Particle sizes often determine the type of crystal structure and are important for understanding the occurrence of many chemical reactions. The size of atoms, ions, and molecules is determined by valence electrons. The basis for understanding this issue - the patterns of changes in orbital radii - are presented in subsection. 2.4. An atom has no boundaries and its size is a relative value. Nevertheless, it is possible to characterize the size of a free atom by its orbital radius. But of practical interest are usually atoms and ions in the composition of a substance (in a molecule, polymer, liquid or solid), and not free ones. Since the states of a free and bound atom differ significantly (and, above all, their energy), the sizes must also differ.

For bonded atoms, you can also enter quantities characterizing their size. Although electron clouds of bound atoms can differ significantly from spherical ones, the sizes of atoms are usually characterized by effective (apparent) radii .

The sizes of atoms of the same element significantly depend on the composition of which chemical compound and what type of bond the atom has. For example, for hydrogen, half of the interatomic distance in the H 2 molecule is 0.74/2 = 0.37 Å, and in metallic hydrogen the radius value is 0.46 Å. Therefore, they highlight covalent, ionic, metallic and van der Waals radii . As a rule, in the concepts of effective radii, interatomic distances (more precisely, internuclear distances) are considered the sum of the radii of two neighboring atoms, taking the atoms to be incompressible spheres. In the presence of reliable and accurate experimental data on interatomic distances (and such data have been available for a long time for both molecules and crystals with an accuracy of thousandths of an angstrom), one problem remains to determine the radius of each atom - how to distribute the interatomic distance between two atoms . It is clear that this problem can be solved unambiguously only by introducing additional independent data or assumptions.

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Properties of a chemical bond

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Covalent radii
The most obvious situation is with covalent radii for atoms that form nonpolar diatomic molecules. In such cases, the covalent radius is exactly half the interatomic distance

Ionic radii
Since under n. u. It is difficult to observe molecules with ionic bonds and at the same time a large number of compounds are known that form ionic crystals, then when it comes to ionic radii,

Metal radii
Determining metal radii in itself is not a problem - it is enough to measure the internuclear distance in the corresponding metal and divide in half. In table 20 are some meth

Vander Waals radii
Van der Waals radii can be determined by measuring the distances between atoms in a crystal when there is no chemical bond between them. In other words, the atoms belong to different molecules

Self-test questions
1. What are orbital and effective radii? 2. What is the difference between the radius of a pellet and an atom or ion? 3. In what cases is the covalent radius equal to half the length?

Effective atomic charges
When a chemical bond is formed, a redistribution of electron density occurs, and in the case of a polar bond, the atoms become electrically charged. These charges are called effective. They are hara

Effective charges in some ionic crystals
Substance CsF CsCl NaF NaCl LiF LiCl LiI DEO 3.3

Effective charges of atoms in oxides (according to N. S. Akhmetov)
Oxide Na2O MgO Al2O3 SiO2 P2O5 SO

Self-test questions
1. What is the effective charge of an atom? 2. Can the effective charge exceed (in absolute value) the oxidation state of an atom? 3. What is the degree of ionicity of a bond? 4. K

Valence
In general, valence characterizes the ability of the atoms of an element to form compounds containing a certain composition (certain ratios of the amounts of different elements in the compound). Often in

Self-test questions
1. Define the concepts: degree of oxidation; covalency; coordination number; steric number. 2. Determine covalency, oxidation state and CN for: H2S; H

Communication energy
The amount of energy is the most important characteristic of a bond, determining the resistance of substances to heat, lighting, mechanical stress, and reactions with other substances[†]. There are various methods

Binding energies of diatomic molecules in a gas (N. N. Pavlov)
Molecule H2 Li2 Na2 K2 F2 Cl2

Self-test questions
1. Predict the change in the energy of the C–N bond in the series Н3СNН2, Н2СНН, НННН. 2. Predict the change in binding energy in the series O2, S2, Se2

Chemical Bonding and the Periodic Table of Elements
Let us consider the regularities of the structure and properties of some simple substances and the simplest compounds, determined by the electronic structure of their atoms. The noble gas atoms (group VIIIA) are completely

Changes in interatomic distances for simple substances of group VIA
Substance Distance between atoms, Å inside molecules between molecules difference S

Additional
3. General chemistry / ed. E. M. Sokolovskaya. M.: Moscow State University Publishing House, 1989. 4. Ugai Ya. O. General chemistry. M.: Higher. school, 1984. 5. Same. General and inorganic chemistry. M..

To understand the question of what is called the radius of an atom in modern science, let us remember what an atom itself is. According to classical concepts, at the center of the atom there is a nucleus consisting of protons and neutrons, and electrons each rotate around the nucleus in their own orbit.

Atomic radius in physics

Since in this model of the structure of an atom, electrons are spatially limited particles, i.e., corpuscles, it is logical to consider the atomic radius (a.r.) to be the distance from its nucleus to the farthest, or outer, orbit in which the so-called valence electrons rotate.

However, according to modern quantum mechanical ideas, this parameter cannot be determined as unambiguously as is done in the classical model. Here electrons are no longer represented as particle-corpuscles, but acquire the properties of waves, that is, spatially unlimited objects. In such a model, it is simply impossible to accurately determine the position of the electron. Here this particle is already represented in the form of an electron orbital, the density of which varies depending on the distance to the atomic nucleus.

So, in the modern model of the structure of the atom, its radius cannot be determined unambiguously. Therefore, in quantum physics, general chemistry, solid state physics and other related sciences, this value is today defined as the radius of a sphere in the center of which there is a nucleus, within which 90-98% of the density of the electron cloud is concentrated. In fact, this distance determines the boundaries of the atom.

If you consider the Periodic Table of Chemical Elements (Mendeleev's Table), which lists atomic radii, you can see certain patterns, which are expressed in the fact that within a period these numbers decrease from left to right, and within a group they increase from top to bottom. Such patterns are explained by the fact that within a period, when moving from left to right, the charge of an atom increases, which increases the force of attraction of electrons by it, and when moving inside a group from top to bottom, more and more electron shells are filled.

Atomic radius in chemistry and crystallography

What are the types

This characteristic varies greatly depending on what chemical bond the atom is in. Since all substances in nature overwhelmingly consist of molecules, the concept of a. R. used to determine interatomic distances in a molecule. And this characteristic depends on the properties of the atoms included in the molecule, i.e., their position in the Periodic Table of chemical elements. Having different physical and chemical properties, molecules form a huge variety of substances.

In essence, this value outlines the scope of the force of electrical attraction between the nucleus of an atom and its outer electron shells. Outside this sphere, the force of electrical attraction of a neighboring atom comes into play. Exists several types of chemical bonds between atoms in a molecule:

• covalent;
• ionic;
• metal;
• van der Waals.

According to these connections, the same will be atomic radius.

How depends on the type of chemical bond

In a covalent bond, AR is defined as half the distance between neighboring atoms in a single chemical bond X-X, and X is a non-metal, since this bond is characteristic of non-metals. For example, for halogens the covalent radius will be equal to half the internuclear distance X-X in the X2 molecule, for selenium Se and sulfur S molecules - half the X-X distance in the X8 molecule, for carbon C it will be equal to half the shortest C-C distance in a diamond crystal .

This chemical bond has the property of additivity, i.e. summation, which makes it possible to determine internuclear distances in polyatomic molecules. If the bond in the molecule is double or triple, then the covalent AR decreases, since the lengths of multiple bonds are less than single bonds.

For ionic bonds formed in ionic crystals, ionic AR values ​​are used to determine the distance between the nearest anion and cation located at the sites of the crystal lattice. This distance is defined as the sum of the radii of these ions.

Exists several ways to determine ionic radii, at which the values ​​of individual ions differ. But as a result, these methods give approximately the same values ​​of internuclear distances. These methods or systems were named after scientists who conducted relevant research in this area:

• Goldschmidt;
• Pauling;
• Belova and Bokiya;
• other scientists.

In the case of a metallic bond that occurs in metal crystals, the APs are taken to be equal to half the shortest distance between them. The metallic radius depends on the coordination number K. At K = 12, its value is conventionally taken as unity. For coordination numbers 4, 6 and 8, the metallic radii of the same element will be 0.88, 0.96 and 0.98, respectively.

If we take two different metals and compare the metallic radii of their elements, then the proximity of these values ​​to each other will mean a necessary, but not sufficient condition for the mutual solubility of these metals according to the type of substitution. For example, liquid potassium K and lithium Li do not mix under normal conditions and form two liquid layers, because their metallic radii are very different (0.236 nm and 0.155 nm, respectively), and potassium K with cesium Cs form a solid solution due to the proximity of their radii (0.236 nm and 0.268 nm).

van der Waals AR is used to determine the effective sizes of noble gas atoms, as well as the distances between the nearest atoms of the same name that belong to different molecules and are not connected by a chemical bond (for example, molecular crystals). If such atoms come close to a distance less than the sum of their van der Waals radii, strong interatomic repulsion will arise between them. These radii determine the minimum permissible boundaries of contact between two atoms belonging to neighboring molecules.

In addition, AR data are used to determine the shape of molecules, their conformations and packing in molecular crystals. The principle of “dense packing” is known, when molecules forming a crystal, enter each other with their “protrusions” and “hollows”. Based on this principle, crystallographic data are interpreted and the structures of molecular crystals are predicted.

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This helpful video will help you understand what atomic radius is.

EFFECTIVE ATOMIC RADIUS - see Radius is atomic.

Geological Dictionary: in 2 volumes. - M.: Nedra. Edited by K. N. Paffengoltz et al.. 1978 .

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Periodic properties of elements

Periodicity is expressed in the structure of the electron shell of atoms, therefore, properties that depend on the state of electrons are in good agreement with the periodic law: atomic and ionic radii, ionization energy, electron affinity, electronegativity and valence of elements. But the composition and properties of simple substances and compounds depend on the electronic structure of atoms, therefore periodicity is observed in many properties of simple substances and compounds: temperature and heat of melting and boiling, length and energy of chemical bonds, electrode potentials, standard enthalpies of formation and entropies of substances, etc. d. The periodic law covers more than 20 properties of atoms, elements, simple substances and compounds.

According to quantum mechanics, an electron can be located at any point around the nucleus of an atom, both close to it and at a considerable distance. Therefore, the boundaries of atoms are vague and indefinite. At the same time, in quantum mechanics the probability of electron distribution around the nucleus and the position of the maximum electron density for each orbital are calculated.

Orbital radius of an atom (ion)is the distance from the nucleus to the maximum electron density of the most distant outer orbital of this atom (ion).

Orbital radii (their values ​​are given in the reference book) decrease over periods, because An increase in the number of electrons in atoms (ions) is not accompanied by the appearance of new electronic layers. The electron shell of an atom or ion of each subsequent element in a period becomes denser compared to the previous one due to an increase in the charge of the nucleus and an increase in the attraction of electrons to the nucleus.

Orbital radii in groups increase because the atom (ion) of each element differs from its superior one by the appearance of a new electron layer.

The change in orbital atomic radii for five periods is shown in Fig. 13, from which it is clear that the dependence has a “sawtooth” shape characteristic of the periodic law.

Rice. 13. Dependence of orbital radius

from the atomic number of elements of the first – fifth periods.

But during periods, the decrease in the size of atoms and ions does not occur monotonically: small “bursts” and “dips” are observed in individual elements. As a rule, the “gaps” contain elements whose electronic configuration corresponds to a state of increased stability: for example, in the third period it is magnesium (3s 2), in the fourth period it is manganese (4s 2 3d 5) and zinc (4s 2 3d 10) etc.

Note. Calculations of orbital radii have been carried out since the mid-seventies of the last century thanks to the development of electronic computing technology. Previously used effective radii of atoms and ions, which are determined from experimental data on internuclear distances in molecules and crystals. It is assumed that the atoms are incompressible balls that touch their surfaces in compounds. The effective radii determined in covalent molecules are called covalent radii, in metal crystals – metal radii, in compounds with ionic bonds – ionic radii. Effective radii differ from orbital radii, but their change with atomic number is also periodic.

The division of chemical bonds into types is conditional.

A metallic bond, caused by the attraction of electrons and metal ions, has some characteristics of a covalent bond, if we take into account the overlap of the atomic orbitals of the atoms. In the formation of a hydrogen bond, in addition to electrostatic interaction, the donor-acceptor nature of the interaction plays an important role.

It is also impossible to draw a sharp boundary between ionic and covalent polar bonds. Any metal-nonmetal bond cannot be classified as ionic. It is customary to consider an ionic bond between atoms whose electronegativity difference is greater than or equal to 2 (according to the Pauling scale). For example, in sodium oxide the Na 2 O bond (3.44 – 0.93 = 2.51) is an ionic bond, and in magnesium bromide MgBr there is a covalent polar bond (2.96 – 1.31 = 1.65).

In real substances, all types of chemical bonds do not occur in their pure form. For most connections, the type of connection is intermediate. This is possible, since the nature of the chemical bond is the same - this is the electrostatic interaction of electrons and nuclei within and between atoms brought closer together at a distance, when effective overlap of electron shells occurs.

Therefore, a continuous transition between all limiting cases is possible: ionic, covalent, metallic and residual bonds. The transition can be visually represented in the form of a tetrahedron, at the vertices of which extreme representatives are placed, along the edges there are transitions between two types, and on the faces and inside the volume of the tetrahedron there are complex mixed types of connections.

Effective radii of atoms and ions

Under effective radii of atoms and ions understand the radii of action of spheres of atoms or ions, that is, the minimum distances at which the centers of spheres of atoms or ions can approach the surface of neighboring atoms.

To determine the effective radius of an atom or ion, the crystal structure is represented in the form of touching balls, the distance between which is equal to the sum of their radii. Depending on the type of chemical bond between the structural units of the crystal, there are: metallic radii, ionic radii, covalent radii and van der Waals radii.

Metal radii
Defined as half the distance between neighboring atoms obtained from X-ray diffraction analysis:

Ionic radii
To calculate the radii of ions, we proceed from the assumption that with a sufficiently large difference in the sizes of cations and anions, large anions will be in contact, and smaller cations will be located in the voids between the anions, then the anion radius will be equal to:

the radius of the cation is equal to: .

Covalent radii
Covalent radii are defined as half the interatomic distance (bond length): .

In addition, when calculating the covalent radius, the ability of some elements to form multiple bonds, which reduce the distances between atoms and the type of hybridization of the central atom, is taken into account.

Van der Waals radii are calculated for atoms that are bound to each other only by intermolecular interaction forces. Calculated as half the distance between the centers of atoms: .

Since the methods for calculating atomic and ionic radii are different, there are a large number of radius tables.

Ionic crystals

The combination of cations and anions into a crystal is carried out due to the Coulomb attraction of electric charges. In a molecule, charges interact with force. Magnitude R– distance between two ions. If this distance is infinitely far away, then the force is zero. At a finite distance, the force of interaction between two oppositely charged ions is negative, which corresponds to attraction; the ions tend to approach each other to the minimum allowable distance, which corresponds to a stable bound state. The force of interaction between two equally charged ions is positive, which corresponds to repulsion. The ions tend to fly apart and do not form a stable connection at any distance. Thus, the energy of crystal formation must be negative. This condition is realized during the formation of an ionic crystal.

There are no molecules in ionic crystals, so there are no boundaries between structural units. Ions can be thought of as charged balls whose force fields are uniformly distributed in all directions in space. Therefore, each ion can attract ions of the opposite sign to itself in any direction, therefore ionic bonding has no direction.

The interaction of two ions of opposite sign cannot lead to complete mutual compensation of their force fields. Because of this, they retain the ability to attract ions of the opposite sign in other directions. Therefore, the ionic bond is not saturated.

Cations tend to surround themselves with as many anions as possible so that the Coulomb repulsion of ions of the same sign from each other is compensated by the mutual Coulomb attraction of cations and anions. Therefore, structures with an ionic type of chemical bond are characterized by high coordination numbers and dense spherical packings. The symmetry of ionic crystals is usually high.

Crystalline substances with an ionic type of chemical bond are characterized by dielectric properties, fragility, average values ​​of hardness and density, low thermal and electrical conductivity.