron cannot be a one-component particle and consist 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 conduct a complete analysis of all the advantages and disadvantages of the proposed options and choose the only correct version of the internal structure of the electron in this work.
Part 5. "Wave properties of an 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 at that time was a graduate student, was struck by a brilliant idea: why the same thing cannot be for substance? Louis de Broglie did the reverse work on particles that Einstein did on light waves. Einstein connected electromagnetic waves with particles of light; de Broglie associated the motion of particles with the propagation of waves, which he called waves of matter. De Broglie's hypothesis was based on the similarity of the equations describing the behavior of light rays and particles of matter, and was of an exclusively theoretical nature. To confirm or refute it, experimental facts were required. ”(c)
5.2. “In 1927, American physicists K.Davisson and K.Jermer discovered that when electrons are “reflection” from the surface of a nickel crystal, maxima appear at certain angles of reflection. Similar data (the appearance of maxima) were already available from the observation of the diffraction of x-ray waves by crystalline structures. Therefore, the appearance of these maxima in reflected electron beams could not be explained in any other way than on the basis of ideas about waves and their diffraction. Thus, the wave properties of particles - electrons (and de Broglie's hypothesis) were proved by experiment. ”(c)
5.3. However, consideration of the process of the appearance of corpuscular properties of a photon described in this paper (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 electric and magnetic fields of a photon are condensed
(C)(C)(C)(C)(C)(C)(C)(C)(C)(C) b) when the electric and magnetic fields are compacted, a rapid increase in the "density" of fields begins at the "separation line" and already in the X-ray range the field density is commensurate with the density of an "ordinary" particle.
c) therefore, an 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 are so condensed that it is very difficult to detect their wave properties. Quote: "The smaller 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 appear in it."
b) in the hard X-ray and gamma range, photons behave like 100% particles, and it is almost impossible to detect wave properties in them. That is: the X-ray and gamma-ray photon completely loses the properties of the wave and turns into a 100% particle. Quote: "The energy of quanta in the X-ray and gamma range is so great that the radiation behaves almost like a stream of particles" (c).
c) therefore, in experiments on the scattering of an X-ray photon from the surface of a crystal, it was no longer a wave that was observed, but an ordinary particle that bounced off the surface of the crystal and repeated the structure of the crystal lattice.
5.5. Prior to the experiments of K. Davisson and K. Germer, there were already experimental data on the observation of the diffraction of X-ray waves on crystal structures. Therefore, having obtained similar results in experiments with the scattering of electrons on a nickel crystal, they automatically attributed wave properties to the electron. However, an electron is a “solid” particle that 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. Not an electron is reflected from an obstacle as a photon, but an X-ray photon is reflected from an obstacle as a particle.
5.6. Therefore: the electron (and other particles) did not have any “wave properties”, there is not and cannot be. And there are no prerequisites, much less opportunities to change 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 named an electron and given a minus sign (matter), and the other was called a positron and given a plus sign (antimatter). “The electric charge of the 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 separation of the elementary quanta of a photon in the longitudinal direction into two component parts: negative - from which a minus particle (electron) is formed and positive - from which a plus particle (positron) is formed. The separation of an electrically neutral photon in the longitudinal direction into two absolutely equal in mass, but different in charges (and magnetic fields) parts is a natural property of the photon, which follows from the laws of charge conservation, etc. The presence of “inside” the electron even negligible amounts of “particles-plus” , and "inside" the positron - "particles-minus" - is excluded. It also excludes the presence of electrically neutral "particles" (cuts, pieces, fragments, etc.) of the parent photon inside the electron and proton.
6.5. For unknown reasons, absolutely all electrons and positrons are born as reference "maximum-minimum" particles (i.e. 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 particles-minus (electrons) from electromagnetic photons is excluded.
6.6. The internal structure of the electron is unambiguously predetermined by the sequence of its appearance: the electron is formed as a two-component particle, which is 50% compacted electric field-minus (electric monopole-minus), and 50% dense magnetic field (magnetic monopole-N). These two monopoles can be considered as differently charged particles, between which forces of mutual attraction (adhesion) 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" the electron is necessary, since only a magnetic monopole-(N) can form with a singly charged electric monopole-minus the strongest (and unprecedented in strength) bond.
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) separation of an electron or positron into several calibrated or “different-sized” parts is excluded.
6.9. The electron is eternal and it cannot “disappear” until it meets another particle that has equal in magnitude but opposite in sign electric and magnetic charges (positron).
6.10. Since only two standard (calibrated) particles can appear from electromagnetic waves: an electron and a positron, then only standard quarks, protons and neutrons can appear on their basis. Therefore, all visible (baryonic) matter of our and all other universes consists of the same chemical elements (Mendeleev's table) and everywhere there are uniform physical constants and fundamental laws similar to "our" laws. The appearance at any point of the infinite space of "other" elementary particles and "other" chemical elements is excluded.
6.11. All visible matter of 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 “materials” for its formation in the Cosmos, and there cannot be.
P.S. Is the electron inexhaustible?
Introduction………………………………………………………………………… | ||
Main part……………………………………………………………… | ||
Definition of the electron, its discovery …………..………………… | ||
Electron properties ………………………………………………… | ||
The structure of electron shells ……..………………………….. | ||
Conclusions ………………………………………………………………. | ||
Conclusion…………………………………………………………………… | ||
Bibliography………………………………………………………….. | ||
Applications | ||
Attachment 1………………………………………………………………. |
Introduction
The first idea of what an atom, electron, electron shells were given to us back in the 8th grade. These were the basics, the simplest explanation of the most difficult, as it turned out, material. For me in the 8th grade, the simplest explanations were enough. But not so long ago, about 2-3 months ago, I began to think about how an atom actually works, how an electron moves, what an “electronic orbital” is in its full understanding. At first I tried to think about it myself, but nothing “sensible”, according to my ideas, came out of my head. Then I began to study additional literature in order to get a complete picture of the microworld and answer questions that interest me. With each new line from what I read, something new opened up for me. Further, I tried to present what I could study and partially (because knowledge of such a high level is given at universities and studied by many scientists around the world, and it is very difficult for a schoolchild to fully understand such material) to understand during this time.
Main part
1. Definition of the electron, its discovery.
Electron - stable, negatively charged elementary particle , one of the basic structural units of matter.
Is fermion (that is, has half-whole spin ). Refers to leptons (the only stable particle among charged leptons). They are made up of electrons electron shells of atoms , where their number and position determines almost everything Chemical properties substances. The movement of free electrons causes such phenomena as electric current in conductors and vacuum.
opening date electron is considered to be 1897 when Thomson An experiment was set up to study cathode rays. The first pictures of the tracks of individual electrons were obtained Charles Wilson with the help of the fog chamber.
2. Properties of an electron.
A. Mass and charge of a particle.
The electron charge is indivisible and equal to −1,(35) 10−19 C. It was first directly measured in the experiments of A. F. Ioffe (1911) and R. Milliken (1912). This value serves as a unit of measurement of the electric charge of other elementary particles (unlike the charge of an electron, the elementary charge is usually taken with a positive sign). The electron mass is 9.(40) 10−31 kg.
B. The impossibility of describing the electron through the classical laws of mechanics and electrodynamics.
For a long time there was no knowledge about the actual structure of the atom. At the end of XIX - beginning of XX century. in. it was proved that the atom is a complex particle consisting of simpler (elementary) particles. In 1911, on the basis of experimental data, the English physicist E.Rutherford proposed a nuclear model of the atom with an almost complete concentration of mass in a relatively small volume. The nucleus of an atom, consisting of protons and neutrons, has a positive charge. It is surrounded by electrons that carry a negative charge.
It is impossible to describe the motion of electrons in an atom from the standpoint of classical mechanics and electrodynamics, since:
If we assert that an electron (as a solid body) moves in a closed circular orbit around the nucleus with V ~ m / s (i.e., considered from the standpoint of classical mechanics), then under the action of a centripetal force it must in the shortest possible time (~ sec) will fall on the nucleus of the atom, which will lead to the non-existence of the atom as such and the non-existence of molecules, since electrons interact between atoms;
If we consider an electron as a charged body (i.e., consider it from the standpoint of electrodynamics), then it must inevitably be attracted by a positively charged nucleus, and when moving, it will radiate an electromagnetic field and lose energy, which will inevitably lead to a similar situation, which and in the case of consideration from the standpoint of classical mechanics.
Here is what Niels Bohr wrote:
“The insufficiency of classical electrodynamics for explaining the properties of an atom on the basis of a Rutherford-type model is clearly manifested when considering the simplest system consisting of a very small positively charged nucleus and an electron moving in a closed orbit around the nucleus. For the sake of simplicity, we assume that the mass of an electron is negligible compared to the mass of the nucleus, and the speed of electrons is small compared to the speed of light.
Let us first assume that there is no radiation of energy. In this case, the electron will move in stationary elliptical orbits ... Now consider the effect of energy radiation, as it is usually measured by the acceleration of the electron. In this case, the electron will no longer move in stationary orbits. The energy W will continuously decrease, and the electron will approach the nucleus, describing ever smaller orbits with ever increasing frequency; while the electron gains kinetic energy on average, the system as a whole loses energy. This process will continue until the dimensions of the orbits become of the same order as the dimensions of the electrons or the nucleus. A simple calculation shows that the energy emitted during this process is immeasurably greater than that emitted during ordinary molecular processes. Obviously, the behavior of such a system is completely different from what actually happens to an atomic system in nature. First, real atoms have a certain size and frequency for a long time. Further, it seems that if we consider any molecular process, then after the emission of a certain amount of energy, which is characteristic of the emitted system, this system will always again be in a state of stable equilibrium, in which the distances between the particles will be of the same order of magnitude as before the process. .
B. Bohr's postulates.
The main assumptions formulated Niels Bohr in 1913 to explain the pattern line spectrum of the hydrogen atom and hydrogen-like ions, as well as quantum nature of emission and absorption Sveta. Bohr came from planetary model of the atom Rutherford.
· Atom can only be in special stationary, or quantum, states, each of which corresponds to a certain energy. In a stationary state, an atom does not radiate electromagnetic waves.
· Electron in an atom , without losing energy, moves along certain discrete circular orbits for which angular momentum is quantized . The stay of an electron in orbit determines the energy of these stationary states.
When an electron moves from orbit (energy level) to orbit, it is emitted or absorbed energy quantum hν = En − Em , where En; Em – energy levels between which the transition is made. When moving from the upper level to the lower one, energy is emitted, and when moving from the lower to the upper one, it is absorbed.
a) “The dynamic equilibrium of a system in stationary states can be considered with the help of ordinary mechanics, while the transition of a system from one stationary state to another cannot be interpreted on this basis.
b) This transition is accompanied by the emission of monochromatic radiation, for which the ratio between the frequency and the amount of energy released is exactly the same as that given by Planck's theory ... "
allowed Bohr to formulate his theory of the structure of the atom or Bohr model of the atom.
It is a semiclassical model of the atom based on Rutherford's theory of the structure of the atom. Using the above assumptions and the laws of classical mechanics, namely the equality of the force of attraction of an electron from the nucleus and the centrifugal force acting on a rotating electron, Bohr obtained the following values for the radius of a stationary orbit and the energy of an electron located in this orbit:
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It is this expression for energy that can be obtained by applying Schrödinger equation , solving the problem of electron motion in the central Coulomb field.
The radius of the first orbit in the hydrogen atom R0=5,(36) 10−11 m, now called Bohr radius , or atomic unit of length and is widely used in modern physics. The energy of the first orbit eV is ionization energy a hydrogen atom.
Note: This model is a rough application of the laws of electrodynamics with some assumptions to explain the motion of an electron solely in the hydrogen atom. For more complex systems with a large number of electrons, this theory is unacceptable. It is a consequence of more general quantum laws.
G. Corpuscular-wave dualism.
In classical mechanics, two types of motion are considered: body movement with the localization of a moving object at each point of the trajectory at a certain point in time and wave motion , delocalized in the space of the medium. For micro-objects, such a delimitation of motion is impossible. This feature of motion is called wave-particle duality.
Wave-particle duality – the ability of a microparticle, having a mass, size and charge, to simultaneously exhibit the properties characteristic of waves, for example, the ability to diffraction. Depending on what properties of the particles are studied, they exhibit either one or the other properties.
The author of the idea of corpuscular-wave dualism was A. Einstein , who proposed to consider the quanta of electromagnetic radiation - photons - as particles moving at the speed of light, having zero rest mass. Their energy is E = mc 2 = hν = hc / λ ,
where m is the mass of the photon, With is the speed of light in vacuum, h- Planck's constant, ν - radiation frequency, λ - wavelength.
In 1924 the French physicist Louis de Broglie put forward the idea that the wave nature of propagation, established for photons, has a universal character. It should appear for any particles with momentum . All particles with a finite momentum , have wave properties, in particular, are subject to interference and diffraction .
Formula de Broglie establishes the dependence of the wavelength associated with a moving particle of matter on the momentum of the particle:
where is the mass of the particle, is its velocity, - Planck's constant . The waves in question are called de Broglie waves. Formula de Broglie experimentally confirmed by experiments on the scattering of electrons and other particles on crystals and on the passage of particles through substances. A sign of the wave process in all such experiments is the diffraction pattern of the distribution of electrons (or other particles) in the particle receivers.
Waves de Broglie have a specific nature that has no analogy among the waves studied in classical physics: the square of the modulus of the de Broglie wave amplitude at a given point is a measure of the probability that a particle is detected at that point. The diffraction patterns that are observed in the experiments are a manifestation of a statistical regularity, according to which particles fall into certain places in the receivers - where the intensity of the de Broglie wave is greatest. Particles are not found in those places where, according to the statistical interpretation, the square of the modulus of the amplitude of the "probability wave" vanishes.
This theory marked the beginning of the formation of quantum mechanics. At present, the concept of wave-particle duality is only of historical interest, since it served only as an interpretation, a way to describe the behavior of quantum objects, choosing analogies from classical physics for it. In fact, quantum objects are neither classical waves nor classical particles, acquiring the properties of the former or the latter only in some approximation.
E. Heisenberg's uncertainty principle.
In 1927 a German theoretical physicist AT. Heisenberg formulated the principle of uncertainty, which consists in the fundamental impossibility of simultaneously accurately determining the position of a microparticle in space and its momentum:
Δ px · Δ x ≥ h/ 2π,
where ∆ px = m Δ vx x - uncertainty (error in determination) of the momentum of the micro-object along the coordinate X; Δ x- uncertainty (error in determination) of the position of the micro-object along this coordinate.
Thus, the more precisely the velocity is determined, the less is known about the location of the particle, and vice versa.
Therefore, for a microparticle (in this case, an electron), the concept of the trajectory of motion becomes unacceptable, since it is associated with specific coordinates and momentum of the particle. We can only talk about the probability of finding it in some areas of space.
There was a transition from the "orbits of motion" of electrons, introduced by Bohr, to the concept orbitals – regions of space where the probability of electrons being present is maximum.
3. Structure of electron shells.
The electron shell of the atom – region of space where electrons are likely to be located, characterized by the same value of the principal quantum number n and, as a result, located at close energy levels. The number of electrons in each electron shell does not exceed a certain maximum value.
The electron shell of the atom – it's a collection atomic orbitals with the same value of the principal quantum number n.
a) The concept of the atomic orbital.
atomic orbital – this is a one-electron wave function in the spherically symmetric electric field of the atomic nucleus, given by the main n, orbital l and magnetic m quantum numbers.
1) wave function - a complex function describing the state of a quantum mechanical system. (The hydrogen atom is taken as the simplest quantum system. It is on its basis that all calculations related to the wave function are made.)
The most important is the physical meaning of the wave function. It consists of the following:
« probability density location of a particle at a given point in space at a given time is considered equal tosquare absolute valuewave function of this state in the coordinate representation.
The wave function of the system A of particles contains the coordinates of all particles: ψ(1,2,...,A, t).
The square of the modulus of the wave function of an individual particle |ψ(,t)|2 = ψ*(,t)ψ(,t) gives the probability of detecting a particle at time t at a point in space described by coordinates , namely, |ψ(,t) |2dv ≡ |ψ(x, y, z, t)|2dxdydz is the probability of finding a particle in a region of space with a volume of dv = dxdydz around the point x, y, z. Similarly, the probability to find a system A of particles with coordinates 1,2,...,A in the volume element of a multidimensional space at time t is given by |ψ(1,2,...,A, t)|2dv1dv2...dvA .
The Heisenberg uncertainty principle imposes some limits on the accuracy of calculating the wave function.
The value of the wave function is found by solving the so-called Schrödinger equations.
2) Schrödinger equation - equation describing change in space and time pure (quantum) state , given wave function.
It was proposed in 1926 by a German physicist E. Schrödinger to describe the state of an electron in a hydrogen atom.
3) The physical meaning of the wave function makes it possible to understand the geometric meaning of the atomic orbital, which is as follows:
"An atomic orbital is a region of space bounded by a surface of equal densityprobabilitiesorcharge. The probability density on the boundary surface is chosen based on the problem being solved, but usually in such a way that the probability of finding an electron in a limited area lies in the range of 0.9 - 0.99 "
4) quantum numbers – these are the numbers that define the shape of the orbital, the energy and angular momentum of the electron.
The principal quantum number n can take any positive integer values, starting from one ( n= 1,2,3, … ∞) and determines the total energy of an electron in a given orbital (energy level):
Energy for n= ∞ corresponds to single electron ionization energy for a given energy level.
The orbital quantum number (also called the azimuthal or complementary quantum number) determines angular momentum electron and can take integer values from 0 to n - 1 (l = 0,1, …, n - 1). angular momentum is given by the ratio
Atomic orbitals are usually named according to the letter designation of their orbital number:
The letter designations of atomic orbitals originated from the description of spectral lines in atomic spectra: s (sharp) is a sharp series in atomic spectra, p (principal)- home, d (diffuse) - diffuse, f (Fundamental) is fundamental.
· Magnetic quantum number ml
The movement of an electron in a closed orbit causes the appearance of a magnetic field. The state of the electron, due to the orbital magnetic moment of the electron (as a result of its orbital motion), is characterized by the third quantum number - magnetic ml. This quantum number characterizes the orientation of the orbital in space, expressing the projection of the orbital angular momentum on the direction of the magnetic field.
According to the orientation of the orbital relative to the direction of the vector of the external magnetic field, the magnetic quantum number can take on the values of any integers, both positive and negative, from -l to +l, including 0, i.e., in total (2l + 1) values. For example, for l = 0, ml= - 1, 0, +1.
In this way, ml characterizes the value of the projection of the vector of the orbital angular momentum on the selected direction. For example, a p-orbital in a magnetic field can be oriented in space in 3 different positions. [ 9. 55]
5) Shells.
The electron shells are denoted by letters K, L, M, N, O, P, Q or numbers from 1 to 7. Shell sublevels are denoted by letters s, p, d, f, g, h, i or numbers from 0 to 6. The electrons of the outer shells have more energy, and, compared with the electrons of the inner shells, are farther from the nucleus, which makes them more important in the analysis of the behavior of an atom in chemical reactions and in the role of a conductor, since their connection with the core is weaker and breaks more easily.
6) Sublevels.
Each shell consists of one or more sublevels, each of which consists of atomic orbitals. For example, the first shell (K) consists of one sublevel "1s". The second shell (L) consists of two sublevels, 2s and 2p. The third shell is from "3s", "3p" and "3d".
To fully explain the structure of electron shells, it is necessary to highlight the following 3 very important provisions:
1) Pauli principle.
It was formulated by the Swiss physicist W. Pauli in 1925. It is as follows:
An atom cannot have two electrons that have the same properties.
In fact, this principle is more fundamental. It applies to all fermions.
2) The principle of least energy.
In an atom, each electron is located so that its energy is minimal (which corresponds to its greatest bond with the nucleus).
Since the energy of an electron in the ground state is determined by the main quantum number n and the secondary quantum number l, then those sublevels are filled first for which the sum of the quantum numbers n and l is the smallest.
Based on this For the first time in 1961, he formulated a general position stating that:
An electron in the ground state occupies a level not with a minimum valuen, and with the smallest value of the sumn+ l.
3) Gund's rule.
For this valuel(i.e., within a certain sublevel), the electrons are arranged in such a way that the total spin is maximum.
If, for example, it is necessary to distribute three electrons in three p-cells of a nitrogen atom, then they will each be located in a separate cell, i.e., placed on three different p-orbitals:
conclusions:
1) The motion and properties of an electron cannot be described by the classical laws of mechanics and electrodynamics. The electron can only be described within the framework of quantum physics.
2) The electron does not have a clear orbit of rotation. Around the nucleus there is an electron "cloud", where the electron is located at any point in space at any time.
3) An electron has the properties of a particle and a wave.
4) There are different physical and mathematical methods for describing the characteristics of an electron.
5) Atomic orbitals, each of which consists of no more than 2 electrons, make up the electron shell of the atom, the electrons of which participate in the formation of interatomic bonds in molecules.
Conclusion.
At school, at the initial stage, they do not fully reveal the real idea of \u200b\u200bthe structure of an atom, an electron. To better understand its structure, it is necessary to study additional literature. And those who are interested in this topic have every opportunity to deepen their knowledge, and even contribute to the knowledge of microparticles.
Initial knowledge about the laws of physics is not enough to fully describe the objects of the microworld, in this case, electrons.
Without understanding the foundations of the universe, the fundamental concepts of the microworld, it is impossible to understand the macro and mega world that surrounds us.
Bibliography
1. Wikipedia. Article "Atomic Orbital".
2. Wikipedia. "Wave Function".
3. Wikipedia. Article "Discovery of the electron".
4. Wikipedia. Article "Bohr's Postulates".
5. Wikipedia. "The Schrödinger Equation".
6. Wikipedia. Article "Electron".
7. , . Reader in physics: a textbook for students "p. 168: From the article by N. Bohr "On the structure of the atom and molecules." Part one. "Binding of electrons by a positive nucleus".
8. Department of MITHT. Fundamentals of the structure of matter.
9. , . Beginnings of chemistry.
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1. Sir Joseph John Thomson(December 18, 1856 - August 30, 1940) - English physicist who discovered the electron, winner of the Nobel Prize in Physics in 1906. Most of his works are devoted to electrical phenomena, but more recently, especially to the passage of electricity through gases, to the study of X-rays and Becquerel.
2. Charles Thomson Reese Wilson(February 14, 1869, Glencore - November 15, 1959, Carlops, a suburb of Edinburgh) - Scottish physicist, for the development of the cloud chamber named after him, which gave "a method of visual detection of the trajectories of electrically charged particles by means of vapor condensation", Wilson was awarded in 1927 (together with Arthur Compton) Nobel Prize in Physics.
3. Ernest Rutherford(August 30, 1871, Spring Grove - October 19, 1937, Cambridge) - British physicist of New Zealand origin. Known as the "father" of nuclear physics, he created the planetary model of the atom. Winner of the Nobel Prize in Chemistry in 1908.
4. Niels Henrik David Bohr(October 7, 1885, Copenhagen - November 18, 1962, Copenhagen) - Danish theoretical physicist and public figure, one of the founders of modern physics. Nobel Prize in Physics (1922). He was a member of more than 20 academies of sciences of the world, including a foreign honorary member of the Academy of Sciences of the USSR (1929; a corresponding member from 1924).
Bohr is known as the creator of the first quantum theory of the atom and an active participant in the development of the foundations of quantum mechanics. He also made a significant contribution to the development of the theory of the atomic nucleus and nuclear reactions, the processes of interaction of elementary particles with the environment.
5. Albert Einstein March 14, 1879, Ulm, Württemberg, Germany - April 18, 1955, Princeton, New Jersey, USA) - theoretical physicist, one of the founders of modern theoretical physics, Nobel Prize winner in physics in 1921, humanist public figure. Lived in Germany (1879-1893, 1914-1933), Switzerland (1893-1914) and the USA (1933-1955). Honorary doctor of about 20 leading universities in the world, a member of many Academies of Sciences, including a foreign honorary member of the USSR Academy of Sciences (1926). Author of numerous books and articles. Author of the most important physical theories: General Relativity, Quantum Theory of the Photoelectric Effect, etc.
6. Raymond, 7th Duke of Broglie, better known as Louis de Broglie(August 15, 1892, Dieppe - March 19, 1987, Louveciennes) - French theoretical physicist, one of the founders of quantum mechanics, Nobel Prize in Physics for 1929, member of the French Academy of Sciences (since 1933) and its permanent secretary (since 1942) year), member of the French Academy (since 1944).
Louis de Broglie is the author of works on fundamental problems of quantum theory. He owns a hypothesis about the wave properties of material particles (de Broglie waves or matter waves), which marked the beginning of the development of wave mechanics. He proposed an original interpretation of quantum mechanics, developed the relativistic theory of particles with arbitrary spin, in particular photons (the neutrino theory of light), dealt with radiophysics, classical and quantum field theories, thermodynamics and other branches of physics.
7. Werner Karl Heisenberg(German December 5, 1901, Würzburg - February 1, 1976, Munich) - German theoretical physicist, one of the founders of quantum mechanics. Nobel Prize in Physics (1932). Member of a number of academies and scientific societies of the world.
8. Erwin Rudolf Joseph Alexander Schrödinger(August 12, 1887, Vienna - January 4, 1961, ibid) - Austrian theoretical physicist, one of the founders of quantum mechanics. Nobel Prize in Physics (1933). Member of a number of world academies of sciences, including a foreign member of the USSR Academy of Sciences (1934).
Schrödinger owns a number of fundamental results in the field of quantum theory, which formed the basis of wave mechanics: he formulated the wave equations (stationary and time-dependent Schrödinger equations), developed the wave-mechanical perturbation theory, and obtained solutions to a number of specific problems. Schrödinger proposed an original interpretation of the physical meaning of the wave function. He is the author of many works in various fields of physics: statistical mechanics and thermodynamics, dielectric physics, color theory, electrodynamics, general relativity and cosmology; he made several attempts to construct a unified field theory.
Fermion- according to modern scientific ideas: elementary particles that make up matter. Fermions include quarks, electron, muon, tau-lepton, neutrino. In physics, a particle (or quasi-particle) with a half-integer spin. They got their name in honor of the physicist Enrico Fermi.
Leptons- fermions, that is, their spin is 1/2. Leptons, together with quarks, constitute a class of fundamental fermions - particles that make up matter and which, as far as is known, have no internal structure.
Line spectrum of hydrogen(or Spectral series of hydrogen) - a set of spectral lines resulting from the transition of electrons from any of the higher stationary levels to one lower one, which is the main one for this series.
Angular moment − a quantity that depends on how much mass of a given body is rotating, how it is distributed relative to the axis of rotation, and at what speed the rotation occurs.
steady state is the state of a quantum system in which its energy and other dynamic quantities characterizing the quantum state do not change.
quantum state- any possible state in which a quantum system can be.
In wave mechanics, it is described by a wave function.
