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The effective radius of an atom or ion is understood as the radius of its sphere of action, and the atom (ion) is considered an incompressible ball. Using the planetary model of an atom, it is represented as a nucleus around which electrons orbit. The sequence of elements in Mendeleev's Periodic Table corresponds to the sequence of filling electron shells. The effective radius of the ion depends on the filling of the electron shells, but it is not equal to the radius of the outer orbit. To determine the effective radius, atoms (ions) in the crystal structure are represented as touching rigid balls, so that the distance between their centers is equal to the sum of the radii. Atomic and ionic radii are determined experimentally from X-ray measurements of interatomic distances and calculated theoretically based on quantum mechanical concepts.

The sizes of ionic radii obey the following laws:

1. Inside one vertical row In the periodic system, the radii of ions with the same charge increase with increasing atomic number, since the number of electron shells increases, and therefore the size of the atom.

2. For the same element, the ionic radius increases with increasing negative charge and decreases with increasing positive charge. The radius of the anion is greater than the radius of the cation, since the anion has an excess of electrons, and the cation has a deficiency. For example, for Fe, Fe 2+, Fe 3+ the effective radius is 0.126, 0.080 and 0.067 nm, respectively, for Si 4-, Si, Si 4+ the effective radius is 0.198, 0.118 and 0.040 nm.

3. The sizes of atoms and ions follow the periodicity of the Mendeleev system; exceptions are elements from No. 57 (lanthanum) to No. 71 (lutetium), where the radii of the atoms do not increase, but uniformly decrease (the so-called lanthanide contraction), and elements from No. 89 (actinium) onwards (the so-called actinide contraction).

Atomic radius chemical element depends on the coordination number. An increase in the coordination number is always accompanied by an increase in interatomic distances. In this case, the relative difference in the values ​​of atomic radii corresponding to two different coordination numbers does not depend on the type of chemical bond (provided that the type of bond in the structures with the compared coordination numbers is the same). A change in atomic radii with a change in coordination number significantly affects the magnitude of volumetric changes during polymorphic transformations. For example, when cooling iron, its transformation from a modification with a face-centered cubic lattice to a modification with a body-centered cubic lattice, which takes place at 906 o C, should be accompanied by an increase in volume by 9%, in reality the increase in volume is 0.8%. This is due to the fact that due to a change in the coordination number from 12 to 8, the atomic radius of iron decreases by 3%. That is, changes in atomic radii during polymorphic transformations largely compensate for those volumetric changes that should have occurred if the atomic radius had not changed. Atomic radii of elements can only be compared if they have the same coordination number.

Atomic (ionic) radii also depend on the type of chemical bond.

In metal bonded crystals, the atomic radius is defined as half the interatomic distance between adjacent atoms. In the case of solid solutions, metallic atomic radii change in a complex way.

The covalent radii of elements with a covalent bond are understood as half the interatomic distance between nearest atoms connected by a single covalent bond. A feature of covalent radii is their constancy in different covalent structures with the same coordination numbers. So, distances in single S-S relations in diamond and saturated hydrocarbons are the same and equal to 0.154 nm.

Ionic radii in substances with ionic bonds cannot be determined as half the sum of the distances between nearby ions. As a rule, the sizes of cations and anions differ sharply. In addition, the symmetry of the ions differs from spherical. There are several approaches to estimating the ionic radii. Based on these approaches, the ionic radii of elements are estimated, and then the ionic radii of other elements are determined from experimentally determined interatomic distances.

Van der Waals radii determine the effective sizes of noble gas atoms. In addition, van der Waals atomic radii are considered to be half the internuclear distance between the nearest identical atoms that are not connected to each other by a chemical bond, i.e. belonging to different molecules (for example, in molecular crystals).

When using atomic (ionic) radii in calculations and constructions, their values ​​should be taken from tables constructed according to one system.

Particle sizes often determine the type crystal structure, are important for understanding the course 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 balls. 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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All topics in this section:

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 it is known a large number of compounds forming 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
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

Self-test questions
Effective charges of atoms in oxides (according to N. S. Akhmetov)

Oxide Na2O MgO Al2O3 SiO2 P2O5 SO
1. What is the effective charge of an atom?

Self-test questions
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?
The amount of energy is the most important characteristic of a bond, determining the resistance of substances to heat, lighting, mechanical stress, reactions with other substances[†]. Exist various methods uh

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 patterns of structure and properties of some simple substances and the simplest compounds, defined electronic structure

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.. Atomic radii

atomic radii characteristics that make it possible to approximately estimate interatomic (internuclear) distances in molecules and crystals. Atomic radii are on the order of 0.1 nm. Determined mainly from X-ray data.

ATOMIC RADIUS
ATOMIC RADIUS, characteristics that allow one to approximately estimate interatomic (internuclear) distances in molecules and crystals. (The effective radius of an atom or ion is understood as the radius of its sphere of action, and the atom (ion) is considered an incompressible ball. Using the planetary model of an atom, it is represented as a nucleus around which in orbits cm. ORBITALS)
electrons rotate. The sequence of elements in Mendeleev's Periodic Table corresponds to the sequence of filling electron shells. The effective radius of the ion depends on the filling of the electron shells, but it is not equal to the radius of the outer orbit. To determine the effective radius, atoms (ions) in the crystal structure are represented as touching rigid balls, so that the distance between their centers is equal to the sum of the radii. Atomic and ionic radii are determined experimentally from X-ray measurements of interatomic distances and calculated theoretically based on quantum mechanical concepts.
1. Within one vertical row of the periodic table, the radii of ions with the same charge increase with increasing atomic number, since the number of electron shells, and therefore the size of the atom, increases.
2. For the same element, the ionic radius increases with increasing negative charge and decreases with increasing positive charge. The radius of the anion is greater than the radius of the cation, since the anion has an excess of electrons, and the cation has a deficiency. For example, for Fe, Fe 2+, Fe 3+ the effective radius is 0.126, 0.080 and 0.067 nm, respectively, for Si 4-, Si, Si 4+ the effective radius is 0.198, 0.118 and 0.040 nm.
3. The sizes of atoms and ions follow the periodicity of the Mendeleev system; exceptions are elements from No. 57 (lanthanum) to No. 71 (lutetium), where the radii of the atoms do not increase, but uniformly decrease (the so-called lanthanide contraction), and elements from No. 89 (actinium) onwards (the so-called actinide contraction).
The atomic radius of a chemical element depends on the coordination number (The effective radius of an atom or ion is understood as the radius of its sphere of action, and the atom (ion) is considered an incompressible ball. Using the planetary model of an atom, it is represented as a nucleus around which in orbits COORDINATION NUMBER). An increase in the coordination number is always accompanied by an increase in interatomic distances. In this case, the relative difference in the values ​​of atomic radii corresponding to two different coordination numbers does not depend on the type of chemical bond (provided that the type of bond in the structures with the compared coordination numbers is the same). A change in atomic radii with a change in coordination number significantly affects the magnitude of volumetric changes during polymorphic transformations. For example, when cooling iron, its transformation from a modification with a face-centered cubic lattice to a modification with a body-centered cubic lattice, which takes place at 906 o C, should be accompanied by an increase in volume by 9%, in reality the increase in volume is 0.8%. This is due to the fact that due to a change in the coordination number from 12 to 8, the atomic radius of iron decreases by 3%. That is, changes in atomic radii during polymorphic transformations largely compensate for those volumetric changes that should have occurred if the atomic radius had not changed. Atomic radii of elements can only be compared if they have the same coordination number.
Atomic (ionic) radii also depend on the type of chemical bond.
In metal bonded crystals (The effective radius of an atom or ion is understood as the radius of its sphere of action, and the atom (ion) is considered an incompressible ball. Using the planetary model of an atom, it is represented as a nucleus around which in orbits METAL LINK) atomic radius is defined as half the interatomic distance between nearest atoms. In the case of solid solutions (The effective radius of an atom or ion is understood as the radius of its sphere of action, and the atom (ion) is considered an incompressible ball. Using the planetary model of an atom, it is represented as a nucleus around which in orbits SOLID SOLUTIONS) metallic atomic radii vary in complex ways.
The covalent radii of elements with a covalent bond are understood as half the interatomic distance between nearest atoms connected by a single covalent bond. A feature of covalent radii is their constancy in different covalent structures with the same coordination numbers. Thus, the distances in single C-C bonds in diamond and saturated hydrocarbons are the same and equal to 0.154 nm.
Ionic radii in substances with ionic bonds (The effective radius of an atom or ion is understood as the radius of its sphere of action, and the atom (ion) is considered an incompressible ball. Using the planetary model of an atom, it is represented as a nucleus around which in orbits IONIC BOND) cannot be determined as half the sum of the distances between nearby ions. As a rule, the sizes of cations and anions differ sharply. In addition, the symmetry of the ions differs from spherical. There are several approaches to estimating the ionic radii. Based on these approaches, the ionic radii of elements are estimated, and then the ionic radii of other elements are determined from experimentally determined interatomic distances.
Van der Waals radii determine the effective sizes of noble gas atoms. In addition, van der Waals atomic radii are considered to be half the internuclear distance between the nearest identical atoms that are not connected to each other by a chemical bond, i.e. belonging to different molecules (for example, in molecular crystals).
When using atomic (ionic) radii in calculations and constructions, their values ​​should be taken from tables constructed according to one system.

encyclopedic Dictionary. 2009 .

See what “atomic radii” are in other dictionaries:

Characteristics of atoms that make it possible to approximately estimate interatomic (internuclear) distances in molecules and crystals. Atoms do not have clear boundaries, however, according to the concepts of quantum. mechanics, the probability of finding an electron for a certain distance from the core... ... Physical encyclopedia

Characteristics that allow one to approximately estimate interatomic (internuclear) distances in molecules and crystals. Determined mainly from X-ray structural analysis data... Big Encyclopedic Dictionary

Effective characteristics of atoms, allowing to approximately estimate the interatomic (internuclear) distance in molecules and crystals. According to the concepts of quantum mechanics, atoms do not have clear boundaries, but the probability of finding an electron... ... Chemical encyclopedia

Characteristics of atoms that make it possible to approximately estimate interatomic distances in substances. According to quantum mechanics, the atom has no definite boundaries, but the probability of finding an electron at a given distance from the nucleus of the atom, starting from... ... Great Soviet Encyclopedia

One of the most important characteristics chemical elements involved in the formation of a chemical bond is the size of the atom (ion): with its increase, the strength of interatomic bonds decreases. The size of an atom (ion) is usually determined by the value of its radius or diameter. Since an atom (ion) does not have clear boundaries, the concept of “atomic (ionic) radius” implies that 90–98% of the electron density of an atom (ion) is contained in a sphere of this radius. Knowing the values ​​of atomic (ionic) radii allows one to estimate internuclear distances in crystals (that is, the structure of these crystals), since for many problems the shortest distances between the nuclei of atoms (ions) can be considered the sum of their atomic (ionic) radii, although such additivity is approximate and is satisfied not in all cases.

Under atomic radius chemical element (about the ionic radius, see below) involved in the formation of a chemical bond, in the general case it was agreed to understand half the equilibrium internuclear distance between the nearest atoms in the crystal lattice of the element. This concept, which is very simple if we consider atoms (ions) in the form of hard balls, actually turns out to be complex and often ambiguous. The atomic (ionic) radius of a chemical element is not a constant value, but varies depending on a number of factors, the most important of which are the type of chemical bond

and coordination number.

If the same atom (ion) in different crystals forms different types chemical bond, then it will have several radii - covalent in a crystal with a covalent bond; ionic in a crystal with an ionic bond; metallic in metal; van der Waals in a molecular crystal. The influence of the type of chemical bond can be seen in the following example. In diamond, all four chemical bonds are covalent and are formed sp 3-hybrids, so all four neighbors of a given atom are on the same

the same distance from it ( d= 1.54 A˚) and the covalent radius of carbon in diamond will be

is equal to 0.77 A˚. In an arsenic crystal, the distance between atoms connected by covalent bonds ( d 1 = 2.52 A˚), significantly less than between atoms bound by van der Waals forces ( d 2 = 3.12 A˚), so As will have a covalent radius of 1.26 A˚ and a van der Waals radius of 1.56 A˚.

The atomic (ionic) radius also changes very sharply when the coordination number changes (this can be observed during polymorphic transformations of elements). The lower the coordination number, the lower the degree of filling of space with atoms (ions) and the smaller the internuclear distances. An increase in the coordination number is always accompanied by an increase in internuclear distances.

From the above it follows that the atomic (ionic) radii of different elements participating in the formation of a chemical bond can be compared only when they form crystals in which the same type of chemical bond is realized, and these elements have the same coordination numbers in the formed crystals .

Let us consider the main features of atomic and ionic radii in more detail.

Under covalent radii of elements It is customary to understand half the equilibrium internuclear distance between nearest atoms connected by a covalent bond.

A feature of covalent radii is their constancy in different “covalent structures” with the same coordination number Z j. In addition, covalent radii, as a rule, are additively related to each other, that is, the A–B distance is equal to half the sum of the A–A and B–B distances in the presence of covalent bonds and the same coordination numbers in all three structures.

There are normal, tetrahedral, octahedral, quadratic and linear covalent radii.

The normal covalent radius of an atom corresponds to the case when the atom forms as many covalent bonds as corresponds to its place in periodic table: for carbon - 2, for nitrogen - 3, etc. This gives different meanings normal radii depending on the multiplicity (order) of the bond (single bond, double, triple). If a bond is formed when hybrid electron clouds overlap, then they speak of tetrahedral

(Z k = 4, sp 3-hybrid orbitals), octahedral ( Z k = 6, d 2sp 3-hybrid orbitals), quadratic ( Z k = 4, dsp 2-hybrid orbitals), linear ( Z k = 2, sp-hybrid orbitals) covalent radii.

It is useful to know the following about covalent radii (the values ​​of covalent radii for a number of elements are given in).

1. Covalent radii, unlike ionic radii, cannot be interpreted as the radii of atoms having a spherical shape. Covalent radii are used only to calculate internuclear distances between atoms united by covalent bonds, and do not say anything about the distances between atoms of the same type that are not covalently bonded.

2. The magnitude of the covalent radius is determined by the multiplicity of the covalent bond. A triple bond is shorter than a double bond, which in turn is shorter than a single bond, so the covalent radius of a triple bond is smaller than the covalent radius of a double bond, which is smaller

single. It should be kept in mind that the order of multiplicity of the bond does not have to be an integer. It can also be fractional if the bond is of a resonant nature (benzene molecule, Mg2 Sn compound, see below). In this case, the covalent radius has an intermediate value between the values ​​corresponding to entire orders of bond multiplicity.

3. If the bond is of a mixed covalent-ionic nature, but with a high degree of covalent component of the bond, then the concept of covalent radius can be introduced, but the influence of the ionic component of the bond on its value cannot be neglected. In some cases, this influence can lead to a significant decrease in the covalent radius, sometimes down to 0.1 A˚. Unfortunately, attempts to predict the magnitude of this effect in different

cases have not yet been successful.

4. The magnitude of the covalent radius depends on the type of hybrid orbitals that take part in the formation of a covalent bond.

Ionic radii, naturally, cannot be determined as half the sum of the distances between the nuclei of the nearest ions, since, as a rule, the sizes of cations and anions differ sharply. In addition, the symmetry of the ions may differ slightly from spherical. However, for real ionic crystals under ionic radius It is customary to understand the radius of the ball by which the ion is approximated.

Ionic radii are used to approximate internuclear distances in ionic crystals. It is believed that the distances between the nearest cation and anion are equal to the sum of their ionic radii. The typical error in determining internuclear distances through ionic radii in such crystals is ≈0.01 A˚.

There are several systems of ionic radii, differing in the values ​​of the ionic radii of individual ions, but leading to approximately the same internuclear distances. The first work on determining ionic radii was carried out by V. M. Goldshmit in the 20s of the 20th century. In it, the author used, on the one hand, internuclear distances in ionic crystals, measured by X-ray structural analysis, and, on the other hand, the values ​​of ionic radii F− and O2−, determined

by refractometry method. Most other systems also rely on internuclear distances in crystals determined by diffraction methods and on some “reference” values ​​of the ionic radius of a particular ion. In the most widely known system

Pauling this reference value is the ionic radius of the peroxide ion O2−, equal to

1.40 A˚ This value for O2− is in good agreement with theoretical calculations. In the system of G.B. Bokiy and N.V. Belov, which is considered one of the most reliable, the ionic radius of O2− is taken equal to 1.36 A˚.

In the 70–80s, attempts were made to directly determine the radii of ions by measuring the electron density using X-ray structural analysis methods, provided that the minimum electron density on the line connecting the nuclei is taken as the ion boundary. It turned out that this direct method leads to overestimated values ​​of the ionic radii of cations and to underestimated values ​​of the ionic radii of anions. In addition, it turned out that the values ​​of ionic radii determined directly cannot be transferred from one compound to another, and the deviations from additivity are too large. Therefore, such ionic radii are not used to predict internuclear distances.

It is useful to know the following about ionic radii (the tables below give the values ​​of ionic radii according to Bokiy and Belov).

1. The ionic radius for ions of the same element varies depending on its charge, and for the same ion it depends on the coordination number. Depending on the coordination number, tetrahedral and octahedral ionic radii are distinguished.

2. Within one vertical row, more precisely within one group, periodic

systems, the radii of ions with the same charge increase with increasing atomic number of the element, since the number of shells occupied by electrons increases, and hence the size of the ion.

3. For positively charged ions of atoms from the same period, the ionic radii decrease rapidly with increasing charge. The rapid decrease is explained by the action in one direction of two main factors: the strong attraction of “their” electrons by the cation, the charge of which increases with increasing atomic number; an increase in the strength of interaction between the cation and the surrounding anions with increasing charge of the cation.

4. For negatively charged ions of atoms from the same period, the ionic radii increase with increasing negative charge. The two factors discussed in the previous paragraph act in opposite directions in this case, and the first factor predominates (an increase in the negative charge of an anion is accompanied by an increase in its ionic radius), therefore the increase in ionic radii with increasing negative charge occurs significantly slower than the decrease in previous case.

5. For the same element, that is, with the same initial electronic configuration, the radius of the cation is less than that of the anion. This is due to a decrease in the attraction of external “additional” electrons to the anion core and an increase in the screening effect due to internal electrons (the cation has a lack of electrons, and the anion has an excess).

6. The sizes of ions with the same charge follow the periodicity of the periodic table. However, the ionic radius is not proportional to the nuclear charge Z, which is due to the strong attraction of electrons by the nucleus. In addition, an exception to the periodic dependence are lanthanides and actinides, in whose series the radii of atoms and ions with the same charge do not increase, but decrease with increasing atomic number (the so-called lanthanide compression and actinide compression).11

11Lanthanide compression and actinide compression are due to the fact that in lanthanides and actinides the electrons added with increasing atomic number fill internal d And f-shells with a principal quantum number less than the principal quantum number of a given period. Moreover, according to quantum mechanical calculations in d and especially in f states the electron is much closer to the nucleus than in s And p states of a given period with a large quantum number, therefore d And f-electrons are located in the internal regions of the atom, although the filling of these states with electrons ( we're talking about about electronic levels in energy space) happens differently.

Metal radii are considered equal to half the shortest distance between the nuclei of atoms in the crystallizing structure of the metal element. They depend on the coordination number. If we take the metallic radius of any element at Z k = 12 per unit, then with Z k = 8, 6 and 4 metal radii of the same element will be respectively equal to 0.98; 0.96; 0.88. Metal radii have the property of additivity. Knowledge of their values ​​makes it possible to approximately predict the parameters of the crystal lattices of intermetallic compounds.

The atomic radii of metals are characterized by following features(data on the values ​​of the atomic radii of metals can be found in).

1. The metallic atomic radii of transition metals are generally smaller than the metallic atomic radii of non-transition metals, reflecting the greater bond strength in transition metals. This feature is due to the fact that metals of transition groups and those closest to them in periodic table metals have electronic d-shells, and electrons in d-states can take part in the formation of chemical bonds. The strengthening of the bond may be due partly to the appearance of a covalent component of the bond and partly to the van der Waals interaction of the ionic cores. In iron and tungsten crystals, for example, electrons in d-states make a significant contribution to the binding energy.

2. Within one vertical group, as we move from top to bottom, the atomic radii of metals increase, which is due to a consistent increase in the number of electrons (the number of shells occupied by electrons increases).

3. Within one period, more precisely, starting from the alkali metal to the middle of the group of transition metals, the atomic metal radii decrease from left to right. In the same sequence it increases electric charge atomic nucleus and the number of electrons in the valence shell increases. As the number of bonding electrons per atom increases, the metallic bond becomes stronger, and at the same time, due to the increase in the charge of the nucleus, the attraction of the core (internal) electrons by the nucleus increases, therefore the value of the metallic atomic radius decreases.

4. Transition metals of groups VII and VIII from the same period, to a first approximation, have almost identical metallic radii. Apparently, when it comes to elements having 5 and larger number d-electrons, an increase in the charge of the nucleus and the associated effects of attraction of core electrons, leading to a decrease in the atomic metal radius, are compensated by the effects caused by the increasing number of electrons in the atom (ion) that are not involved in the formation of a metal bond, and leading to an increase in the metal radius (increases number of states occupied by electrons).

5. An increase in radii (see point 2) for transition elements, which occurs during the transition from the fourth to the fifth period, is not observed for transition elements at

transition from the fifth to the sixth period; metallic atomic radii of the corresponding (comparison is vertical) elements in these two recent periods almost the same. Apparently, this is due to the fact that the elements located between them have a relatively deep-lying f-shell, so the increase in nuclear charge and the associated attractive effects are more significant than the effects associated with an increasing number of electrons (lanthanide compression).

6. Usually metallic radii are much larger than ionic radii, but do not differ so significantly from the covalent radii of the same elements, although without exception they are all larger than covalent radii. The large difference in the values ​​of the metallic atomic and ionic radii of the same elements is explained by the fact that the bond, which owes its origin to almost free conduction electrons, is not strong (hence the observed relatively large interatomic distances in the metal lattice). The significantly smaller difference in the values ​​of the metallic and covalent radii of the same elements can be explained if we consider metal bond as some special “resonant” covalent bond.

Under van der Waals radius It is customary to understand half the equilibrium internuclear distance between nearest atoms connected by a van der Waals bond. Van der Waals radii determine the effective sizes of noble gas atoms. In addition, as follows from the definition, the van der Waals atomic radius can be considered half the internuclear distance between the nearest atoms of the same name, connected by a van der Waals bond and belonging to different molecules (for example, in molecular crystals). When atoms approach each other at a distance less than the sum of their van der Waals radii, strong interatomic repulsion occurs. Therefore, van der Waals atomic radii characterize the minimum permissible contacts of atoms belonging to different molecules. Data on the values ​​of van der Waals atomic radii for some atoms can be found in).

Knowledge of van der Waals atomic radii allows one to determine the shape of molecules and their packing in molecular crystals. Van der Waals radii are much larger than all the radii listed above for the same elements, which is explained by the weakness of van der Waals forces.

Atomic ions; have the meaning of the radii of the spheres representing these atoms or ions in molecules or crystals. Atomic radii make it possible to approximately estimate internuclear (interatomic) distances in molecules and crystals.

The electron density of an isolated atom decreases rapidly as the distance to the nucleus increases, so the radius of an atom could be defined as the radius of the sphere in which the bulk (for example, 99%) of the electron density is concentrated. However, to estimate internuclear distances, it turned out to be more convenient to interpret atomic radii differently. This led to the emergence of different definitions and systems of atomic radii.

The covalent radius of an X atom is defined as half the length of a simple chemical bond X—X. Thus, for halogens, covalent radii are calculated from the equilibrium internuclear distance in the X 2 molecule, for sulfur and selenium - in S 8 and Se 8 molecules, for carbon - in a diamond crystal. The exception is the hydrogen atom, for which the covalent atomic radius is taken to be 30 pm, while half the internuclear distance in the H 2 molecule is 37 pm. For compounds with a covalent bond, as a rule, the additivity principle is satisfied (the length of the X-Y bond is approximately equal to the sum of the atomic radii of the X and Y atoms), which makes it possible to predict the bond lengths in polyatomic molecules.

Ionic radii are defined as values ​​whose sum for a pair of ions (for example, X + and Y -) is equal to the shortest internuclear distance in the corresponding ionic crystals. There are several systems of ionic radii; systems differ in numerical values ​​for individual ions depending on which radius and which ion is taken as the basis when calculating the radii of other ions. For example, according to Pauling, this is the radius of the O 2- ion, taken equal to 140 pm; according to Shannon - the radius of the same ion, taken equal to 121 pm. Despite these differences, different systems when calculating internuclear distances in ionic crystals they lead to approximately the same results.

Metallic radii are defined as half the shortest distance between atoms in a metal's crystal lattice. For metal structures that differ in the type of packing, these radii are different. The closeness of the atomic radii of various metals often indicates the possibility of the formation of solid solutions by these metals. The additivity of radii allows one to predict the parameters of crystal lattices of intermetallic compounds.

Van der Waals radii are defined as quantities whose sum is equal to the distance to which two chemically unrelated atoms of different molecules or different groups of atoms of the same molecule can approach each other. On average, van der Waals radii are approximately 80 pm larger than covalent radii. Van der Waals radii are used to interpret and predict the stability of molecular conformations and the structural ordering of molecules in crystals.

Lit.: Housecroft K., Constable E. Modern course general chemistry. M., 2002. T. 1.