Orbitals exist regardless of whether an electron is on them (occupied orbitals) or absent (vacant orbitals). The atom of every element, starting with hydrogen and ending with the last element obtained to date, has a complete set of all orbitals at all electronic levels. Their filling with electrons occurs as the serial number, that is, the charge of the nucleus, increases.

s- Orbitals, as shown above, have a spherical shape and, therefore, the same electron density in the direction of each axis of three-dimensional coordinates:

The first electronic level of each atom contains only one s- orbital. Starting from the second electronic level, in addition to s- orbitals also appear three R-orbitals. They have the shape of voluminous eights, this is what the area of ​​\u200b\u200bthe most likely location looks like R-electron in the region of the atomic nucleus. Each R-orbital is located along one of three mutually perpendicular axes, in accordance with this in the title R-orbitals indicate, using the corresponding index, the axis along which its maximum electron density is located:

In modern chemistry, an orbital is a defining concept that allows one to consider the processes of formation of chemical bonds and analyze their properties, while attention is focused on the orbitals of those electrons that participate in the formation of chemical bonds, that is, valence electrons, usually these are electrons of the last level.

The carbon atom in its initial state on the second (last) electronic level has two electrons per s-orbitals (marked in blue) and one electron per two R-orbitals (marked in red and yellow), the third orbital - pz-vacant:

Hybridization.

In the case when the carbon atom is involved in the formation of saturated compounds (not containing multiple bonds), one s- orbital and three R-orbitals combine to form new orbitals that are hybrids of the original orbitals (a process called hybridization). The number of hybrid orbitals is always equal to the number of original ones, in this case, four. The resulting hybrid orbitals are identical in shape and outwardly resemble asymmetric volume eights:

The whole structure appears as if inscribed in a regular tetrahedron - a prism assembled from regular triangles. In this case, hybrid orbitals are located along the axes of such a tetrahedron, the angle between any two axes is 109°. The four valence electrons of carbon are located in these hybrid orbitals:

Participation of orbitals in the formation of simple chemical bonds.

The properties of electrons located in four identical orbitals are equivalent, respectively, the chemical bonds formed with the participation of these electrons when interacting with atoms of the same type will be equivalent.

The interaction of a carbon atom with four hydrogen atoms is accompanied by mutual overlapping of elongated hybrid carbon orbitals with spherical hydrogen orbitals. There is one electron in each orbital, as a result of overlapping, each pair of electrons begins to move along the combined - molecular orbital.

Hybridization leads only to a change in the shape of the orbitals within one atom, and the overlapping of the orbitals of two atoms (hybrid or ordinary) leads to the formation of a chemical bond between them. In this case ( cm. the figure below) the maximum electron density is located along the line connecting the two atoms. Such a bond is called an s-bond.

In the traditional spelling of the structure of the resulting methane, the valence bar symbol is used instead of overlapping orbitals. For a three-dimensional image of the structure, the valency directed from the plane of the drawing to the viewer is shown as a solid wedge-shaped line, and the valency that goes beyond the plane of the drawing is shown as a dashed wedge-shaped line:

Thus, the structure of the methane molecule is determined by the geometry of the carbon hybrid orbitals:

The formation of an ethane molecule is similar to the process shown above, the difference is that when the hybrid orbitals of two carbon atoms overlap, a C-C bond is formed:

The geometry of the ethane molecule resembles methane, the bond angles are 109°, which is determined by the spatial arrangement of the carbon hybrid orbitals:

Participation of orbitals in the formation of multiple chemical bonds.

The ethylene molecule is also formed with the participation of hybrid orbitals, however, one s-orbital and only two R-orbitals ( p x and RU), the third orbital is pz, directed along the axis z, does not participate in the formation of hybrids. From the initial three orbitals, three hybrid orbitals arise, which are located in the same plane, forming a three-beam star, the angles between the axes are 120 °:

Two carbon atoms attach four hydrogen atoms, and also connect with each other, forming a C-C s-bond:

two orbitals pz, which did not participate in hybridization, mutually overlap, their geometry is such that overlap occurs not along the C-C bond line, but above and below it. As a result, two regions with increased electron density are formed, where two electrons (marked in blue and red) are placed, participating in the formation of this bond. Thus, one molecular orbital is formed, consisting of two regions separated in space. A bond in which the maximum electron density is located outside the line connecting two atoms is called a p-bond:

The second valence line in the designation of a double bond, which has been widely used to depict unsaturated compounds for more than one century, in the modern sense implies the presence of two regions with increased electron density located on opposite sides of the C-C bond line.

The structure of the ethylene molecule is given by the geometry of hybrid orbitals, the H-C-H bond angle is 120°:

In the formation of acetylene, one s-orbital and one p x-orbital (orbitals py and pz, are not involved in the formation of hybrids). The two resulting hybrid orbitals are located on the same line, along the axis X:

The mutual overlapping of hybrid orbitals with each other and with the orbitals of hydrogen atoms leads to the formation of s-bonds C-C and C-H, depicted using a simple valence line:

Two pairs of remaining orbitals py and pz overlap. In the figure below, the colored arrows show that, from purely spatial considerations, the most likely overlap of orbitals with the same indices x-x and wow. As a result, two p-bonds are formed, surrounding a simple s-bond C-C:

As a result, the acetylene molecule has a rod-shaped form:

In benzene, the backbone of the molecule is assembled from carbon atoms that have hybrid orbitals composed of one s- and two R-orbitals arranged in the form of a three-ray star (like ethylene), R-orbitals not involved in hybridization are shown as translucent:

Vacancies, that is, orbitals not containing electrons (), can also participate in the formation of chemical bonds.

high level orbitals.

Starting from the fourth electronic level, atoms have five d-orbitals, their filling with electrons occurs in transition elements, starting with scandium. Four d-orbitals have the form of voluminous quatrefoils, sometimes called "cloverleaf", they differ only in orientation in space, the fifth d-orbital is a three-dimensional figure eight threaded into a ring:

d Orbitals can form hybrids with s- and p- orbitals. Options d-orbitals are usually used in the analysis of the structure and spectral properties in transition metal complexes.

Starting from the sixth electronic level, atoms have seven f-orbitals, their filling with electrons occurs in the atoms of lanthanides and actinides. f-Orbitals have a rather complex configuration, the figure below shows the shape of three of the seven such orbitals, which have the same shape and are oriented in space in different ways:

f-Orbitals are very rarely used when discussing the properties of various compounds, since the electrons located on them practically do not take part in chemical transformations.

Perspectives.

The eighth electronic level contains nine g-orbitals. Elements containing electrons in these orbitals should appear in the eighth period, while they are not available (element No. 118, the last element of the seventh period of the Periodic System, is expected to be obtained in the near future, its synthesis is carried out at the Joint Institute for Nuclear Research in Dubna).

The form g-orbitals, calculated by the methods of quantum chemistry, is even more complex than that of f-orbitals, the region of the most probable location of the electron in this case looks very bizarre. Below is the appearance of one of the nine such orbitals:

In modern chemistry, the concepts of atomic and molecular orbitals are widely used in describing the structure and reaction properties of compounds, as well as in analyzing the spectra of various molecules, and in some cases, to predict the possibility of reactions.

Mikhail Levitsky

Systems. In this case, the orbital is determined by the one-electron Schrödinger equation with the effective one-electron Hamiltonian; orbital energy is usually correlated with (see ). Depending on system, for a cut the orbital is defined, distinguish atomic, molecular and crystal orbitals.

Atomic orbitals (AO) are characterized by three quantum numbers: principal n, orbital / and magnetic w. The value l = 0, 1, 2,... specifies the square of the orbital (angular) momentum (-Planck constant), the value m = l,l - 1,..., +1, 0, - 1,..., - l + 1, - l-projection of the moment on some chosen axis z; n numbers the orbital energies. States with a given / are numbered by the numbers n = l + 1, l + 2,... coordinate system centered on the AO core has the form , where and-polar angles, r-distance from to the nucleus. R nl (r) the radial part of the AO (radial function), a Y lm (q, j)-spherical. harmonica. When rotating the coordinate system spherical. the harmonic is replaced by a linear combination of harmonics with the same value of l; the radial part of the AO does not change during turns, and the energy corresponding to this AO. the level is (21 + 1)-fold degenerate. Usually - an indicator of the orbital exponent, and Р pl - a polynomial of degree (n - l - 1). In abbreviated notation, AO is described by the symbol nl m, and n is denoted by the numbers 1, 2, 3,..., the values ​​\u200b\u200bof l = 0, 1, 2, 3, 4,... correspond to the letters s, p, d, f, g ,...; m indicate at the bottom right, e.g. 2p +1 , 3d -2 .

More convenient are AO containing non-complex spherical. harmonics, and their linear combinations having . values. Such AOs are called cubic (tesseral). They have the form , where (x, y, z) is a homogeneous polynomial (angular function) of degree l relative to the Cartesian coordinates x, y, z centered on the core (the direction of the axes is arbitrary); AO is denoted by symbols , eg.

If the polynomial P nl (r) is determined by the solution of the Schrödinger equation for in the Coulomb field of the nucleus, AO is called. hydrogen-like. Naib. commonly used hydrogen-like cubes. AO are shown in the table.

HYDROGEN-LIKE ORBITALS s. p, d, f-TYPES

In chem. applications often lead to AO contours, to-rye m. b. built differently. Naib. common so-called. phase surfaces, on which the cubic values ​​are depicted. (or spherical) harmonics: at given polar angles, the modulus of the angular part of the AO is equal to the distance to the origin. On fig. 1 shows other, more illustrative pov-sti, to-ryh abs. the values ​​of some AO have a constant value. Both methods of AR imaging are practically the same only near the origin of coordinates. In all cases, the + and - signs (or shading) indicate which sign the AO has in the given area. Like all wave functions, AO can be multiplied by - 1, which will changefunction sign, however, it is not the signs of AO that have meaning in themselves,and the alternation of signs for the AO system when describing the pier. orbitals. Graphic the AO image doesn't always make sense. Thus, the squares of modules are spherical. the harmonics do not depend on the angle , so the image of, for example, AO 2p x and 2p y will be completely different from the image of AO 2p + and 2p -, although both AO are completely equivalent.

molecular orbitals(MO) describe in the field of all nuclei and the average field of the rest. As a rule, MOs do not have a simple analyte. representations and are used for them (see). In the methods they say. orbitals multi-electron wave function is built as a product or determinant, composed of spin-orbitals, i.e. orbitals multiplied by the spin function or (see ).

where 0 = 0.372, b = 0.602, is the atomic orbital 2p z С i (i=1, 2, 3, 4). The 1-orbital has one nodal plane (xy), the 2-orbital has a complement. nodal plane perpendicular to this plane and passing between

ORBITAL - the region of the most probable location of an electron in an atom (atomic orbital) or in a molecule (molecular orbital).

So far, five types of orbitals have been described: s, p, d, f, and g.
The names of the first three were formed historically, then the alphabetical principle was chosen. Orbital shapes are calculated by quantum chemistry methods.

s-Orbitals - have a spherical shape and the same electron density in the direction of each axis of three-dimensional coordinates
s-orbital - orbital sphere

Each p-orbital is located along one of three mutually perpendicular axes, in accordance with this, in the name of the p-orbital, the axis along which its maximum electron density is located is indicated using the corresponding index:
p-orbital - dumbbell orbital

d-orbital - complex shape orbital

Energy of electronic levels

Quantum numbers of electrons

The state of each electron in an atom is usually described using four quantum numbers:

n - energy level of the electron (remoteness of the level from the nucleus)
l - what type of orbital it moves in (s,p,d...)
m- magnetic (on which of p (out of three possible), d (out of 5 possible), etc.
s - spin (electron movement around its own axis).

Orbital Filling Principles

1. There cannot be two electrons in an atom, for which the values ​​of all quantum numbers (n, l, m, s) would be the same, i.e. Each orbital can contain no more than two electrons (with opposite spins) (Pauli principle).

2. In the ground state, each electron is located so that its energy is minimal.
The energy of the orbitals increases in the series:
1S< 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s < 5d » 4f < 6p < 7s.
There is no need to memorize this sequence. It can be extracted from the Periodic table of D.I. Mendeleev

3. Electrons prefer to settle in orbitals of the same energy (for example, in three p-orbitals), first one by one, and only when there is already one electron in each such orbital, the filling of these orbitals with second electrons begins. When an orbital is populated by two electrons, these electrons are called paired .(Hund's rule)

The full electronic formula of the element

A record that reflects the distribution of electrons in an atom of a chemical element over energy levels and sublevels is called the electronic configuration of this atom. In the ground (unexcited) state of an atom, all electrons satisfy the principle of minimum energy. This means that the sublevels are filled first, for which:

1. The number n is minimal
2. Inside the level, the s-sublevel is first filled, then p- and only then d- (l is minimal)
3. One sublevel contains the largest number of unpaired electrons.
4. When filling electronic atomic orbitals, the Pauli principle is fulfilled. Its consequence is that the energy level with number n can have no more than 2n2 electrons located on n2 sublevels.

The electronic formula of the element with the serial number 7 (this is the element nitrogen, which has the symbol “N”) looks like this.

Electronic configuration an atom is a numerical representation of its electron orbitals. Electron orbitals are regions of various shapes located around the atomic nucleus, in which it is mathematically probable that an electron will be found. The electronic configuration helps to quickly and easily tell the reader how many electron orbitals an atom has, as well as determine the number of electrons in each orbital. After reading this article, you will master the method of compiling electronic configurations.

Steps

Distribution of electrons using the periodic system of D. I. Mendeleev

Find the atomic number of your atom. Each atom has a certain number of electrons associated with it. Find the symbol for your atom in the periodic table. The atomic number is a positive integer starting from 1 (for hydrogen) and increasing by one for each subsequent atom. The atomic number is the number of protons in an atom, and therefore it is also the number of electrons in an atom with zero charge.

Determine the charge of an atom. Neutral atoms will have the same number of electrons as shown in the periodic table. However, charged atoms will have more or fewer electrons, depending on the magnitude of their charge. If you are working with a charged atom, add or subtract electrons as follows: add one electron for every negative charge and subtract one for every positive charge.

• For example, a sodium atom with a charge of -1 will have an extra electron in addition to its base atomic number of 11. In other words, an atom will have 12 electrons in total.
• If we are talking about a sodium atom with a charge of +1, one electron must be subtracted from the base atomic number 11. So the atom will have 10 electrons.

1. Memorize the basic list of orbitals. As the number of electrons increases in an atom, they fill the various sublevels of the electron shell of the atom according to a certain sequence. Each sublevel of the electron shell, when filled, contains an even number of electrons. There are the following sublevels:

   Understand the electronic configuration record. Electronic configurations are written down in order to clearly reflect the number of electrons in each orbital. Orbitals are written sequentially, with the number of atoms in each orbital written as a superscript to the right of the orbital name. The completed electronic configuration has the form of a sequence of sublevel designations and superscripts.

   • Here, for example, is the simplest electronic configuration: 1s 2 2s 2 2p 6 . This configuration shows that there are two electrons in the 1s sublevel, two electrons in the 2s sublevel, and six electrons in the 2p sublevel. 2 + 2 + 6 = 10 electrons in total. This is the electronic configuration of the neutral neon atom (neon atomic number is 10).

2. Remember the order of the orbitals. Keep in mind that electron orbitals are numbered in ascending order of electron shell number, but arranged in ascending energy order. For example, a filled 4s 2 orbital has less energy (or less mobility) than a partially filled or filled 3d 10, so the 4s orbital is written first. Once you know the order of the orbitals, you can easily fill them in according to the number of electrons in the atom. The order in which the orbitals are filled is as follows: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p.

   • The electronic configuration of an atom in which all orbitals are filled will have the following form: 10 7p 6
   • Note that the above notation, when all orbits are filled, is the electron configuration of the element Uuo (ununoctium) 118, the highest numbered atom in the Periodic Table. Therefore, this electronic configuration contains all currently known electronic sublevels of a neutrally charged atom.

3. Fill in the orbitals according to the number of electrons in your atom. For example, if we want to write down the electronic configuration of a neutral calcium atom, we must start by looking up its atomic number in the periodic table. Its atomic number is 20, so we will write the configuration of an atom with 20 electrons according to the above order.

   • Fill in the orbitals in the above order until you reach the twentieth electron. The first 1s orbital will have two electrons, the 2s orbital will also have two, the 2p orbital will have six, the 3s orbital will have two, the 3p orbital will have 6, and the 4s orbital will have 2 (2 + 2 + 6 +2 +6 + 2 = 20 .) In other words, the electronic configuration of calcium has the form: 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 .
   • Note that the orbitals are in ascending order of energy. For example, when you are ready to move to the 4th energy level, then first write down the 4s orbital, and then 3d. After the fourth energy level, you move on to the fifth, where the same order is repeated. This happens only after the third energy level.

4. Use the periodic table as a visual cue. You have probably already noticed that the shape of the periodic table corresponds to the order of electronic sublevels in electronic configurations. For example, atoms in the second column from the left always end in "s 2 ", while atoms on the right edge of the thin middle section always end in "d 10 ", and so on. Use the periodic table as a visual guide to writing configurations - as the order in which you add to the orbitals corresponds to your position in the table. See below:

   • In particular, the two leftmost columns contain atoms whose electronic configurations end in s orbitals, the right block of the table contains atoms whose configurations end in p orbitals, and at the bottom of the atoms end in f orbitals.
   • For example, when you write down the electronic configuration of chlorine, think like this: "This atom is located in the third row (or "period") of the periodic table. It is also located in the fifth group of the orbital block p of the periodic table. Therefore, its electronic configuration will end in. ..3p 5
   • Note that the elements in the d and f orbital regions of the table have energy levels that do not correspond to the period in which they are located. For example, the first row of a block of elements with d-orbitals corresponds to 3d orbitals, although it is located in the 4th period, and the first row of elements with f-orbitals corresponds to the 4f orbital, despite the fact that it is located in the 6th period.

5. Learn the abbreviations for writing long electronic configurations. The atoms on the right side of the periodic table are called noble gases. These elements are chemically very stable. To shorten the process of writing long electron configurations, simply write in square brackets the chemical symbol for the nearest noble gas with fewer electrons than your atom, and then continue to write the electronic configuration of subsequent orbital levels. See below:

   • To understand this concept, it will be helpful to write an example configuration. Let's write the configuration of zinc (atomic number 30) using the noble gas abbreviation. The full zinc configuration looks like this: 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 . However, we see that 1s 2 2s 2 2p 6 3s 2 3p 6 is the electronic configuration of argon, a noble gas. Simply replace the electronic configuration part of zinc with the chemical symbol for argon in square brackets (.)
   • So, the electronic configuration of zinc, written in abbreviated form, is: 4s 2 3d 10 .
   • Note that if you are writing the electronic configuration of a noble gas, say argon, you cannot write! One must use the abbreviation of the noble gas in front of this element; for argon it will be neon ().

   Using ADOMAH Periodic Table

   1. Master the ADOMAH periodic table. This method of recording the electronic configuration does not require memorization, however, it requires a modified periodic table, since in the traditional periodic table, starting from the fourth period, the period number does not correspond to the electron shell. Find the ADOMAH periodic table, a special type of periodic table designed by scientist Valery Zimmerman. It is easy to find with a short internet search.

      • In the ADOMAH periodic table, the horizontal rows represent groups of elements such as halogens, noble gases, alkali metals, alkaline earth metals, etc. Vertical columns correspond to electronic levels, and so-called "cascades" (diagonal lines connecting blocks s, p, d and f) correspond to periods.
      • Helium is moved to hydrogen, since both of these elements are characterized by a 1s orbital. The period blocks (s,p,d and f) are shown on the right side and the level numbers are given at the bottom. Elements are represented in boxes numbered from 1 to 120. These numbers are the usual atomic numbers, which represent the total number of electrons in a neutral atom.

   2. Find your atom in the ADOMAH table. To write down the electronic configuration of an element, find its symbol in the ADOMAH periodic table and cross out all elements with a higher atomic number. For example, if you need to write down the electronic configuration of erbium (68), cross out all the elements from 69 to 120.

      • Pay attention to the numbers from 1 to 8 at the base of the table. These are the electronic level numbers, or column numbers. Ignore columns that contain only crossed out items. For erbium, columns with numbers 1,2,3,4,5 and 6 remain.

   3. Count the orbital sublevels up to your element. Looking at the block symbols shown to the right of the table (s, p, d, and f) and the column numbers shown at the bottom, ignore the diagonal lines between the blocks and break the columns into block-columns, listing them in order from bottom to top. And again, ignore the blocks in which all the elements are crossed out. Write the column blocks starting from the column number followed by the block symbol, thus: 1s 2s 2p 3s 3p 3d 4s 4p 4d 4f 5s 5p 6s (for erbium).

      • Please note: The above electronic configuration Er is written in ascending order of the electronic sublevel number. It can also be written in the order in which the orbitals are filled. To do this, follow the cascades from bottom to top, not columns, when you write column blocks: 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 4p 6 5s 2 4d 10 5p 6 6s 2 4f 12 .

   4. Count the electrons for each electronic sublevel. Count the elements in each column block that have not been crossed out by attaching one electron from each element, and write their number next to the block symbol for each column block as follows: 1s 2 2s 2 2p 6 3s 2 3p 6 3d 10 4s 2 4p 6 4d 10 4f 12 5s 2 5p 6 6s 2 . In our example, this is the electronic configuration of erbium.

   5. Be aware of incorrect electronic configurations. There are eighteen typical exceptions related to the electronic configurations of atoms in the lowest energy state, also called the ground energy state. They do not obey the general rule only in the last two or three positions occupied by electrons. In this case, the actual electronic configuration assumes that the electrons are in a state of lower energy compared to the standard configuration of the atom. Exception atoms include:

      • Cr(..., 3d5, 4s1); Cu(..., 3d10, 4s1); Nb(..., 4d4, 5s1); Mo(..., 4d5, 5s1); Ru(..., 4d7, 5s1); Rh(..., 4d8, 5s1); Pd(..., 4d10, 5s0); Ag(..., 4d10, 5s1); La(..., 5d1, 6s2); Ce(..., 4f1, 5d1, 6s2); Gd(..., 4f7, 5d1, 6s2); Au(..., 5d10, 6s1); AC(..., 6d1, 7s2); Th(..., 6d2, 7s2); Pa(..., 5f2, 6d1, 7s2); U(..., 5f3, 6d1, 7s2); Np(..., 5f4, 6d1, 7s2) and cm(..., 5f7, 6d1, 7s2).
      • To find the atomic number of an atom when it is written in electronic form, simply add up all the numbers that follow the letters (s, p, d, and f). This only works for neutral atoms, if you are dealing with an ion, then nothing will work - you will have to add or subtract the number of extra or lost electrons.
      • The number following the letter is a superscript, do not make a mistake in the control.
      • The "stability of a half-filled" sublevel does not exist. This is a simplification. Any stability that pertains to "half-full" sublevels is due to the fact that each orbital is occupied by one electron, so repulsion between electrons is minimized.
      • Each atom tends to a stable state, and the most stable configurations have filled sublevels s and p (s2 and p6). Noble gases have this configuration, so they rarely react and are located on the right in the periodic table. Therefore, if a configuration ends in 3p 4 , then it needs two electrons to reach a stable state (it takes more energy to lose six, including s-level electrons, so four is easier to lose). And if the configuration ends in 4d 3 , then it needs to lose three electrons to reach a stable state. In addition, half-filled sublevels (s1, p3, d5..) are more stable than, for example, p4 or p2; however, s2 and p6 will be even more stable.
      • When you're dealing with an ion, that means the number of protons is not the same as the number of electrons. The charge of the atom in this case will be shown at the top right (usually) of the chemical symbol. Therefore, an antimony atom with a charge of +2 has the electronic configuration 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 4p 6 5s 2 4d 10 5p 1 . Note that 5p 3 has changed to 5p 1 . Be careful when the configuration of a neutral atom ends at sublevels other than s and p. When you take electrons, you can only take them from valence orbitals (s and p orbitals). Therefore, if the configuration ends with 4s 2 3d 7 and the atom gets +2 charge, then the configuration will end with 4s 0 3d 7 . Please note that 3d 7 not changes, instead electrons of the s-orbital are lost.
      • There are conditions when an electron is forced to "move to a higher energy level." When a sublevel lacks one electron to be half or full, take one electron from the nearest s or p sublevel and move it to the sublevel that needs an electron.
      • There are two options for writing an electronic configuration. They can be written in ascending order of the numbers of energy levels or in the order in which the electron orbitals are filled, as was shown above for erbium.
      • You can also write the electronic configuration of an element by writing only the valence configuration, which is the last s and p sublevel. Thus, the valence configuration of antimony will be 5s 2 5p 3 .
      • Ions are not the same. It's much more difficult with them. Skip two levels and follow the same pattern depending on where you started and how high the number of electrons is.

After the completion of the formal description of quantum mechanical motion, it became clear that in atomic space each object has such a characteristic as an atomic orbital.

atomic orbital(AO) - the region of space around the nucleus of an atom, in which, according to the laws of quantum mechanics, an electron with a given energy is most likely to be located.

The energy state of an electron is described by a function of three integer parameters n ) I, m 1Y which are called quantum numbers. For certain values ​​of quantum numbers, it is possible to obtain characteristics of the region where an electron can be located.

Quantum numbers have the following physical meaning:

• n is the principal quantum number, characterizes the energy level and size of the orbital;
• / - orbital quantum number, characterizes the energy sublevel and the shape of the orbital;
• m ( - magnetic quantum number, takes into account the influence of the external magnetic field on the energy state of the electron.

Principal quantum number n is natural and corresponds to the numbers of periods in the table of D. I. Mendeleev (1, 2, 3, 4, 5, 6, 7). The principal quantum number determines the main fraction of the energy of an electron in a given orbital. This quantum number is also called energy level number. The more P, the larger the size of the orbital.

Atoms in which electrons are in orbitals with a large value n(n> 8) are called Rydberg atoms. The first experimental data on Rydberg atoms in radio astronomy were obtained in 1964 by FIAP staff (RS Sorochenko et al.) on a 22-meter mirror radio telescope. When the telescope was oriented towards the Omega Nebula, in the spectrum of its radio emission, an emission line with a wavelength X= 3.4 cm. This wavelength corresponds to the transition between the Rydberg states n = 90 and n = 91 in the spectrum of the hydrogen atom. Today, Rydberg atoms have been obtained in the laboratory with P~ 600! These are almost macroscopic objects with a size of about 0.1 mm and a lifetime of ~1 s. The study of the Rydberg states of atoms turned out to be useful in the work on the creation of quantum computers.

In this case, an increase in size does not change the shape of the orbital. The more p y the greater the energy of the electron. Electrons with the same value of the principal quantum number are on the same energy level. Number P energy level indicates the number of sublevels that make up this level.

Orbital quantum number I can take values ​​/ = 0, 1,2,... up to (P - 1), i.e. for a given principal quantum number P orbital quantum number / can take P values. The orbital quantum number determines the geometric shape of the orbitals and determines the orbital angular momentum (momentum) of the electron, i.e. the contribution of a given sublevel to the total electron energy. In addition to numerical values, the orbital quantum number / also has a letter designation:

Forms 5-, p-, (1-,/-orbitals are shown in fig. 1.1. The signs on the geometric elements of the orbitals are not charge signs, but refer to the values ​​of the wave function y for these elements. Since the calculation of the probability is considered | n/| 2 is the square of the magnitude modulo, then the regions of the orbitals of the wave function y with the signs "+" and "-" become equivalent.

Rice. 1.1.

The complex shape of most orbitals is due to the fact that the wave function of an electron in polar coordinates has two components - radial and angular. In this case, the probability of finding an electron at a given point depends both on its distance from the nucleus and on the direction in space of the vector connecting the nucleus with this point. These functions depend both on / (for 5- and p-orbitals) and on t 1 (for c1- and /-orbitals).

For example, the outline (outer contour) of all 5-orbitals is a sphere. But it turns out that the probability of finding an electron inside this sphere is not uniform, but directly depends on the distance of the given orbital from the nucleus. On fig. 1.2 shows the internal structure of the 15 and 25 orbitals. As follows from the figure, the 25-orbital is similar to a "two-layer onion" with inner shells located at a distance of 1 and 4 Bohr orbital radii. As a rule, in chemistry, the fact of the complexity of the internal structure of orbitals does not play a significant role and is not considered in this course.

Rice. 1.2. The distribution of the probability of finding an electron in a hydrogen atom in the statesisand2s. G (\u003d 5.29 * 10 11 m - radius of the first Bohr orbit

Source: wvw.college.ru/enportal/physics/content/chapter9/section/paragraph3/theory.html

Orbital magnetic quantum number m t can take values ​​from -/ to +/, including zero. This quantum number determines orientation of the orbital in space under the influence of an external magnetic field and characterizes the change in the energy of an electron located in this orbital under the influence of an external magnetic field. Number of orbitals with a given value t 1 is (2/ + 1).

Three quantum numbers considered P, /, t ( are a consequence of solving the Schrödinger wave equation and make it possible to determine the energy of an electron through a description of its wave properties. At the same time, the dual nature of the nature of elementary particles, their corpuscular-wave dualism in the description of the energy state of the electron was not taken into account.

Own magnetic quantum number of electron m s (spin). How a consequence of the corpuscular properties of the electron, another number plays a role in the description of its energy state - own quantum number m s of the electron (spin). This quantum number characterizes not the orbital, but the property of the electron itself, located in this orbital.

Spin (from English, spin- rotate [-sya], rotation) - the intrinsic angular momentum of elementary particles, which has a quantum nature and is not associated with the movement of the particle as a whole. The often used analogy to describe the spin as a property associated with the rotation of an electron around its axis turned out to be untenable. Such a description leads to a contradiction with the special theory of relativity - the equatorial speed of rotation of an electron in this model exceeds the speed of light. The introduction of the spin was a successful application of a new physical idea: it is postulated that there is a space of states that have nothing to do with the movement of a particle in ordinary space. The need to introduce such a space of states indicates the need to consider a more general question about the reality of the physical many worlds.

The electron shows its own magnetic properties in that in an external electric field, the intrinsic angular momentum of the electron is oriented either along the field or against zero. In the first case, it is assumed that the electron's own quantum number m s= +1/2, and in the second m s= -1/2. Note that the spin single fractional number among a set of quantum characteristics that determine the state of an electron in an atom.