Energy levels and sublevels of atomic orbitals. How electronic levels, sublevels and orbitals are filled as the atom becomes more complex

multi-electron atom

Energy level n	Energy sublevel	Orbital notation	Number of orbitals n	Number of electrons 2n
l	type of orbital
		s	1s
2		s p	2s 2p	3 4	2 8
3		s p d	3s 3p 3d	3 9	6 18
4		s p d f	4s 4p 4d 4f	3 16	6 32

Magnetic quantum number m l within this sublevel ( n, l = const) takes all integer values ​​from + l before - l, including zero. For the s-sublevel ( n = const, l = 0) only one value is possible ml = 0, whence it follows that the s-sublevel of any (from the first to the seventh) energy level contains one s-AO.

For the p-sublevel ( n> 1, l = 1) m l can take three values ​​+1, 0, -1, therefore, the p-sublevel of any (from the second to the seventh) energy level contains three p-AOs.

For the d-sublevel ( n> 2, l = 2) m l has five values ​​+2, +1, 0, -1, -2 and, as a result, d- the sublevel of any (from the third to the seventh) energy level necessarily contains five d- AO.

Likewise, for each f- sublevel ( n> 3, l = 3) m has seven values ​​+3, +2, +1, 0, -1, -2, -3 and therefore any f- sublevel contains seven f- AO.

Thus, each atomic orbital is uniquely determined by three quantum numbers - the main n, orbital l and magnetic m l.

At n = const all values ​​related to a given energy level are strictly defined l, and when l = const - all values ​​related to a given energy sublevel m l.

Due to the fact that each orbital can be filled with a maximum of two electrons, the number of electrons that can be accommodated in each energy level and sublevel is twice the number of orbitals in a given level or sublevel. Since electrons in the same atomic orbital have the same quantum numbers n, l and m l, then for two electrons in one orbital, the fourth is used, spin quantum number s, which is determined by the electron spin.

According to the Pauli principle, it can be argued that each electron in an atom is uniquely characterized by its own set of four quantum numbers - the main n, orbital l, magnetic m and spin s.

The population of energy levels, sublevels and atomic orbitals by electrons obeys the following rule (principle of minimum energy): In the unexcited state, all electrons have the lowest energy.

This means that each of the electrons filling the shell of an atom occupies such an orbital that the atom as a whole has a minimum energy. A successive quantum increase in the energy of sublevels occurs in the following order:

1s- 2s- 2p- 3s- 3p- 4s- 3d- 4p- 5s-…..

The filling of atomic orbitals within one energy sublevel occurs in accordance with the rule formulated by the German physicist F. Hund (1927).

Hund's rule: atomic orbitals belonging to the same sublevel are each filled first with one electron, and then they are filled with second electrons.

Hund's rule is also called the maximum multiplicity principle, i.e. the maximum possible parallel direction of electron spins of one energy sublevel.

At the highest energy level of a free atom, there can be no more than eight electrons.

Electrons located at the highest energy level of an atom (in the outer electron layer) are called external; The number of outer electrons in an atom of any element is never more than eight. For many elements, it is the number of outer electrons (with filled inner sublevels) that largely determines their chemical properties. For other electrons whose atoms have an unfilled inner sublevel, such as 3 d- the sublevel of atoms of such elements as Sc, Ti, Cr, Mn, etc., the chemical properties depend on the number of both internal and external electrons. All these electrons are called valence; in abbreviated electronic formulas of atoms, they are written after the symbol for the atomic core, that is, after the expression in square brackets.

Similar information.

Energy sublevels - section Chemistry, Fundamentals of inorganic chemistry Orbital Quantum Number L For...

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:

Poduro-ven	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:

p- sublevel + 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 with oppositely directed (antiparallel) spins can be located in one orbital:

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 period number; 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 justification for the structure of the periodic system, the length of periods (i.e., the number of elements in periods) follows directly from the capacitance of the electronic layers and the sequence of increasing energy of sublevels:

Each period begins with an s-element with an outer layer structure of s 1 (alkali metal) and ends with a p-element with an outer layer structure of …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

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 the 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?

Decision. 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).

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