Youth and beauty 

Zone theory of solid bodies, energy levels and the formation of energy zones. The concept of the zone theory

Name of parameter Value
Theme of article: Energy levels
Rubric (thematic category) Education

Building atom

1. Development of the theory of the structure of the atom. FROM

2. The core and the electronic shell of the atom. FROM

3. The structure of the nucleus of the atom. FROM

4. Nuclides, isotopes, mass number. FROM

5. Energy levels.

6. Quantum-mechanical explanation of the structure.

6.1. Orbital model atom.

6.2. Rules for filling orbitals.

6.3. Orbitals with S-electrons (atomic S-orbitals).

6.4. Orbitals with p-electrons (atomic p-orbitals).

6.5. Orbital with D-F electrons

7. Energy pins of a multielectronic atom. Quantum numbers.

Energy levels

The structure of the electron shell is determined by the different reserve of energy-reader electrons in the atom. In accordance with the model of the boron atom, electrons may occupy in the atom that accurately defined (quantized) energy states correspond. These states are called energy levels.

The number of electrons that may be in a separate energy level is determined by formula 2N 2, where the N-level of the level, which is indicated arabic numbers 1 - 7. Maximum filling of the first four energy levels in. In accordance with formula 2N 2 is: for the first level - 2 electrons, for the second - 8, for the third -18 and for the fourth level - 32 electrons. The maximum filling with electrons by higher energy levels in the atoms of the known elements is not achieved.

Fig. 1 Shows the filling of the electron levels of the first twenty elements (from hydrogen n to calcium sa, black circles). Filling the energy levels in the specified order, the simplest models of the atoms of the elements are obtained, while the fill order is observed (from the bottom up and left to right in the figure) so while the last electron will indicate the symbol of the corresponding elementary elementary energy level M.(maximum capacity is 18 e -) Elements of NA - AR contain only 8 electrons, then the fourth energy level begins to be built. N.- It appears two electrons for elements to and sa. The following 10 electrons again occupy the level M.(The elements of SC - Zn (not shown), and then the filling of the level N is continued by six more electrons (the elements of CA-KR, white circles).

Fig. one Fig. 2.

If the atom is in the main state, its electrons occupy the levels with minimal energy, i.e. each subsequent electron occupies the energy of the most advantageous position, as in Fig. 1. Ply external impact An atom associated with the transfer of energy to it, for example, by heating, electrons are transferred to higher energy levels (Fig. 2). This state of the atom is called excited. The place freed at the lower energy level is filled (as a favorable position) by an electron with a higher energy level. When moving the electron gives no energy, ĸᴏᴛᴏᴩᴏᴇ corresponds to the energy difference between the levels. As a result of electronic transitions, characteristic radiation occurs. The spectral lines of the absorbed (emitted) light include quantitative conclusion on the energy levels of the atom.

In accordance with the quantum model of the boron atom, an electron, which has a determined energy state, moves in an atom on a circular orbit. Electrons with the same energy reserve are at equal distances from the kernel, each energy level Replies its electron set called by a boron electron layer. Τᴀᴋᴎᴍ ᴏϭᴩᴀᴈᴏᴍ, along Bor, the electrons of the same layer are moving along a ball surface, the electrons of the next layer on another ball surface. The sphere is inscribed in one to another with the center that meets the atomic kernel.

Energy levels - concepts and types. Classification and features of the category "Energy Levels" 2017, 2018.

Fig. 7. Image of forms and orientations

s.-,p.-,d.-, orbital with boundary surfaces.

Quantum numberm. l. Call magnetic . It determines the spatial location of the atomic orbital and takes the integer values \u200b\u200bfrom l. up to +. l. through zero, that is 2 l. + 1 values \u200b\u200b(Table 27).

Orbital one sublevel ( l. \u003d Const) have the same energy. This condition is called degenerate energy. So p.-Orbital - three times, d. - five times, and f. - Severately degenerate. Boundary surfaces s.-,p.-,d.-, orbitals are shown in Fig. 7.

s. -Orbitali spherically symmetrical for any n. and differ from each other only the size of the sphere. Their maximum symmetric form is due to the fact that l. \u003d 0 and μ l. = 0.

Table 27.

The number of orbitals on energy suits

Orbital quantum number

Magnetic quantum number

Number of orbitals with this value l.

m. l.

–2, –1, 0, +1, +2

–3, –2, –1, 0, +1, +2, +3

p. -Orbitali exist when n. ≥ 2 I. l. \u003d 1, so there are three orientation options in space: m. l. \u003d -1, 0, +1. All P-orbitals have a nodal plane dividing an orbital into two areas, therefore, the boundary surfaces have the form of dumbbells oriented in space at an angle of 90 ° relative to each other. Axes of symmetry for them are the coordinate axes that are indicated p. x. , p. y. , p. z. .

d. -Orbitali Defined by a quantum number l. = 2 (n. ≥ 3), in which m. l. \u003d -2, -1, 0, +1, +2, that is, characterized by five orientation options in space. d.-Obitals, oriented with blades on the axes of coordinates, are indicated d. z. ² I. d. x. ²– y. ², but oriented by blades on bisector of coordinate angles - d. xY. , d. yz. , d. xz. .

Seven f. -Orbitalcorresponding l. = 3 (n. ≥ 4), are depicted in the form of boundary surfaces.

Quantum numbers n., l. and m. Do not fully characterize the state of the electron in the atom. It is experimentally established that the electron has another property - spin. Simplified spin can be represented as an electron rotation around its own axis. Spin quantum number M s. has only two values m. s. \u003d ± 1/2, which are two projections of the angular momentum of the electron on the selected axis. Electrons with different m. s. Denote by arrows directed up and down.

Sequence Filling atomic orbitals

The population by electrons of atomic orbitals (AO) is carried out according to the principle of the lowest energy, the principle of Paulia rule Gund, and for multi-electronic atoms - the rule of Clachkovsky.

The principle of least energy It requires the electrons to populate an AO in order to increase the energy of electrons in these orbital. This reflects the general rule - the maximum sustainability of the system corresponds to the minimum of its energy.

Principle Pauli. (1925) prohibits in a multi-electron atom to be electrons with the same set of quantum numbers. This means that two any electrons in the atom (or molecule, or ion) should differ from each other by the value of at least one quantum number, that is, on the same orbital there may be no more than two electrons with various spins (paired electrons). Each sublayer contains 2 l. + 1 orbitals, on which no more than 2 are placed (2 l. + 1) electrons. It follows that the container s.-Subitals - 2, p.-Subitals - 6, d.-Evubitals - 10 and f.-Evubitals - 14 electrons. If the number of electrons is given l. sum up from 0 to n. - 1, then we get the formula BoraBeuriedetermining the total number of electrons at the level of the specified n.:

This formula does not take into account the interelectronic interaction and ceases to be performed when n. ≥ 3.

Orbitals with the same energies (degenerate) are filled in accordance with rule Gunda : The lowest energy has an electronic configuration with maximum spin. This means that if there are three electrons on P-orbitals, then they are located like this: and the total spin S.\u003d 3/2, and not:, S.=1/2.

Clekkovsky rule (The principle of least energy). In the multielectronic atoms, as in the hydrogen atom, the state of the electron is determined by the values \u200b\u200bof the same four quantum numbers, but in this case the electron is not only in the core field, but also in the field of other electrons. Therefore, the energy in multielectronic atoms is determined not only by the main, but also a orbital quantum number, and rather their amount: the energy of atomic orbitals increases as the amount increasesn. + l.; At the same amount, the level with a smaller level is first filled.n. and bigl.. The energy of atomic orbitals increases according to a row:

1s.<2s.<2p.<3s.<3p.<4s.≈3d.<4p.<5s.≈4d.<5p.<6s.≈4f.≈5d.<6p.<7s.≈5f.≈6d.<7p..

So, four quantum numbers describe the state of the electron in the atom and characterize the electron energy, its spin, the form of an electronic cloud and its orientation in space. In the transition of an atom from one state to another, the electronic cloud is restructuring, that is, the values \u200b\u200bof quantum numbers change, which is accompanied by the absorption or emission of the energy quanta atom.

Within the framework of the electronic gas model, it is impossible to answer the question of why some substances are conductors, the second semiconductors, and the third insulators. The interaction between atoms and atoms and electrons should be taken into account. Suppose that the crystal metal grid or semiconductor is formed as a result of atoms rapprochement. Valence electrons of metals atoms are significantly weaker associated with atomic nuclei than such electronic semiconductors. Under rapprochement of atoms, electrons come into interaction. As a consequence, valence electrons are separated from metal atoms and become free, having the ability to move throughout the metal. In semiconductors, due to the stronger coupling of electrons with atomic cores in order for a valence electron to tear to inform him the energy, which is called the ionization energy. For various semiconductors, the ionization energy is different from 0.1 to 2 eV, while the average kinetic energy of the thermal motion of the atom of about 0.04 eV. The number of atoms whose energy is greater than or equal to the energy of ionization is relatively large. Consequently, some free electrons in semiconductors. With an increase in temperature, the number of atoms with the ionization energy increases, it means that the electrical conductivity of the semiconductor increases.

The ionization process is accompanied by the reverse process - recombination. In a state of equilibrium, the average ionization acts are equal to the number of acts of recombination.

The concept of the zone theory

The quantum theory of electrical conductivity of solid bodies is based on the zone theory, which is based on the study of the electron energy spectrum. This spectrum is divided into zones that are separated by prohibited intervals. In the event that in the upper zone where electrons are present, they are not filled with all quantum states (within the zone there is an opportunity to redistribute energy and pulse), then this substance is a conductor. Such a zone is called the conduction zone, the substance is an electric current conductor, the type of conductivity is electronic. If there are many electrons and free quantum states in the conductivity zone, the electrical conductivity is large. Electrons in the conduction zone are charge carriers when the electric current is passed. The movement of such electrons is described by the laws of quantum mechanics. The number of such electrons is small compared to the total number of electrons.

Energy levels

The energy levels of the valence electron in one insulated atom can be represented as shown in Fig. 1. Vertically from the bottom up in Fig. 1 postponed: the values \u200b\u200bof the total energy of the electron and the minimum energy of the conduction electrons $ E_C \\ $ and the highest energy of the associated electrons $ E_v are noted. $ Possible values \u200b\u200bof electron energies are filled with some area or energy zone $ W \\ GE E_C $. This zone is called the conduction zone. Energy of communication electron form another zone with $ w \\ le e_v $. This zone is called the zone of valence electrons (valence zone). These zones are separated by an energy gap width:

This energy gap is called the zone of prohibited energies. If there are no impurity atoms, and lattice defects, the stationary movements of electrons with energy inside the prohibited zone are impossible.

Picture 1

A chemical bond, which leads to an electron of conduction and a positive hole - is an electronic transition of the valence zone - the conduction zone (see Fig.1 of the figure 1). The reverse process is the recombination of the conduction electron and a positive hole - electronic transition 2 (Fig. 1). In the existence of impurity atoms, the formation of discrete allowed energy levels is possible (for example, in Fig. 1 is the level $ E_D $). These levels may not exist in the entire volume of the crystal, but only in those places where the impurity atoms are (these levels are called local). Each local level gives an electron energy when it is on an impurity atom. Local energy levels make additional electronic transitions possible. Thus, the ionization of the donor with the formation of an electron conductivity is reflected in Fig. 1 by electronic transition 3. The reverse of the electron capture process on the donor atom is an electronic transition of 4 of the conduction zone on an empty donor level.

Formation of energy zones

The solution of the electron movement problem in the periodic potential field shows that there are systems of zones of allowed energies (Fig. 2). Each zone is limited to below with some energy $ W_ (min) $ (bottom zone), and from above has $ W_ (max) $ - zone ceiling. These zones are separated by bands for prohibited energies. The width of the allowed zones increases with increasing energy. Wide upper zones can overlap each other, so the single complex zone is formed.

Suppose that there are n isolated atoms that do not interact. In each of them, the electron energy can only vary with a jump, therefore, is characterized by a set of sharp, discrete energy levels. In such a system of non-benefit atoms, instead of each atomic energy level, there are N coinciding levels of energy. Railway atoms, before the formation of a crystal lattice. Atoms begin to interact, energy levels are changed. Previously, the energies' levels previously become different. Such a system of inadequate energy levels is a permitted energy zone. It turns out that the energy zones appear as a result of the splitting of discrete levels of electron energy in atoms under the action of the lattice atoms.

The number of energy levels in each zone is very large (the procedure for the number of atoms in the crystal), energy levels are located close. So, in some cases, it can be assumed that inside zones, the electron energy changes continuously (as in the classical theory). But the fact that the number of levels is certainly has a fundamental importance.

So, the combination of energy levels to which the multiple level is cleaving is called the energy zone (crystal zone). The zone appearing as a result of the splitting of the N-multiple of the degenerate main level, is called the base zone, all other zones are excitation zones.

Energy zones can not be identified with spatial zones, areas of space where electron is located. In the zone theory, it is assumed that the electron is moving in a constant electric field, which is created by ions and other electrons. The ions have relatively large masses and are considered fixed. Electrons are taken into account in total. They seem like a negatively charged fluid that fills the space between ions. The role of electrons in such a model is reduced to compensation of the charge of ions. The electric field of the model is periodic in space, periods are spatial periods of the lattice. The task is reduced to the problem of the movement of one electron in a constant periodic field. The solution to such a task in quantum mechanics leads to the zone structure of energy levels.

Example 1.

Task: Describe the zone structures of metals, dielectrics and semiconductors.

Electrical properties of bodies are connected to the width of the prohibited energy zone and differences in filling the allowed zones. The required conductivity condition is the presence in the permitted zone of free energy levels. On this level, the field of third-party power can translate an electron. The zone that is filled in part or empty called the conduction zone. The zone filled with electrons is entirely called valence. Metals, dielectrics and semiconductors differ in the degree of filling in the valence zone by electrons and the width of the forbidden zone.

  1. Metals have a partially conduction zone, has free upper levels. At T \u003d 0, the valence electrons fill in pairwise lower levels of the valence zone. Electrons that are localized at the upper levels, it is enough to inform the energy $ (10) ^ (- 23) - \\ (10) ^ (- 22) eV $ in order to translate them to higher levels.
  2. Dielectrics have the first, unfilled zone, separated from the lower entirely filled zone with a wide forbidden zone. To transfer the electron to the free zone, it is required to provide energy to a large or equal width of the forbidden zone. In dielectrics, the width of the forbidden zone is equal to several electron solts. The heat movement cannot be sent a large number of electrons into the free zone.
  3. The crystalline semiconductors have the width of the forbidden zone between the fully filled valence zone and the first unfilled zone is not large. If the width of the forbidden zone is equal to several tenths of eV, the heat of the heat movement is enough to deliver electrons into the free inspection zone. At the same time, it is possible to transition an electron inside the valence zone to the liberated levels.

Example 2.

Task: List the basic assumptions of the zone theory.

The main assumptions of zone theory can be attributed:

  1. Ions in the nodes of the crystal lattice are treated as fixed, as they have a relatively large mass. Ions are sources of electric field. This field acts on electrons.
  2. Placing positive ions is periodic, as they are located in the nodes of the perfect crystal lattice.
  3. Electron interaction is replaced with an effective external field. Electrons interact in accordance with the law of the coulon. This assumption allows you to replace the multielectronic problem with one electrical task.

Human energy is a stock of vitality and energy that has a specific personality. We can increase our energy with various ways (they are described in detail in another article). But there are certain limitations - every person from nature has its own energy potential that cannot change significantly. In this article we will tell, how the energy is determined by the date of birth.

When a person is sufficiently filled with vital energy, he feels confidence in his abilities. This is a leader person who does not worry about the opinion of those around himself. It generates various ideas and actively introduces them to life. Such personalities are distinguished by natural behavior, a direct expression of their feelings and emotions.

From nature, the big energy potential is extraordinary, creative people who speak the sources of fresh ideas that can share with their surrounding energy. These are wonderful storytellers, they always have plenty of fans, they easily establish connections with new people at the expense of their politeness, charm and goodwill.

The strong energy field is also manifested by defined external features:

  • characterized subtle lips;
  • massive chin;
  • dense eyebrows;
  • wide jaw;
  • in most cases, such people are dark-haired;
  • people with dark eyes have a very strong aura.

How the date of birth affects the energy

Day, month, year and even time of birth has a huge impact on the entire subsequent life of a person. The concept of which we now speak is also known as "Bioenergy". To date, even such a profession has appeared - bioenergy. Experts of this sphere are able to trace the relationship between a particular person, figures, the universe, and so on.

Bioenergy (based on numerology) found that the date of birth can shed light on the human energy potential. Speaking towards simple mathematical calculations, it is realistic to make a forecast of future events for a specific period of life. Also, these data are used to build a live curve and monitoring changes. The more energy in humans, that respectively there will be a curve.

Bioenergy by date of birth: calculation

As happens calculation of energy

  1. Remember the date of your appearance. For example, May 25, 1994.
  2. Write down the first number - in his capacity is the year of birth - 1994.
  3. The second number is formed by a sequence number of birthday and day - 0525.

Note! If the birthday is formed by an unequivocal number (for example, nine), then write the second number in this way - 809.

  1. Now multiply the first number to the second \u003d 1994 * 0525 \u003d 1,046,850.
  2. After that, calculate the amount of all numbers of the resulting number:

The number that turned out is the bioenergy potential of a person (E) and demonstrates in which the number of vitality (energy) it has.

And now the most interesting thing is to find out who you are:

  • energy vampire - e less than twenty;
  • normal man - Values \u200b\u200bE will range from twenty to thirty;
  • the energy donor - has the potential of energy from thirty and more.

Regardless of the natural energy balance, everyone in life has periods in life when we are in a weakened state and need an additional energy feeding. In this case, a person unconsciously begins to "vampire" around.

At the same time, normal people and donors begin to feel uncomfortable. But the donors, which exceed the "Thirty-three" marks are able to recharge the space energy or feed on energy from nature. They generously give the vitality around others, people seek to be near them to focus with energy.

Where energy is lost

Perhaps you are familiar to you when the forces begin to leave, as if someone "blows up" you like a balloon. You fully feed, sleep enough hours, engaged in physical activity, but internally still feel tired. The symptoms described above describe the state of the outflow of vital energy: you, it seems to do everything for its replenishment, but it becomes less and less.

Why is this happening? You need to analyze your behavior and lifestyle, because there is a reason for something, but what are we now try to install.

So, cause severe energy loss can:

  1. Saving a sense of guilt. Thus, your conscience speaks with you, representing the most strict our judge throughout life. Conscience delivers serious psychological discomfort, because of which energy is squandered.

If you try to drown out the voice of the conscience - face the exact opposite result and even more deterioration of the situation. Externally, this will also appear in the form of a deterioration of the material situation. The most reasonable solution in this case is to find an internal compromise yourself.

  1. Offensealso lead to the energy deficiency. The most popular option is resentment on parents who are likely to be drawn from children's age. If a person and in adult age can not let go of the past and forgive his parents - it will greatly affect the various sides of his life.

What relationships were in your parent family will have their own impact on the model of your own family. And the perennial resentments are negatively affecting people, they contribute to exhaustion, both emotional and energy.

  1. Psychological discomfort, Which provokes energy losses, can be caused by other negative emotions: fear, fear of uncertainty, anxiety, disappointment and spiritual pain.
  2. Envy- Causes a lot of controversy from experts regarding their influence on the human body. One part of the specialists allocates envy, as a motivating emotion, which can accelerate the achievement of success, put on a person specific goals in life.

We listed the main internal causes of energy losses. And there is also an external one, to the number of which relates communication with energy "bloodsuckers", which are bore, whining, idlers, losers, victims and sick, maniacs, as well as ideological wrestlers. Contacting them, you become energetically weaker.

Therefore, it is worth surrounding yourself with positively thoughtful people, try to always be in a good mood, started started in time, not worry about your future (or rather, worrying, but in reasonable limits), to be cleaned from their internal negative emotions (insults, anger, aggression, and so on ) And then your energy field will enhance each day.

In numerous texts on yoga, meditation, and Western mysticism, you can find links to various types of Shakti's strength - a great female energy that exists both inside and outside the body of a person. Shakti supports everything in the universe, from planets on their orbits, to solar radiation.

Shakti is the term used to describe the control force of the cosmos, from its slightest atom to a huge galaxy, gravity forces and the power of light speed. Any type of force or influence comes from Shakti, and ...

Energy is awareness, these are not two different phenomena. What is this energy - awareness? When the energy is free, it becomes awareness. When the energy is captured, it remains ignorance, unconsciousness.

For example, your sexual energy is directed to a woman or man.

It will remain with ignorance, since it is concentrated on the facility; She goes outside, she is an extrovert. And if the energy is released from the object, then where will it go? It will be directed to the subject, in the depths of yours ...

About the exercise of dreams is written hundreds of books and filmed dozens of films. Every year a new bestseller comes out on "How to fulfill your dream" and the author in it tells new ways to achieve success, and for as much as possible.

And now at least two decades of crowd of people read books and watch movies, envy heroes and inspiring examples. And of course, rushing into battle (and who and in the abyss ...) for the sake of carrying out a cherished dream. At the exit (which is no wonder) is formed fruitful ...

Our thoughts and emotions are nothing but the finest form of energy that we generate into the surrounding space. Hate, love, envy, thanks - all this is a certain level of vibrations with some characteristics. Source - esoteric. Live knowledge

Each cell and organ of our body have their own frequency. Everything has its frequency, even our planet is not an exception. It is known that the land "sings" on the chord of the phase-major. By the way, scientists note that its usual "Relicious" - 7 ...

At the same time, what is interesting, becoming more and more enlightened by humanity, does not want to look more closely to look at the cultural heritage, which would seem to be honored not only in words, but also in practice. Take, for example, the Bible is the incredit value of which for worldviews a significant part of the current civilization is hardly someone today will decide to question. As you know, it indicates that after the creation of the first battle in the male bowl - Adam, the creator and ...

Everything in the universe is energy, which means the level of our capabilities directly depends on its level. A person with a small level of energy, to achieve anything in life will be almost impossible.

A person with a huge energy level, it will only be enough to think about something, and it is already implemented.

Thus, magicians can materialize any thing, create a double and much more.

And now there are such strong people, but we do not know them because they do not live among people, and if ...

Chakras are called seven energy centers of the ethereal body located along the spinal column. Indian yogis believe that the vital force they call prana is distributed in the human body at the finest channels - nadi.

It is believed that in the thin body of a person there are about 72,000 nadus.

Chakras are located along the main channel - sushumna, passing along the spine. They are compared with rotating energy wheels, which are absorbed and then convert higher ...

Dear reader.
My task is now to transfer the cosmic doctrine of earthlings. This book is called energy. It will be about energy, its transformations and reincarnations, about the structure of the human essence: souls and body, relations in human society, relations between the Earth and other civilizations, the oceans and the universe. That is how the spirals are developing relationships and relationships. What tasks are facing humanity, what ways can you perform them? These and many other questions ...


All these logos consist of the energy of the highest mind, love and will.

Earth civilization is more interested in the energy of the solar system logo. It is the Logos of the Solar System that organizes and coordinates the activities of all planetary logos. Energy ...