More strictly speaking, the relative arrangement of sublevels is determined not so much by their greater or lesser energy as by the requirement of a minimum of the total energy of the atom.
The distribution of electrons in atomic orbitals occurs, starting from the orbital with the lowest energy (principle of minimum energy), those. The electron enters the nearest orbital to the nucleus. This means that first those sublevels are filled with electrons for which the sum of the values of quantum numbers ( n+l) was minimal. Thus, the energy of an electron at the 4s sublevel is less than the energy of an electron located at the 3d sublevel. Consequently, the filling of sublevels with electrons occurs in the following order: 1s< 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s < 5d ~ 4f < 6p < 7s < 6d ~ 5f < 7p.
Based on this requirement, the minimum energy is reached for most atoms when their sublevels are filled in the sequence shown above. But there are exceptions that you can find in the tables "Electronic Configurations of the Elements", but these exceptions rarely have to be taken into account when considering the chemical properties of the elements.
Atom chrome has an electronic configuration not 4s 2 3d 4 , but 4s 1 3d 5 . This is an example of how the stabilization of states with parallel spins of electrons prevails over the insignificant difference in the energy states of the 3d and 4s sublevels (Hund's rules), that is, the energetically favorable states for the d-sublevel are d5 and d10. Energy diagrams of the valence sublevels of chromium and copper atoms are shown in Fig. 2.1.1.
A similar transition of one electron from the s-sublevel to the d-sublevel occurs in 8 more elements: Cu, Nb, Mo, Ru, Ag, Pt, Au. At the atom Pd there is a transition of two s-electrons to the d-sublevel: Pd 5s 0 4d 10 .
Fig.2.1.1. Energy diagrams of valence sublevels of chromium and copper atoms
Rules for filling electron shells:
1. First, find out how many electrons the atom of the element of interest to us contains. To do this, it is enough to know the charge of its nucleus, which is always equal to the serial number of the element in the Periodic Table of D.I. Mendeleev. The serial number (the number of protons in the nucleus) is exactly equal to the number of electrons in the entire atom.
2. Sequentially fill the orbitals, starting with the 1s orbital, with the available electrons, taking into account the principle of minimum energy. In this case, it is impossible to place more than two electrons with oppositely directed spins on each orbital (Pauli's rule).
3. We write down the electronic formula of the element.
An atom is a complex, dynamically stable microsystem of interacting particles: protons p +, neutrons n 0 and electrons e -.
Fig.2.1.2. Filling of energy levels with electrons of the element phosphorus
The electronic structure of the hydrogen atom (z = 1) can be depicted as follows:
+1 H 1s 1 , n = 1 , where the quantum cell (atomic orbital) is denoted as a line or square, and electrons as arrows.
Each atom of the subsequent chemical element in the periodic system is a multi-electron atom.
The lithium atom, like the hydrogen and helium atom, has the electronic structure of an s-element, because. the last electron of the lithium atom "sits down" on the s-sublevel:
+3 Li 1s 2 2s 1 2p 0
The first electron in the p-state appears in the boron atom:
+5 V 1s 2 2s 2 2p 1
Writing an electronic formula is easier to show with a specific example. Suppose we need to find out the electronic formula of an element with serial number 7. An atom of such an element should have 7 electrons. Let's fill the orbitals with seven electrons, starting from the bottom 1s orbital.
So, 2 electrons will be placed in 1s orbitals, 2 more electrons in 2s orbitals, and the remaining 3 electrons can be placed in three 2p orbitals.
The electronic formula of the element with serial number 7 (this is the element nitrogen, having the symbol “N”) looks like this:
+7 N 1s 2 2s 2 2p 3
Consider the action of Hund's rule on the example of a nitrogen atom: N 1s 2 2s 2 2p 3. At the 2nd electronic level, there are three identical p-orbitals: 2px, 2py, 2pz. Electrons will populate them so that each of these p-orbitals will have one electron. This is explained by the fact that in neighboring cells, electrons repel each other less, as similarly charged particles. The electronic formula of nitrogen obtained by us carries very important information: the 2nd (external) electronic level of nitrogen is not completely filled with electrons (it has 2 + 3 = 5 valence electrons) and three electrons are missing until it is completely filled.
The outer level of an atom is the level farthest from the nucleus that contains valence electrons. It is this shell that comes into contact when it collides with the outer levels of other atoms in chemical reactions. When interacting with other atoms, nitrogen is able to accept 3 additional electrons to its outer level. In this case, the nitrogen atom will receive a completed, that is, the most filled external electronic level, on which 8 electrons will be located.
A completed level is more energetically advantageous than an incomplete one, so the nitrogen atom should easily react with any other atom that can give it 3 extra electrons to complete its outer level.
Principle minimum energy determines the order in which atomic orbitals with different energies are populated. According to the principle of minimum energy, electrons occupy the orbits with the lowest energy first. The energy of sublevels grows in the series:
1s < 2s < 2 p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s < 4f 5d < 6p < 7s < 5f 6d...
The hydrogen atom has one electron, which can be in any orbital. However, in the ground state it should occupy 1 s orbital with the lowest energy.
In the potassium atom, the last nineteenth electron can populate either 3 d- or 4 s-orbital. According to the principle of minimum energy, an electron occupies 4 s-orbital, which is confirmed by experiment.
Attention should be paid to the indeterminacy of the notation 4 f 5d and 5 f 6d. It turned out that some elements have a lower energy 4 f-sublevel, while others have 5 d-sublevel. The same is observed for 5 f- and 6 d-sublevels.
Pauli principle
Principle pauli, often referred to as the exclusion principle, limits the number of electrons that can be in one orbital. According to the Pauli principle, no more than two electrons can be in any orbital, and then only if they have opposite spins (unequal spin numbers). Therefore, there should not be two electrons in an atom with the same four quantum numbers ( n, l, m l , m s).
The lithium atom has three electrons. Lowest energy orbital - 1 s-orbital - can be occupied by only two electrons, and these electrons must have different spins. If spin +1/2 is denoted by an arrow pointing up and spin −1/2 is denoted by an arrow pointing down, then two electrons with opposite ( antiparallel) spins in the same orbital can be schematically represented as follows:
The third electron in a lithium atom must occupy the orbital next in energy to the lowest orbital, that is, 2 s-orbital.
Gund's rule
Hund's (Hund's) rule determines the order in which electrons populate orbitals that have the same energy. It was developed by the German theoretical physicist F. Gundom(Hundom) in 1927 based on the analysis of atomic spectra.
According to Hund's rule, the population of orbitals belonging to the same energy sublevel begins with single electrons with parallel (same in sign) spins, and only after single electrons have occupied all orbitals, the final population of orbitals with pairs of electrons with opposite spins can occur. . As a result, the total spin (and the sum of spin quantum numbers) of all electrons in the atom will be maximum.
For example, a nitrogen atom has three electrons located on 2 R-sublevel. According to Hund's rule, they should be located one by one on each of the three 2 R-orbitals. In this case, all three electrons must have parallel spins:
Electronic configurations of atoms
A schematic representation of orbitals, taking into account their energy, is called the energy diagram of an atom. It reflects the mutual arrangement of energy levels and sublevels.
In the diagram, orbitals are indicated in the form of cells: , and electrons - in the form of arrows: or
An electron can occupy any free orbital, but, according to the principle of minimum energy, it always prefers the orbital with lower energy. The Pauli exclusion principle limits the number of electrons in each orbital. Therefore, in one cell (on an atomic orbital) there can be only one or two electrons. On each s- sublevel (one orbital) can contain two electrons, each p-sublevel (three orbitals) - six electrons, on each d-sublevel (five orbitals) - ten electrons. Hund's rule determines the order in which orbitals with the same energy are populated.
Thus, it is possible to obtain a sequence of population of atomic orbitals with electrons:
Using the principle of minimum energy, the Pauli principle and Hund's rule, one can determine the order in which orbitals are populated by electrons and construct an electronic formula for any element.
The electronic configuration (formula) of an atom is the distribution of electrons along orbitals in the ground (unexcited) state of this atom and its ions: 1 s 2 2s 2 2p 6 3s 2 3p 6 ... The number of electrons in the orbitals of a given sublevel is indicated in the superscript to the right of the letter, for example 3 d 5 is 5 electrons by 3 d-sublevel.
For brevity, the recording of the electronic configuration of an atom, instead of orbitals completely populated by electrons, is sometimes written down as a noble gas symbol, which has the corresponding electronic formula:
1 s 2 =
1 s 2 2s 2 2p 6 =
1 s 2 2s 2 2p 6 3s 2 3p 6 =
For example, the electronic formula of the chlorine atom is 1 s 2 2s 2 2p 6 3s 2 3p 5 , or 3 s 2 3p 5 . The valence electrons that take part in the formation of chemical bonds are taken out of brackets.
For large periods (especially the sixth and seventh), the construction of the electronic configurations of atoms is more complex. For example, 4 f-electron does not appear in the lanthanum atom, but in the atom of the next cerium atom. Sequential filling 4 f-sublevel is interrupted in the gadolinium atom, where there are 5 d-electron
Gibbs free energy(or simply Gibbs energy, or Gibbs potential, or thermodynamic potential in the narrow sense) thermodynamic potential the following form:
The Gibbs energy can be understood as the total chemicalenergy systems (crystal, liquid, etc.)
The concept of the Gibbs energy is widely used in thermodynamics and chemistry.
The exact solution of the Schrödinger equation can only be found in rare cases, for example, for the hydrogen atom and hypothetical one-electron ions such as He + , Li 2+ , Be 3+ . An atom of the element following hydrogen, helium, consists of a nucleus and two electrons, each of which is attracted to both nuclei and repelled from the other electron. Even in this case, the wave equation does not have an exact solution.
Therefore, various approximate methods are of great importance. With the help of such methods, it was possible to establish the electronic structure of atoms of all known elements. These calculations show that the orbitals in multi-electron atoms do not differ much from the orbitals of the hydrogen atom (these orbitals are called hydrogen-like). The main difference is some compression of the orbitals due to the greater charge of the nucleus. In addition, for multielectron atoms, it was found that for each energy level(for a given value of the principal quantum number n) is split into sublevels. The energy of an electron depends not only on n, but also on the orbital quantum number l. It increases along s-, p-, d-, f-orbitals (Fig. 7).
Rice. 7
For high energy levels, the differences in sublevel energies are large enough that one level can penetrate another, for example
6s d4 f p.
The population of atomic orbitals for a multi-electron atom in the ground (that is, the most energetically favorable) state occurs in accordance with certain rules.
The principle of minimum energy
Principle minimum energy determines the order in which atomic orbitals with different energies are populated. According to the principle of minimum energy, electrons occupy the orbits with the lowest energy first. The energy of sublevels grows in the series:
1s s p s p s d p s d p s f5 d p s f6 d...
The hydrogen atom has one electron, which can be in any orbital. However, in the ground state it should occupy 1 s orbital with the lowest energy.
In the potassium atom, the last nineteenth electron can populate either 3 d- or 4 s-orbital. According to the principle of minimum energy, an electron occupies 4 s-orbital, which is confirmed by experiment.
Attention should be paid to the indeterminacy of the notation 4 f 5d and 5 f 6d. It turned out that some elements have a lower energy 4 f-sublevel, while others have 5 d-sublevel. The same is observed for 5 f- and 6 d-sublevels.
More strictly speaking, the relative arrangement of sublevels is determined not so much by their greater or lesser energy as by the requirement for a minimum of the total energy of the atom.
The distribution of electrons in atomic orbitals occurs, starting from the orbital with the lowest energy (principle of minimum energy), those. The electron enters the nearest orbital to the nucleus. This means that first those sublevels are filled with electrons for which the sum of the values of quantum numbers ( n+l) was minimal. Thus, the energy of an electron at the 4s sublevel is less than the energy of an electron located at the 3d sublevel. Consequently, the filling of sublevels with electrons occurs in the following order: 1s< 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s < 5d ~ 4f < 6p < 7s < 6d ~ 5f < 7p.
Based on this requirement, the minimum energy is reached for most atoms when their sublevels are filled in the sequence shown above. But there are exceptions that you can find in the tables "Electronic Configurations of the Elements", but these exceptions rarely have to be taken into account when considering the chemical properties of the elements.
Atom chrome has an electronic configuration not 4s 2 3d 4 , but 4s 1 3d 5 . This is an example of how the stabilization of states with parallel spins of electrons prevails over the insignificant difference in the energy states of the 3d and 4s sublevels (Hund's rules), that is, the energetically favorable states for the d-sublevel are d5 and d10. Energy diagrams of the valence sublevels of chromium and copper atoms are shown in Fig. 2.1.1.
A similar transition of one electron from the s-sublevel to the d-sublevel occurs in 8 more elements: Cu, Nb, Mo, Ru, Ag, Pt, Au. At the atom Pd there is a transition of two s-electrons to the d-sublevel: Pd 5s 0 4d 10 .
Fig.2.1.1. Energy diagrams of valence sublevels of chromium and copper atoms
Rules for filling electron shells:
1. First, find out how many electrons the atom of the element of interest to us contains. To do this, it is enough to know the charge of its nucleus, which is always equal to the ordinal number of the element in the Periodic Table of D.I. Mendeleev. The serial number (the number of protons in the nucleus) is exactly equal to the number of electrons in the entire atom.
2. Sequentially fill the orbitals, starting with the 1s orbital, with the available electrons, taking into account the principle of minimum energy. In this case, it is impossible to place more than two electrons with oppositely directed spins on each orbital (Pauli's rule).
3. We write down the electronic formula of the element.
An atom is a complex, dynamically stable microsystem of interacting particles: protons p +, neutrons n 0 and electrons e -.
Fig.2.1.2. Filling of energy levels with electrons of the element phosphorus
The electronic structure of the hydrogen atom (z=1) can be depicted as follows:
+1 H 1s 1 , n = 1 , where the quantum cell (atomic orbital) is denoted as a line or square, and electrons as arrows.
Each atom of the subsequent chemical element in the periodic system is a multi-electron atom.
The lithium atom, like the hydrogen and helium atom, has the electronic structure of an s-element, because the last electron of the lithium atom "sits down" on the s-sublevel:
+3 Li 1s 2 2s 1 2p 0
The first electron in the p-state appears in the boron atom:
+5 V 1s 2 2s 2 2p 1
Writing an electronic formula is easier to show with a specific example. Suppose we need to find out the electronic formula of an element with serial number 7. An atom of such an element should have 7 electrons. Let's fill the orbitals with seven electrons, starting from the bottom 1s orbital.
So, 2 electrons will be placed in 1s orbitals, 2 more electrons in 2s orbitals, and the remaining 3 electrons can be placed in three 2p orbitals.
The electronic formula of the element with the serial number 7 (this is the element nitrogen, which has the symbol “N”) looks like this:
+7 N 1s 2 2s 2 2p 3
Consider the action of Hund's rule on the example of a nitrogen atom: N 1s 2 2s 2 2p 3. At the 2nd electronic level, there are three identical p-orbitals: 2px, 2py, 2pz. Electrons will populate them so that each of these p-orbitals will have one electron. This is explained by the fact that in neighboring cells, electrons repel each other less, as similarly charged particles. The electronic formula of nitrogen obtained by us carries very important information: the 2nd (external) electronic level of nitrogen is not completely filled with electrons (it has 2 + 3 = 5 valence electrons) and three electrons are missing until it is completely filled.
The outer level of an atom is the level farthest from the nucleus that contains valence electrons. It is this shell that comes into contact when it collides with the outer levels of other atoms in chemical reactions. When interacting with other atoms, nitrogen is able to accept 3 additional electrons to its outer level. In this case, the nitrogen atom will receive a completed, that is, the most filled external electronic level, on which 8 electrons will be located.
A completed level is more energetically advantageous than an incomplete one, so the nitrogen atom should easily react with any other atom that can give it 3 extra electrons to complete its outer level.
Fig.2.1.3. Filling the energy levels of s-, p-,d- and f-elements with electrons
Energy sublevels
According to the limits of changes in the orbital quantum number from 0 to (n-1), a strictly limited number of sublevels is possible in each energy level, namely: the number of sublevels is equal to the level number:
The combination of the principal (n) and orbital (l) quantum numbers completely characterizes the energy of an electron. The energy reserve of an electron is reflected by the sum (n+l).
So, for example, the electrons of the 3d sublevel have a higher energy than the electrons of the 4s sublevel:
The order in which levels and sublevels in an atom are filled with electrons is determined by rule V.M. Klechkovsky: the filling of the electronic levels of the atom occurs sequentially in the order of increasing sum (n + 1).
In accordance with this, the real energy scale of sublevels is determined, according to which the electron shells of all atoms are built:
1s ï 2s2p ï 3s3p ï 4s3d4p ï 5s4d5p ï 6s4f5d6p ï 7s5f6d…
3. Magnetic quantum number (m l) characterizes the direction of the electron cloud (orbital) in space.
The more complex the shape of the electron cloud (i.e., the higher the value of l), the more variations in the orientation of this cloud in space and the more individual energy states of the electron exist, characterized by a certain value of the magnetic quantum number.
Mathematically m l takes integer values from -1 to +1, including 0, i.e. total (21+1) values.
Let us designate each individual atomic orbital in space as an energy cell ð, then the number of such cells in sublevels will be:
| sublevel | Possible values m l | The number of individual energy states (orbitals, cells) in the sublevel | |
| s (l=0) | one | ||
| p (l=1) | -1, 0, +1 | three | |
| d (l=2) | -2, -1, 0, +1, +2 | five |  |
| f (l=3) | -3, -2, -1, 0, +1, +2, +3 | seven |  |
For example, a spherical s-orbital is uniquely directed in space. Dumbbell-shaped orbitals of each p-sublevel are oriented along three coordinate axes
4. Spin quantum number m s characterizes the electron's own rotation around its axis and takes only two values: + 1 / 2 and - 1 / 2, depending on the direction of rotation in one direction or another. According to the Pauli principle, no more than 2 electrons can be located in one orbital with oppositely directed (antiparallel)
p- sublevel spins: .
Such electrons are called paired. An unpaired electron is schematically represented by a single arrow: .
Knowing the capacity of one orbital (2 electrons) and the number of energy states in the sublevel (m s), we can determine the number of electrons in the sublevels:
You can write the result differently: s 2 p 6 d 10 f 14 .
These numbers must be well remembered for the correct writing of the electronic formulas of the atom.
So, four quantum numbers - n, l, m l , m s - completely determine the state of each electron in an atom. All electrons in an atom with the same value of n make up an energy level, with the same values of n and l - an energy sublevel, with the same values of n, l and m l- a separate atomic orbital (quantum cell). Electrons in the same orbital have different spins.
Taking into account the values of all four quantum numbers, we determine the maximum number of electrons in the energy levels (electronic layers):
Large numbers of electrons (18.32) are contained only in the deep-lying electron layers of atoms, the outer electron layer can contain from 1 (for hydrogen and alkali metals) to 8 electrons (inert gases).
It is important to remember that the filling of electron shells with electrons occurs according to principle of least energy: The sublevels with the lowest energy value are filled first, then those with higher values. This sequence corresponds to the energy scale of V.M. Klechkovsky.
The electronic structure of an atom is displayed by electronic formulas, which indicate energy levels, sublevels and the number of electrons in sublevels.
For example, the hydrogen atom 1 H has only 1 electron, which is located in the first layer from the nucleus at the s-sublevel; the electronic formula of the hydrogen atom is 1s 1.
The lithium atom 3 Li has only 3 electrons, 2 of which are in the s-sublevel of the first layer, and 1 is placed in the second layer, which also begins with the s-sublevel. The electronic formula of the lithium atom is 1s 2 2s 1.
The phosphorus atom 15 P has 15 electrons located in three electron layers. Remembering that the s-sublevel contains no more than 2 electrons, and the p-sublevel contains no more than 6, we gradually place all the electrons into sublevels and draw up the electronic formula of the phosphorus atom: 1s 2 2s 2 2p 6 3s 2 3p 3.
When compiling the electronic formula of the manganese atom 25 Mn, it is necessary to take into account the sequence of increasing sublevel energy: 1s2s2p3s3p4s3d…
We gradually distribute all 25 Mn electrons: 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 5 .
The final electronic formula of the manganese atom (taking into account the distance of electrons from the nucleus) looks like this:
| 1s2 | 2s 2 2p 6 | 3s 2 3p 6 3d 5 | 4s 2 |
The electronic formula of manganese fully corresponds to its position in the periodic system: the number of electronic layers (energy levels) - 4 is equal to the number of the period; there are 2 electrons in the outer layer, the penultimate layer is not completed, which is typical for metals of secondary subgroups; the total number of mobile, valence electrons (3d 5 4s 2) - 7 is equal to the group number.
Depending on which of the energy sublevels in the atom -s-, p-, d- or f- is built up last, all chemical elements are divided into electronic families: s-elements(H, He, alkali metals, metals of the main subgroup of the 2nd group of the periodic system); p-elements(elements of the main subgroups 3, 4, 5, 6, 7, 8th groups of the periodic system); d-elements(all metals of secondary subgroups); f-elements(lanthanides and actinides).
The electronic structures of atoms are a deep theoretical substantiation of the structure of the periodic system, the length of the periods (i.e. the number of elements in the periods) follows directly from the capacitance of the electronic layers and the sequence of increasing energy of the sublevels:
Each period starts with an s-element with the structure of the outer layer s 1 (alkali metal) and ends with a p-element with the structure of the outer layer …s 2 p 6 (inert gas). The 1st period contains only two s-elements (H and He), the 2nd and 3rd small periods each contain two s-elements and six p-elements. In the 4th and 5th large periods between the s- and p-elements, 10 d-elements each are “wedged” - transition metals, allocated to side subgroups. In periods VI and VII, 14 more f-elements are added to the analogous structure, which are similar in properties to lanthanum and actinium, respectively, and isolated as subgroups of lanthanides and actinides.
When studying the electronic structures of atoms, pay attention to their graphic representation, for example:
13 Al 1s 2 2s 2 2p 6 3s 2 3p 1
N=2 1s 2s 2p 3s 3p
both versions of the image are used: a) and b):
For the correct arrangement of electrons in orbitals, it is necessary to know Gund's rule: the electrons in the sublevel are arranged so that their total spin is maximum. In other words, the electrons first occupy all free cells of the given sublevel one by one.
For example, if it is necessary to place three p-electrons (p 3) in a p-sublevel, which always has three orbitals, then of the two possible options, the first option corresponds to the Hund's rule:
As an example, consider the graphical electronic circuit of a carbon atom:
6 C 1s 2 2s 2 2p 2
The number of unpaired electrons in an atom is a very important characteristic. According to the theory of covalent bonding, only unpaired electrons can form chemical bonds and determine the valence capabilities of an atom.
If there are free energy states (unoccupied orbitals) in the sublevel, the atom, upon excitation, “steams”, separates the paired electrons, and its valence capabilities increase:
6 C 1s 2 2s 2 2p 3
Carbon in the normal state is 2-valent, in the excited state it is 4-valent. The fluorine atom has no opportunities for excitation (because all the orbitals of the outer electron layer are occupied), therefore fluorine in its compounds is monovalent.
Example 1 What are quantum numbers? What values can they take?
Solution. The motion of an electron in an atom has a probabilistic character. The circumnuclear space, in which an electron can be located with the highest probability (0.9-0.95), is called the atomic orbital (AO). An atomic orbital, like any geometric figure, is characterized by three parameters (coordinates), called quantum numbers (n, l, m l). Quantum numbers do not take any, but certain, discrete (discontinuous) values. Neighboring values of quantum numbers differ by one. Quantum numbers determine the size (n), shape (l) and orientation (m l) of an atomic orbital in space. Occupying one or another atomic orbital, an electron forms an electron cloud, which can have a different shape for electrons of the same atom (Fig. 1). The forms of electron clouds are similar to AO. They are also called electron or atomic orbitals. The electron cloud is characterized by four numbers (n, l, m 1 and m 5).
