The distribution is characterized by the following rules:

the Pauli principle;

Gund's rule;

the principle of least energy and the Klechkovsky rule.

By Pauli principle An atom cannot have two or more electrons with the same value of all four quantum numbers. Based on the Pauli principle, you can set the maximum capacity of each energy level and sublevel.

	Sublevel, ℓ	Sublevel designation	Magnetic quantum number, m	Spin quantum number,s
			3, -2, -1, 0, 1, 2, 3

Thus, maximum number of electrons per:

s -sublevel - 2,

p - sublevel - 6,

d -sublevel - 10,

f -sublevel - 14.

Within the quantum level n, an electron can take on the values ​​of 2n 2 different states, which was established empirically using spectral analysis.

Gund's rule : in each sublevel, electrons tend to occupy the maximum number of free energy cells so that the total spin has the greatest value.

For example:

right wrong wrong

3r 3:

s = +1/2+1/2+1/2=1.5 s =-1/2+1/2+1/2=0.5 s = -1/2+1/2-1/2 =-0.5

The principle of least energy and the Klechkovsky rule: electrons primarily populate quantum orbitals with minimum energy. Since the energy reserve in an atom is determined by the value of the sum of the main and orbital quantum numbers (n + ℓ), the electrons first populate the orbitals for which the sum (n + ℓ) is the smallest.

For example: the sum (n + ℓ) for the 3d sublevel is n = 3, l = 2, hence (n + ℓ) = 5; for the 4s sublevel: n = 4, ℓ = 0, hence (n + ℓ ) = 4. In this case, the 4s sublevel is filled first and only then the 3d sublevel.

If the total energy values ​​are equal, then the level that is closer to the nucleus is populated.

For example: for 3d: n=3, ℓ=2 , (n + ℓ) = 5 ;

for 4p: n = 4, ℓ = 1, (n + ℓ) = 5.

Since n = 3 < n = 4, 3d will be populated with electrons earlier than 4 p.

Thus, the sequence of filling levels and sublevels with electrons in atoms:

1 s 2 <2 s 2 <2 p 6 <3 s 2 <3 p 6 <4 s 2 <3 d 10 <4 p 6 <5 s 2 <4 d 10 <5 p 6 <6 s 2 <5 d 10 ≈ 4 f 14 <6 p 6 <7s 2 …..

Electronic formulas

An electronic formula is a graphic representation of the distribution of electrons over levels and sublevels in an atom. There are two types of formulas:

when writing, only two quantum numbers are used: n and ℓ. The main quantum number is indicated by a number before the letter designation of the sublevel. The orbital quantum number is indicated by the letter s, p, d, or f. The number of electrons is indicated by a number as an exponent.

For example: +1 H: 1s 1 ; +4 Be: 1s 2 2s 2 ;

2 He: 1s 2 ; +10 Ne: 1s 2 2s 2 2p 6 ;

3 Li: 1s 2 2s 1 ; +14 Si: 1s 2 2s 2 2p 6 3s 2 3p 6 .

That is, the sequence

1 s 2 <2 s 2 <2 p 6 <3 s 2 <3 p 6 <4 s 2 <3 d 10 <4 p 6 <5 s 2 <4 d 10 <5 p 6 <6 s 2 <5 d 10 ≈ 4 f 14 <6 p 6 <7s 2 …..

graphic electronic formula - all 4 quantum numbers are used - this is the distribution of electrons in quantum cells. The main quantum number is depicted on the left, the orbital - at the bottom with a letter, the magnetic - the number of cells, the spin - the direction of the arrows.

For example:

8 O:…2s 2 2p 4

The graphical formula is used to write only valence electrons.

Consider the compilation of electronic formulas for elements by periods.

The I period contains 2 elements, in which the I quantum level and the s-sublevel are completely populated with electrons (the maximum number of electrons per sublevel is 2):

2 He: n=1 1s 2

Elements in which the s-sublevel is filled last are assigned to s -family and call s -elements .

The elements of the II period are filling the II quantum level, the s- and p-sublevels (the maximum number of electrons in the p-sublevel is 8).

3 Li: 1s 2 2s 1 ; 4 Be: 1s 2 2s 2 ;

5 B: 1s 2 2s 2 2p 1 ; 10 Ne: 1s 2 2s 2 2p 6

Elements in which the p-sublevel is filled last are assigned to p-family and call p-elements .

The elements of the III period begin to form the III quantum level. Na and Mg are populating the 3s sublevel with electrons. For elements from 13 Al to 18 Ar, the 3p sublevel is populated; The 3d sublevel remains empty, since it has a higher energy level than the 4s sublevel and is not filled for the elements of period III.

The 3d-sublevel begins to be filled at the elements of the IV period, and 4d - at the elements of the V period (in accordance with the sequence):

19 K: 1s 2 2s 2 2p 6 3s 2 3p 6 4s 1 ; 20 Ca: 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 ;

21 Sc: 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 1 ; 25 Mn: 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 5 ;

33 As: 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 4p3; 43 Tc: 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 4p6 5s 2 4d 5

Elements in which the d-sublevel is filled last are assigned to d -family and call d -elements .

4f is filled in only after the 57th element of the VI period:

57 La: 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 4p 5 5s 2 4d 10 5p 6 6s 2 5d 1 ;

58 Ce: 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 4p 5 5s 2 4d 10 5p 6 6s 2 5d 1 4f 1 ;

The population of the V quantum level by electrons proceeds similarly to period IV. Thus, the previously shown sequence of population of levels and sublevels by electrons is observed:

6s 2 5d 10 4f 14 6p 6

the population of a new quantum level by electrons always starts from the s-sublevel. For elements of a given period, only the s and p sublevels of the outer quantum level are populated by electrons;

the population of the d-sublevel is delayed by period I; 3d-sublevel is filled in for elements of period IV, 4d - sublevel for elements of period V, etc.;

the electron population f of the sublevel is delayed by 2 periods; The 4f-sublevel is populated by the elements of period VI, the 5f sublevel is populated by elements of period VII, and so on.

Periodic system of elements of Mendeleev.

Periodic system of chemical elements (periodic table) - classification of chemical elements, establishing the dependence of various properties of elements on the charge of the atomic nucleus.

Groups

A group, or family, is one of the columns in the periodic table. Groups, as a rule, are characterized by more pronounced periodic trends than periods or blocks.

In accordance with the international naming system, groups are assigned numbers from 1 to 18 in the direction from left to right - from alkali metals to noble gases.

Periods

Period - a row in the periodic table. Within a period, the elements show certain patterns in all three of the above aspects (atomic radius, ionization energy and electronegativity), as well as in the energy of electron affinity.

Blocks

In view of the importance of the outer electron shell of an atom, various regions of the periodic table are sometimes described as blocks, named according to which shell the last electron is in. The S-block includes the first two groups, that is, the alkali and alkaline earth metals, as well as hydrogen and helium; The p-block consists of the last six groups (13 to 18 according to the IUPAC naming standard, or IIIA to VIIIA according to the American system) and includes, among other elements, all metalloids. D-block - these are groups from 3 to 12 (IUPAC), they are also from IIIB to IIB in American style, which include all transition metals. The F-block, which is usually taken out of the table, consists of lanthanides and actinides.

The periodic system of D. I. Mendeleev has become an important milestone in the development of atomic and molecular science. Thanks to her, a modern concept of a chemical element was formed, ideas about simple substances and compounds were clarified.

Composition and characteristics of the atomic nucleus.

Atomic nucleus- the central part of the atom, in which its main mass is concentrated (more than 99.9%). The nucleus is positively charged, the charge of the nucleus determines the chemical element to which the atom is assigned.

The atomic nucleus consists of nucleons - positively charged protons and neutral neutrons, which are interconnected by means of a strong interaction.

The atomic nucleus, considered as a class of particles with a certain number of protons and neutrons, is commonly called nuclide.

The number of protons in the nucleus is called its charge number - this number is equal to the ordinal number of the element to which the atom belongs, in the table (Periodic system of elements) of Mendeleev. The number of protons in the nucleus determines the structure of the electron shell of a neutral atom and thus the chemical properties of the corresponding element. The number of neutrons in a nucleus is called its isotopic number. Nuclei with the same number of protons and different numbers of neutrons are called isotopes. Nuclei with the same number of neutrons but different numbers of protons are called isotones.

The total number of nucleons in a nucleus is called its mass number () and is approximately equal to the average mass of an atom, indicated in the periodic table. Nuclides with the same mass number but different proton-neutron composition are called isobars.

Weight

Due to the difference in the number of neutrons, the isotopes of an element have different masses, which is an important characteristic of the nucleus. In nuclear physics, the mass of nuclei is usually measured in atomic mass units ( a. eat.), for one a. e. m. take 1/12 of the mass of the nuclide 12 C [sn 2] . It should be noted that the standard mass that is usually given for a nuclide is the mass of a neutral atom. To determine the mass of the nucleus, it is necessary to subtract the sum of the masses of all electrons from the mass of the atom (a more accurate value will be obtained if we also take into account the binding energy of electrons with the nucleus).

In addition, the energy equivalent of mass is often used in nuclear physics. According to the Einstein relation, each mass value corresponds to the total energy:

Where is the speed of light in vacuum.

The ratio between a. e.m. and its energy equivalent in joules:

and since 1 electron volt \u003d 1.602176 10 −19 J, then the energy equivalent of a. e. m. to MeV is equal to

Radius

An analysis of the decay of heavy nuclei refined Rutherford's estimate [SN 3] and related the radius of the nucleus to the mass number by a simple relationship:

where is a constant.

Since the radius of the nucleus is not a purely geometric characteristic and is primarily associated with the radius of action of nuclear forces, the value depends on the process, during the analysis of which the value was obtained, the average value of m, thus the radius of the nucleus in meters

Charge

The number of protons in the nucleus directly determines its electric charge, isotopes have the same number of protons, but a different number of neutrons. .

The charges of atomic nuclei were first determined by Henry Moseley in 1913. The scientist interpreted his experimental observations by the dependence of the X-ray wavelength on a certain constant , changing by one from element to element and equal to one for hydrogen:

, where

And - permanent.

Binding energy of nuclei.

The binding energy of the nucleus is equal to the minimum energy that must be expended for the complete splitting of the nucleus into individual particles. It follows from the law of conservation of energy that the binding energy is equal to the energy that is released during the formation of a nucleus from individual particles.

The binding energy of any nucleus can be determined by accurately measuring its mass. At present, physicists have learned to measure the masses of particles - electrons, protons, neutrons, nuclei, etc. - with very high accuracy. These measurements show that the mass of any nucleus M i is always less than the sum of the masses of its constituent protons and neutrons:

This energy is released during the formation of the nucleus in the form of radiation of γ-quanta.

Nuclear forces.

nuclear forces are short-range forces. They appear only at very small distances between nucleons in the nucleus of the order of 10–15 m. The length (1.5–2.2) 10–15 m is called range of nuclear forces.

Nuclear forces discover charge independence : the attraction between two nucleons is the same regardless of the charge state of the nucleons - proton or neutron. The charge independence of nuclear forces is seen from a comparison of the binding energies mirror nuclei . What are the nuclei called?,in which the total number of nucleons is the same,but the number of protons in one is equal to the number of neutrons in the other.

Nuclear forces have saturation property , which manifests itself in, that a nucleon in a nucleus interacts only with a limited number of neighboring nucleons closest to it. That is why there is a linear dependence of the binding energies of nuclei on their mass numbers A. Almost complete saturation of nuclear forces is achieved in the α-particle, which is a very stable formation.

Nuclear forces depend on spin orientations interacting nucleons. This is confirmed by the different character of neutron scattering by ortho- and para-hydrogen molecules. In the orthohydrogen molecule, the spins of both protons are parallel to each other, while in the parahydrogen molecule they are antiparallel. Experiments have shown that the scattering of neutrons by parahydrogen is 30 times greater than the scattering by orthohydrogen. Nuclear forces are not central.

So let's list general properties of nuclear forces :

short range of nuclear forces ( R~ 1 fm);

large nuclear potential U~ 50 MeV;

· dependence of nuclear forces on spins of interacting particles;

· tensor character of interaction of nucleons;

· nuclear forces depend on the mutual orientation of the spin and orbital moments of the nucleon (spin-orbit forces);

nuclear interaction has the property of saturation;

charge independence of nuclear forces;

exchange character of nuclear interaction;

attraction between nucleons at large distances ( r> 1 fm), is replaced by repulsion at small ( r < 0,5 Фм).

Since the nuclei of reacting atoms remain unchanged during chemical reactions, the chemical properties of atoms depend primarily on the structure of the electron shells of atoms. Therefore, we will dwell in more detail on the distribution of electrons in an atom, and mainly on those that determine the chemical properties of atoms (the so-called valence electrons), and, consequently, the periodicity in the properties of atoms and their compounds. We already know that the state of electrons can be described by a set of four quantum numbers, but to explain the structure of the electron shells of atoms, you need to know the following three main provisions: 1) the Pauli principle, 2) the principle of least energy, and 3) hit Hund. Pauli principle. In 1925, the Swiss physicist W. Pauli established a rule later called the Pauli principle (or the Pauli exclusion): there can be two electrons in the atom ve that have the same properties. Knowing that the properties of electrons are characterized by quantum numbers, the Pauli principle can also be formulated in this way: there cannot be two electrons in an atom, in which all four quantum numbers would be the same. At least one of the quantum numbers l, /, mt or m3 must necessarily differ. So, electrons with the same quantum - In what follows, we agree to graphically denote electrons having the values ​​s = + lj2> by the arrow T, and those having the values ​​J- ~ lj2 - by the arrow Two electrons having the same spins are often called electrons with parallel spins and are denoted by ft (or C). Two electrons having opposite spins are called electrons with aptiparallel spins and are denoted by | The J-th numbers l, I and mt must necessarily differ in spins. Therefore, in an atom there can be only two electrons with the same n, / and m, one with m = -1/2, the other with m = + 1/2. On the contrary, if the spins of two electrons are the same, one of the quantum numbers must differ: n, / or mh n= 1. Then /=0, mt-0 and t can have an arbitrary value: +1/2 or -1/2. We see that if n - 1, there can be only two such electrons. In the general case, for any given value of n, electrons primarily differ in the side quantum number /, which takes values ​​from 0 to n-1. For given li/ there can be (2/+1) electrons with different values ​​of the magnetic quantum number m. This number must be doubled, since the given values ​​of l, /, and m( correspond to two different values ​​of the spin projection mx. Consequently, the maximum number of electrons with the same quantum number l is expressed by the sum. From this it is clear why there can be no more than 2 electrons on the first energy level, 8 on the second, 18 on the third, etc. Consider, for example, the hydrogen atom iH. There is one electron in the iH hydrogen atom, and the spin of this electron can be directed arbitrarily (i.e. ms ^ + ij2 or mt = -1 / 2), and the electron is in the s-co state at the first energy level with l- 1 (Recall once again that the first energy level consists of one sublevel - 15, the second energy level - of two sublevels - 2s and 2p, the third - of three sublevels - 3 *, Zru 3d, etc.). The sublevel, in turn, is divided into quantum cells * (energy states determined by the number of possible values ​​\u200b\u200bof m (, i.e. 2 / 4-1). It is customary to graphically represent a cell as a rectangle, the direction of the electron spin is arrows. Therefore, the state of an electron in an atom hydrogen iH can be represented as Ijt1, or, what is the same, By “quantum cell” you mean * an orbital characterized by the same set of values ​​of quantum numbers n, I and m * in each cell a maximum of two electrons with ayati-parallel spins can be placed, which is denoted by ti - The distribution of electrons in atoms In the helium atom 2He, the quantum numbers n-1, / \u003d 0 and m (-0) are the same for both of its electrons, and the quantum number m3 is different. Helium electron spin projections can be mt \u003d + V2 and ms \u003d - V2 The structure of the electron shell of the helium atom 2He can be represented as Is-2 or, which is the same, 1S AND Let us depict the structure of the electron shells of five atoms of the elements of the second period of the periodic table: The electron shells 6C, 7N, and VO must be filled in exactly this way, it is not obvious in advance. The given arrangement of spins is determined by the so-called Hund's rule (first formulated in 1927 by the German physicist F. Gund). Gund's rule. For a given value of I (i.e., within a certain sublevel), the electrons are arranged in such a way that the total hundred * is maximum. If, for example, it is necessary to distribute three electrons in three / ^-cells of the nitrogen atom, then they will each be located in a separate cell, i.e., placed on three different p-orbitals: In this case, the total spin is 3/2, since its projection is m3 - 4-1/2 + A/2 + 1/2 = 3/2 * The same three electrons cannot be arranged in this way: 2p NI because then the projection of the total spin is mm = + 1/2 - 1/2+ + 1/2=1/2. For this reason, exactly as above, the electrons are located in the atoms of carbon, nitrogen and oxygen. Let us further consider the electronic configurations of atoms of the next third period. Starting from sodium uNa, the third energy level with the main quantum number n-3 is filled. The atoms of the first eight elements of the third period have the following electronic configurations: Consider now the electronic configuration of the first atom of the fourth period of potassium 19K. The first 18 electrons fill the following orbitals: ls12s22p63s23p6. Seemingly; that the nineteenth electron of the potassium atom must fall on the 3d sublevel, which corresponds to n = 3 and 1=2. However, in fact, the valence electron of the potassium atom is located in the 4s orbital. Further filling of the shells after the 18th element does not occur in the same sequence as in the first two periods. Electrons in atoms are arranged in accordance with the Pauli principle and Hund's rule, but in such a way that their energy is the smallest. The principle of least energy (the greatest contribution to the development of this principle was made by the domestic scientist V. M. Klechkovsky) - in an atom, each electron is located so that its energy is minimal (which corresponds to its greatest connection with the nucleus). The energy of an electron is mainly determined by the main quantum number n and the side quantum number /, therefore, those sublevels for which the sum of the values ​​of quantum numbers pi / is the smallest are filled first. For example, the energy of an electron at the 4s sublevel is less than at the 3d sublevel, since in the first case n+/=4+0=4, and in the second n+/=3+2= 5; at sublevel 5* (n+ /=5+0=5) the energy is less than at Ad (l + /=4+ 4-2=6); by 5p (n+/=5 +1 = 6) the energy is less than by 4/(l-f/= =4+3=7), etc. It was V. M. Klechkovsky who first in 1961 formulated a general proposition that an electron in the ground state occupies a level not with the minimum possible value of n, but with the smallest value of the sum n + / « In the case when the sums of the values ​​of pi / are equal for two sublevels, the sublevel with a lower value n. For example, at the sublevels 3d, Ap, 5s, the sum of the values ​​of pi/ is equal to 5. In this case, the sublevels with smaller values ​​of n are first filled, i.e., 3dAp-5s, etc. In Mendeleev’s periodic system of elements, the sequence of filling with electrons levels and sublevels is as follows (Fig. 2.4). Distribution of electrons in atoms. Scheme of filling energy levels and sublevels with electrons Therefore, according to the principle of least energy, in many cases it is energetically more profitable for an electron to occupy the sublevel of the “overlying” level, although the sublevel of the “lower” level is not filled: That is why in the fourth period the sublevel 4s is filled first and only after that the sublevel 3d .

Each atomic orbital corresponds to a certain energy. The order of the AO in energy is determined by two Klechkovsky rules:

1) the energy of an electron is mainly determined by the values ​​of the principal (n) and orbital ( l) quantum numbers, so first the electrons fill those sublevels for which the sum (n + l) smaller.

For example, one might assume that the 3d sublevel is lower in energy than 4s. However, according to the Klechkovsky rule, the energy of the 4s state is less than 3d, because for 4s the sum (n + l) = 4 + 0 = 4, and for 3d - (n + l) = 3 + 2 = 5.

2) If the sum (n + l) is the same for two sublevels (for example, for the 3d and 4p sublevels this sum is equal to 5), the level with the smaller n. Therefore, the formation of the energy levels of atoms of the elements of the fourth period occurs in the following sequence: 4s - 3d - 4p. For example:

21 Sc 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 1 , 31 Ga 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 4p 1

Thus, taking into account the Klechkovsky rules, the energy of atomic orbitals increases according to the series

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

Note. The sign ≤ means that the AO energies are close, so here a violation of the Klechkovsky rules is possible.

Using this series, one can determine the electronic structure of any atom. To do this, you need to sequentially add and place electrons on sublevels and atomic orbitals. In this case, it is necessary to take into account the Pauli principle and two Hund's rules.

3. Pauli principle determines the capacity of AO: An atom cannot have two electrons with the same set of all four quantum numbers.

In other words, one AO ​​characterized by three quantum numbers can accommodate only two electrons with opposite spins, i.e. for one AO, two possible options for its filling can be written:

one electron and two electrons ↓ .

In this case, the specific direction of the spin for one electron in the orbital does not matter, it is only important that the spins for two electrons in one AO ​​have opposite signs. The Pauli principle and the interdependence between the values ​​of n, l, and m determine the maximum possible number of electrons per orbital, sublevel and level (Table 2.4):

-on one AO ​​- 2 electron;

- at the sublevel l- 2(2l+1) electron;

- at level n - 2n 2 electrons.

Table 2.4

Electron distribution

by energy levels, sublevels and orbitals

Energy level	Principal quantum number	Energy sublevel	atomic orbitals	Maximum number of electrons
				sublevel	level
1		s( l= 0)
		s( l= 0)
2		p( l= 1)
		s( l= 0)
3		p( l= 1)
		d( l=2)

4. Two Hund's rules describe the order in which electrons fill the AO of one sublevel:

The first rule: in a given sublevel, electrons tend to fill energy states (AO) in such a way that the sum of their spins in absolute value is maximum. In this case, the energy of the system is minimal.

For example, consider the electronic configuration of a carbon atom. The atomic number of this element is 6. This means that there are 6 electrons in the atom and they are located on 2 energy levels (the carbon atom is in the second period), i.e. 1s 2 2s 2 2p 2 . Graphically, the 2p sublevel can be represented in three ways:

m 0 0 +1 0 -1 0 0 +1 0 -1 0 0 +1 0 -1

A B C

The amount of spins in the option a equals zero. In options b and in the sum of the spins is: ½ +½ = 1 (two paired electrons always add up to zero, so we take into account unpaired electrons).

When choosing between options b and in follow Hund's second rule : the state with the maximum (in absolute value) sum of magnetic quantum numbers has the minimum energy.

According to Hund's rule, the option has an advantage b(the sum of |1+ 0| is equal to 1) , since in the variant in sum |+1–1| equals 0.

Let us define, for example, the electronic formula of the element vanadium (V). Since its atomic number is Z = 23, 23 electrons must be placed on sublevels and levels (there are four of them, since vanadium is in the fourth period). We sequentially fill in: 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 3 (underlined unfinished levels and sublevels). The placement of electrons on 3d-AO according to Hund's rule will be:

For selenium (Z = 34) the full electronic formula is: 1s 2 2s 2 2p 6 3s 2 3p 6 3d 10 4s 2 4p 4, the fourth level is incomplete.

Filling this sublevel according to Hund's rule: 4p

A special role in chemistry is played by the electrons of the last unoccupied levels and sublevels, which are called valence(in the formulas V, Se are underlined). For example, in vanadium these are the electrons of the unfilled fourth level 4s 2 and the unfilled sublevel 3d 3 , i.e. 5 electrons will be valence 4s 2 3d 3 ; selenium has 6 electrons - 4s 2 4p 4 .

By the name of the last sublevel to be filled, the elements are called s-elements, p-elements, d-elements and f-elements.

The formulas of valence electrons found according to the described rules are called canonical. In fact, real formulas determined from experiment or quantum mechanical calculation differ somewhat from the canonical ones, since Klechkovsky's rules, Pauli's principle and Gund's rules are sometimes violated. The reasons for these violations are discussed below.

Example 1. Write down the electronic formula of an atom of an element with atomic number 16. Draw valence electrons graphically and characterize one of them by quantum numbers.

Decision. Atomic number 16 has a sulfur atom. Therefore, the nuclear charge is 16, in general, the sulfur atom contains 16 electrons. The electronic formula of the sulfur atom is written: 1s 2 2s 2 2p 6 3s 2 3p 4. (Valence electrons underlined).

Graphic formula of valence electrons:

The state of each electron in an atom is characterized by four quantum numbers. The electronic formula gives the values ​​of the principal quantum number and the orbital quantum number. So, for a marked electron, the state 3p means that n = 3 and l= 1(p). The graphic formula gives the value of two more quantum numbers - magnetic and spin. For the marked electron m = -1 and s = 1/2.

Example 2. Characterize the valence electrons of the scandium atom by four quantum numbers.

Decision. Scandium is in the 4th period, i.e. the last quantum layer is the fourth, in the 3rd group, i.e. three valence electrons.

The electronic formula of valence electrons is: 4s 2 3d 1 .

Graphic formula:

If identical particles have the same quantum numbers, then their wave function is symmetric with respect to particle permutation. It follows that two identical fermions included in one system cannot be in the same states, because for fermions, the wave function must be antisymmetric. Summarizing the experimental data, V. Pauli formed principle exceptions , Whereby fermion systems are found in nature only in states,described by antisymmetric wave functions(quantum-mechanical formulation of the Pauli principle).

From this position follows a simpler formulation of the Pauli principle, which was introduced by him into quantum theory (1925) even before the construction of quantum mechanics: in a system of identical fermions any two of them cannot simultaneously be in the same state . Note that the number of identical bosons in the same state is not limited.

Recall that the state of an electron in an atom is uniquely determined by the set four quantum numbers :

main n ;

orbital l , usually these states denote 1 s, 2d, 3f;

magnetic ();

· magnetic spin ().

The distribution of electrons in an atom occurs according to the Pauli principle, which can be formulated for an atom in the simplest form: in the same atom there cannot be more than one electron with the same set of four quantum numbers: n, l, , :

Z (n, l, , ) = 0 or 1,

where Z (n, l, , ) is the number of electrons in a quantum state, described by a set of four quantum numbers: n, l, , . Thus, the Pauli principle states, that two electrons ,bound in the same atom differ in value ,at least ,one quantum number .

The maximum number of electrons in states described by a set of three quantum numbers n, l and m, and differing only in the orientation of the electron spins is equal to:

,

(8.2.1)

because the spin quantum number can take only two values ​​1/2 and –1/2.

The maximum number of electrons that are in states determined by two quantum numbers n and l:

.

(8.2.2)

In this case, the vector of the orbital angular momentum of the electron can take in space (2 l+ 1) different orientations (Fig. 8.1).

The maximum number of electrons in states determined by the value of the principal quantum number n, equals:

.

(8.2.3)

The set of electrons in a multi-electron atom,having the same principal quantum number n,called electron shell or layer .

In each of the shells, the electrons are distributed along subshells corresponding to this l.

area of ​​space,in which there is a high probability of finding an electron, called subshell or orbital . The view of the main types of orbitals is shown in fig. 8.1.

Since the orbital quantum number takes values ​​from 0 to , the number of subshells is equal to the ordinal number n shells. The number of electrons in a subshell is determined by the magnetic and magnetic spin quantum numbers: the maximum number of electrons in a subshell with a given l equals 2(2 l+ 1). The designations of shells, as well as the distribution of electrons over shells and subshells, are given in Table. one.

Table 1

Principal quantum number n

shell symbol

Maximum number of electrons in the shell

Orbital quantum number l

Subshell character

Maximum number electrons in subshell