How to distribute electrons in layers. Distribution of electrons by energy levels
The distribution of electrons over energy levels explains the metallic as well as non-metallic properties of any elements.
Electronic formula
There is a certain rule according to which free and paired negative particles are placed at levels and sublevels. Let us consider in more detail the distribution of electrons over energy levels.There are only two electrons in the first energy level. The filling of the orbital with them is carried out as the energy supply increases. The distribution of electrons in an atom of a chemical element corresponds to an ordinal number. The energy levels with the minimum number have the most pronounced force of attraction of valence electrons to the nucleus.
An example of compiling an electronic formula
Consider the distribution of electrons over energy levels using the example of a carbon atom. Its serial number is 6, therefore, there are six positively charged protons inside the nucleus. Given that carbon is a representative of the second period, it is characterized by the presence of two energy levels. The first has two electrons, the second has four.Hund's rule explains the location in one cell of only two electrons that have different spins. There are four electrons in the second energy level. As a result, the distribution of electrons in an atom of a chemical element has the following form: 1s22s22p2.
There are certain rules according to which the distribution of electrons into sublevels and levels occurs.
Pauli principle
This principle was formulated by Pauli in 1925. The scientist stipulated the possibility of placing in the atom only two electrons that have the same quantum numbers: n, l, m, s. Note that the distribution of electrons over energy levels occurs as the amount of free energy increases.
Klechkovsky's rule
The filling of energy orbitals is carried out according to the increase in quantum numbers n + l and is characterized by an increase in the energy reserve.Consider the distribution of electrons in a calcium atom.
In the normal state, its electronic formula is as follows:
Ca 1s2 2s2 2p6 3s2 3p6 3d0 4s2.
For elements of similar subgroups related to d- and f-elements, there is a “failure” of an electron from an external sublevel, which has a lower energy reserve, to the previous d- or f-sublevel. A similar phenomenon is typical for copper, silver, platinum, gold.
The distribution of electrons in an atom involves the filling of sublevels with unpaired electrons that have the same spins.
Only after the complete filling of all free orbitals with single electrons, the quantum cells are supplemented with second negative particles endowed with opposite spins.
For example, in the unexcited state of nitrogen:
1s2 2s2 2p3.
The properties of substances are influenced by the electronic configuration of valence electrons. By their number, you can determine the highest and lowest valency, chemical activity. If an element is in the main subgroup of the periodic table, you can use the group number to compose an external energy level, determine its oxidation state. For example, phosphorus, which is in the fifth group (the main subgroup), contains five valence electrons, therefore, it is able to accept three electrons or give five particles to another atom.
All representatives of the secondary subgroups of the periodic table act as exceptions to this rule.
Family Features
Depending on what structure the external energy level has, there is a division of all neutral atoms included in the periodic table into four families:- s-elements are in the first and second groups (main subgroups); the p-family is located in groups III-VIII (A subgroups); d-elements can be found in similar subgroups from groups I-VIII; the f-family consists of actinides and lanthanides.
The d-elements in the unexcited state have valence electrons both on the last s- and on the penultimate d-sublevel.
Conclusion
The state of any electron in an atom can be described using a set of basic numbers. Depending on the features of its structure, we can talk about a certain amount of energy. Using the rule of Hund, Klechkovsky, Pauli for any element included in the periodic table, you can make a configuration of a neutral atom.The smallest energy reserve in the unexcited state is possessed by electrons located at the first levels. When a neutral atom is heated, the transition of electrons is observed, which is always accompanied by a change in the number of free electrons, leads to a significant change in the oxidation state of the element, a change in its chemical activity.
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 provision follows a simpler formulation of the Pauli principle, which was introduced by him in quantum theory(1925) even before construction 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. 1.
Table 1
| Principal quantum number n |
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| shell symbol |
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| Maximum number of electrons in the shell |
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| Orbital quantum number l |
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| Subshell symbol |
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| Maximum number electrons in subshell |
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The distribution of electrons in an atom is carried out in accordance with 3 provisions of quantum mechanics: the Pauli principle; the principle of minimum energy; Hund's rule.
According to the Pauli principle An atom cannot have two electrons with the same values of all four quantum numbers. The Pauli principle determines the maximum number of electrons in one orbital, level and sublevel. Since AO is characterized by three quantum numbers n, l, ml, the electrons of a given orbital can differ only in the spin quantum number ms. But ms can only have two values +½ and -½.
Therefore, no more than two electrons with oppositely directed spins can be in one orbital. The maximum number of electrons in an energy level is defined as 2 n 2 , and at the sublevel - as 2 (2 l+1). The maximum number of electrons located at different levels and sublevels are given in Table. 2.1.
Maximum number of electrons at quantum levels and sublevels
| Energy level | Energy sublevel | Possible values of the magnetic quantum number ml | Number of JSCs in | Maximum number of electrons per | ||
| sublevel | level | sublevel | level | |||
| K (n= 1) | s (l= 0) | |||||
| L (n= 2) | s (l= 0) p (l= 1) | -1, 0, 1 | ||||
| M (n= 3) | s (l= 0) p (l= 1) d (l= 2) | -1, 0, 1 -2, -1, 0, 1, 2 | ||||
| N (n= 4) | s (l= 0) p (l= 1) d (l= 2) f (l= 3) | -1, 0, 1 -2, -1, 0, 1, 2 -3, -2, -1, 0, 1, 2, 3 |
The sequence of filling orbitals with electrons is carried out in accordance with minimum energy principle, Whereby electrons fill the orbitals in order of increasing energy level of the orbitals. The order of orbitals in terms of energy is determined by Klechkovsky's rule : an increase in energy, and, accordingly, the filling of orbitals occurs in the order of increasing sum (n + l), and with an equal sum (n + l) - in increasing order of n.
The order of distribution of electrons over energy levels and sublevels in the shell of an atom called him electronic configuration. When writing an electronic configuration, the level number (principal quantum number) is denoted by the numbers 1, 2, 3, 4 ..., the sublevel (orbital quantum number) - by letters s, p, d, f. The number of electrons in a sublevel is indicated by a number, which is written at the top of the sublevel symbol. For example, the electronic configuration of a sulfur atom is 16 S 1 s 2 2s 2 2p 6 3s 2 3p 4, and vanadium 23 V 1 s 2 2s 2 2p 6 3s 2 3p 6 3d°/i> 3 4 s 2 .
The chemical properties of atoms are determined mainly by the structure of the outer energy levels, which are called valence. Completed energy levels do not participate in chemical interaction. Therefore, for brevity, they are often denoted by the symbol of the preceding noble gas for brevity. So, for sulfur: 3 s 2 3p 4 ; for vanadium: 3 d 3 4s 2. At the same time, the abbreviated notation clearly highlights the valence electrons that determine Chemical properties element atoms.
Depending on which sublevel in the atom is filled last, all chemical elements are divided into 4 electronic families: s-, p-, d-, f- elements. Elements whose atoms are the last to fill the s-sublevel of the outer level are called s-elements. At s- elements are valence s-electrons of the outer energy level.
At p-elements the p-sublevel of the outer level is filled last. They have valence electrons in p- And s- sublevels of the outer layer. At d-elements, the d-sublevel of the pre-outer level is filled last and valence are s- electrons of the outer and d- electrons of the pre-external energy levels. At f-elements, the f-sublevel of the third outside energy level is filled last.
The electronic configuration of an atom can also be depicted in the form of electron placement schemes in quantum cells, which are a graphical representation of the atomic orbital. Each quantum cell can contain no more than two electrons with oppositely directed spins. The order of placement of electrons within one sublevel is determined by Hund's rule: within a sublevel, electrons are arranged so that their total spin is maximum. In other words, the orbitals of a given sublevel are filled first by one electron with the same spins, and then by the second electron with opposite spins.
Total spin R- electrons of the third energy level of the sulfur atom S ms= ½ - ½ + ½ + ½ = 1; d- electrons of the vanadium atom -
S ms\u003d ½ + ½ + ½ \u003d 3 / 2.
Often, not the entire electronic formula is graphically depicted, but only those sublevels on which the valence electrons are located, for example,
16S…3 s 2 3p 4 ; 23V…3 d 3 4s 2 .
In a graphical representation of the electronic configuration of an atom in an excited state, along with filled ones, vacant valence orbitals are depicted. For example, in the phosphorus atom at the third energy level there is one s-AO, three R-ao and five d-AO. The electronic configuration of the phosphorus atom in the ground state has the form
15 R… 3 s 2 3p 3 .
The valence of phosphorus, determined by the number of unpaired electrons, is 3. When an atom passes into an excited state, the electrons of state 3 are depaired s and one of the electrons s-sublevel can go to d-sublevel:
R*… 3 s2 3p 3 3d 1
In this case, the valency of phosphorus changes from three (PCl 3) in the ground state to five (PCl 5) in the excited state.
Each electron in an atom moves in the first approximation in a centrally symmetric non-Coulomb field The state of an electron in this case is determined by three quantum numbers , the physical meaning of which was clarified in § 28. In connection with the existence of an electron spin, one must add to the indicated quantum numbers a quantum number that can take values and determines the projection of the spin onto the given direction. In what follows, for the magnetic quantum number, we will instead use the notation to emphasize the fact that this number determines the projection of the orbital angular momentum, the value of which is given by the quantum number l.
Thus, the state of each electron in an atom is characterized by four quantum numbers:
The energy of a state depends mainly on numbers.
In addition, there is a weak dependence of energy on numbers, since their values are related to the mutual orientation of the moments, on which the magnitude of the interaction between the orbital and intrinsic magnetic moments of the electron depends. The energy of a state increases more strongly with increasing number than with increasing Therefore, as a rule, a state with a large one has, regardless of the value, more energy.
In the normal (unexcited) state of an atom, electrons should be located at the lowest energy levels available to them. Therefore, it would seem that in any atom in the normal state, all electrons should be in the state and the basic terms of all atoms should be of the -term type. However, experience shows that this is not so.
The explanation of the observed types of terms is as follows. According to one of the laws of quantum mechanics, called the Pauli principle, in the same atom (or in any other quantum system) there cannot be two electrons that have the same set of quantum numbers. In other words, two electrons cannot be in the same state at the same time.
In § 28 it was shown that the given corresponds to states that differ in the values of l and the Quantum number can take two values: Therefore, in states with a given value, no more than electrons can be in the atom:
A set of electrons having the same values of the quantum number , forms a shell. The shells are subdivided into subshells that differ in the value of the quantum number l. In accordance with the meaning, shells are given designations borrowed from X-ray spectroscopy:
Table 36.1
The division of the possible states of an electron in an atom into shells and subshells is shown in Table. 36.1, in which symbols are used instead of symbols for clarity: . Subshells, as indicated in the table, can be designated in two ways (for example, either ).
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) less.
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 it is possible to write two possible options its filling:
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 variants b And V 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 V 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 V 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.
Solution. 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 marked electron m = -1 and s = 1/2.
Example 2. Characterize the valence electrons of the scandium atom by four quantum numbers.
Solution. 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: 