For s- and p-elements, the change in radii both in periods and in subgroups is more pronounced than for d- and f-elements, since the d- and f-electrons are internal. Sizes of atoms and ions (radii of atoms and ions). 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.

Therefore, the atom is assigned a certain radius, believing that the vast majority of the electron density (about 90 percent) is contained in the sphere of this radius. The radius of an atom is the boundaries of the electron cloud. The change in atomic radii in the periodic system is periodic in nature, as it is determined by the properties of the electron shells. The radii of atoms connected to each other are called effective. Effective radii are determined by studying the structure of molecules and crystals.

The radius of an atom refers to the distance between the nucleus of a given atom and its outermost electron orbit. Today, the generally accepted unit of measurement for atomic radius is the picometer (pm).

The structure of planet Earth is divided into a core, mantle and crust. The core is the central part located farthest from the surface. In addition, in the structure of the Earth's core there is a solid inner core, with a radius of about 1300 kilometers, and a liquid outer core with a radius of about 2200 kilometers. To estimate the radius of the planet, indirect geochemical and geophysical methods are used.

The dependence of the core mass on the radius is not linear. This is due to the fact that electrons, like planets solar system, move around the Sun - the nuclei of an atom. The orbits of electron motion are constant.

This created difficulties in the construction of the track and created incredible noise. Next... ATOMIC RADIUS is a characteristic of an atom that allows one to approximately estimate interatomic (internuclear) distances in molecules and crystals. Since atoms do not have clear boundaries, when introducing the concept of “A. r." imply that 90-98% of the electron density of an atom is contained in a sphere of this radius.

Ionic radii are used for approximate estimates of internuclear distances in ionic crystals. It is believed that the distance between the nearest cation and anion is equal to the sum of their ionic radii. A. r. cations and to underestimated values ​​of A. r. anions. When atoms approach each other at a distance less than the sum of their van der Waals radii, strong interatomic repulsion occurs.

6.6. Features of the electronic structure of atoms of chromium, copper and some other elements

Knowledge of van der Waals A. r. allows you to determine the shape of molecules, the conformation of molecules and their packaging in molecular crystals. Using this principle, it is possible to interpret the available crystallographic data, and in some cases, predict the structure of molecular crystals.

2.6. Periodicity of atomic characteristics

We know (pp. 31, 150) that even at temperature absolute zero nuclear vibrations occur in molecules and crystals. Molybdenum and tungsten, due to lanthanide compression, have close radii of atoms and ions E +. This explains the greater similarity in the properties of Mo and III among themselves than between each of them and chromium.

Changing the properties of diagonal elements

As shown in table. 14, the radii of rare earth atoms and ions naturally decrease from La to Lu. This phenomenon is known as lanthanide compression. The reason for compression is the screening of one electron by another in the same shell.

Until now, secondary periodicity has been noted mainly for elements of the main subgroups of Fig. 62 indicates that it exists for s-electrons and in additional subgroups. The concept of coordination theory is used not only when considering the environment of atoms in crystals, but also in free molecules (in gases) and in polyatomic ions existing in solutions.

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.

Particle identity principle

Atomic and ionic radii are determined experimentally from X-ray measurements of interatomic distances and calculated theoretically based on quantum mechanical concepts. 2. For the same element, the ionic radius increases with increasing negative charge and decreases with increasing positive charge. 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 the case of solid solutions, metallic atomic radii change in a complex way. A feature of covalent radii is their constancy in different covalent structures with the same coordination numbers. Ionic radii in substances with ionic bonds cannot be determined as half the sum of the distances between nearby ions.

Electron affinity is not known for all atoms. In many cases, the shortest distance between two atoms is indeed approximately equal to the sum of the corresponding atomic radii. The radius of a free atom is taken to be the position of the main maximum of the density of the outer electron shells. The radii of atoms and ions depend on the c.n. The value of the radius Ha or ri for a different c.n. can be found by multiplying g for a given number. by a certain ratio.

Determining atomic radii also poses some problems. Firstly, an atom is not a sphere with a strictly defined surface and radius. Recall that an atom is a nucleus surrounded by a cloud of electrons. The probability of detecting an electron as it moves away from the nucleus gradually increases to a certain maximum, and then gradually decreases, but becomes equal to zero only at infinity long distance. Secondly, if we nevertheless choose some condition for determining the radius, such a radius still cannot be measured experimentally.

The experiment allows us to determine only internuclear distances, in other words, bond lengths (and then with certain reservations given in the caption to Fig. 2.21). To determine them, X-ray diffraction analysis or the electron diffraction method (based on electron diffraction) is used. The radius of an atom is assumed to be equal to half the smallest internuclear distance between identical atoms.

Vander Waals radii. For unbonded atoms, half of the smallest internuclear distance is called the van der Waals radius. This definition is illustrated by Fig. 2.22.

Rice. 2.21. Link length. Because molecules continually vibrate, the internuclear distance, or bond length, does not have a fixed value. This drawing schematically represents the linear vibration of a simple diatomic molecule. Vibrations do not allow bond length to be defined simply as the distance between the centers of two bonded atoms. More precise definition looks like this: bond length is the distance between bonded atoms, measured between the centers of mass of two atoms and corresponding to the minimum bond energy. The minimum energy is shown on the Morse curve (see Fig. 2.1).

Table 2.6. Densities of carbon and sulfur allotropes Table 2.7. Length of carbon-carbon bonds

Covalent radii.Covalent radius is defined as half the internuclear distance (bond length) between two identical atoms connected to each other by a covalent bond(Fig. 2.22, b). As an example, let's take the chlorine molecule Cl2, the bond length of which is 0.1988 nm. The covalent radius of chlorine is assumed to be 0.0944 nm.

Knowing the covalent radius of an atom of one element, you can calculate the covalent radius of an atom of another element. For example, the experimentally determined value of the C-Cl bond length in CH3Cl is 0.1767 nm. Subtracting the covalent radius of chlorine (0.0994 nm) from this value, we find that the covalent radius of carbon is 0.0773 nm. This calculation method is based on the principle of additivity, according to which atomic radii obey simple law addition. Thus, the C-Cl bond length is the sum of the covalent radii of carbon and chlorine. The principle of additivity applies only to simple covalent bonds. Double and triple covalent bonds are shorter (Table 2.7).

The length of a simple covalent bond also depends on its environment in the molecule. For example, length C-H bonds varies from 0.1070 nm at the trisubstituted carbon atom to 0.115 nm in the CH3CN compound.

Metal radii. The metallic radius is assumed to be equal to half the internuclear distance between neighboring ions in crystal lattice metal (Fig. 2.22, c). The term atomic radius usually refers to the covalent radius of atoms of non-metallic elements, and the term metallic radius to atoms of metallic elements.

Ionic radii. The ionic radius is one of two parts of the internuclear distance between adjacent monoatomic (simple) ions in a crystalline ionic compound (salt). Determining the ionic radius is also fraught with considerable problems, since interionic distances are measured experimentally, and not the ionic radii themselves. The interion distances depend on the packing of ions in the crystal lattice. In Fig. 2.23 shows three possible ways packing of ions in a crystal lattice. Unfortunately, the experimentally measured interionic distances

Rice. 2.23. Ionic radii, c-anions touch each other, but cations do not touch anions; b-cations are in contact with anions, but the anions are not in contact with each other; into the conventionally accepted arrangement of ions, in which cations are in contact with anions and anions are in contact with each other. Distance a is determined experimentally. It is taken to be twice the radius of the anion. This allows us to calculate the interionic distance b, which is the sum of the radii of the anion and cation. Knowing the interionic distance b, we can calculate the radius of the cation.

do not allow us to judge which of these three packaging methods is actually carried out in each specific case. The problem is to find the proportion in which to divide the interionic distance into two parts corresponding to the radii of the two ions, in other words, to decide where one ion actually ends and where the other begins. As shown, for example, in Fig. 2.12, this question cannot be resolved even by the electron density maps of salts. To overcome this difficulty, it is usually assumed that: 1) the interionic distance is the sum of two ionic radii, 2) the ions are spherical in shape, and 3) adjacent spheres are in contact with each other. The last assumption corresponds to the ion packing method shown in Fig. 2.23, f. If one ionic radius is known, other ionic radii can be calculated based on the principle of additivity.

Radius matching various types. In table 2.8 shows the values ​​of radii of various types for three elements of the 3rd period. It is easy to see that the largest values ​​belong to the anion and van der Waals radii. In Fig. 11.9 compares the sizes of ions and atoms for all elements of the 3rd period, with the exception of argon. The sizes of atoms are determined by their covalent radii. It should be noted that cations are smaller than atoms, and anions are large sizes than atoms of the same elements. For each element from all types of radii smallest value always belongs to the cation radius.

Table 2.8. Comparison of atomic radii of different types

Experimental determination. To determine the shape of simple molecules and polyatomic ions, and more precisely, bond lengths and bond angles (angles between bonds), a variety of experimental methods are used. These include microwave spectroscopy, as well as methods for studying the diffraction of x-rays (x-ray diffraction), neutrons (neutron diffraction) or electrons (electron diffraction). The next chapter details how crystal structure can be determined using X-ray diffraction. However, electron diffraction (a method for studying electron diffraction) is usually used to determine the shape of simple molecules in the gas phase. This method is based on the use of the wave properties of electrons. A beam of electrons is passed through a sample of the gas under study. Gas molecules scatter electrons, resulting in a diffraction pattern. By analyzing it, it is possible to determine bond lengths and bond angles in molecules. This method is similar to that used in the analysis of the diffraction pattern formed by the scattering of X-rays.

Atoms do not have clear boundaries, but the probability of finding an electron associated with the nucleus of a given atom at a certain distance from that nucleus decreases rapidly with increasing distance. Therefore, the atom is assigned a certain radius, believing that the vast majority of the electron density (about 90 percent) is contained in the sphere of this radius.

A typical estimate of the radius of an atom is 1 angstrom (1 Å), equal to 10 -10 m.

Atomic radius and internuclear distances

In many cases, the shortest distance between two atoms is indeed approximately equal to the sum of the corresponding atomic radii. Depending on the type of bond between atoms, metallic, ionic, covalent and some other atomic radii are distinguished.

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atomic radius

The branch of physics that studies the internal structure of atoms. Atoms, originally thought to be indivisible, are complex systems. They have a massive core consisting of protons and neutrons, around which they move in empty space... ... Collier's Encyclopedia

Bohr radius (Bohr radius), the radius of the electron orbit of a hydrogen atom closest to the nucleus in the atomic model proposed by Niels Bohr in 1913 and which was the forerunner of quantum mechanics. In the model, electrons move in circular orbits... ... Wikipedia

Van der Waals radii determine effective dimensions noble gas atoms. In addition, van der Waals radii are considered to be half the internuclear distance between the nearest atoms of the same name that are not chemically connected... ... Wikipedia

atomic radius- atomo spindulys statusas T sritis fizika atitikmenys: engl. atomic radius vok. Atomradius, m rus. atomic radius, m; atomic radius, m pranc. rayon atomique, m; rayon de l'atome, m … Fizikos terminų žodynas

Radius a 0 of the first (closest to the nucleus) electron orbit in a hydrogen atom, according to the atomic theory of N. Bohr (1913); a 0= 5.2917706(44)*10 11 m. In quantum mech. atomic theory B. r. corresponds to the distance from the core, to the rum with Naib. it is possible... ... Chemical encyclopedia

The radius of the first (closest to the nucleus) electron orbit in a hydrogen atom, according to N. Bohr’s theory of the atom; denoted by the symbol a0 or a. B. r. equal to (5.29167±0.00007)×10 9 cm = 0.529 Å; expressed through universal constants: а0 = ћ2/me2, where... Great Soviet Encyclopedia

Radius ao of the first (closest to the nucleus) electron orbit in a hydrogen atom, according to N. Bohr’s theory of atomic structure (1913); a0 = 0.529 x 10 10 m = 0.529 A ... Natural science. Encyclopedic Dictionary

Bohr model of a hydrogen-like atom (Z nuclear charge), where a negatively charged electron is contained in an atomic shell surrounding a small, positively charged atomic nucleus... Wikipedia

Books

• Quantum mechanics in the general theory of relativity, A.K. Gorbatsevich. The monograph shows that the general covariant Dirac equation can be considered as a special coordinate representation (with non-orthonormal basis vectors in the Hilbert...

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 structural analysis 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.
The sizes of ionic radii obey the following laws:
1. Inside one vertical row periodic table The radii of ions with the same charge increase with increasing atomic number, since the number of electron shells increases, and hence 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).
The atomic radius of a chemical element depends on the coordination number (cm. 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 (cm. METAL LINK) atomic radius is defined as half the interatomic distance between nearest atoms. In the case of solid solutions (cm. 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. 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 (cm. 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 magnitude of 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.

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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, an atom has no definite boundaries, but the probability of finding an electron at a given distance from the nucleus of an atom, starting from... ... Great Soviet Encyclopedia

Characteristics that allow an approximate assessment of interatomic (internuclear) distances in molecules and crystals. A. r. are on the order of 0.1 nm. Defined by ch. arr. from X-ray structural analysis data... Natural science. Encyclopedic Dictionary

At the end of the article, you will be able to describe- Definition of atomic radius, periodic table trend, Largest atomic radius, Atomic radius chart. Let's start discussing one by one.

Atomic Radius Definition

The general picture of the atom in our minds is that of a sphere. If this is considered correct, then this definition is:

However, there is no certainty about the exact position of the electrons at any given time. Theoretically, an electron may at one time be very close to the nucleus, while at other times it may be far from the nucleus. Also, it is impossible to measure the exact value of the atomic radius of an element's atom, since the atom is very much smaller in size.

Why is there no way to accurately determine?
A. It is not possible to isolate one atom.
B. It is impossible to measure the exact distance of an atom that does not have a clearly defined shape or boundary and the probability of an electron is zero level, even at a great distance from the nucleus.
C.It may change due to influence environment and many other reasons.

However, we can express various shapes atom depending on the nature of the bond between atoms. Despite the above limitations, there are three operational concepts:

Covalent Radius

In homoatomic molecules (containing the same type of atoms), the covalent radius is defined as

Van der Waals radius

In fact, van der Waals forces are weak, their magnitude (power) of attraction is less, in gaseous and in liquid state substances. Therefore, the radius is determined in the solid state when the magnitude of the force is expected to be at its maximum.

• The van der Waal value is greater than the covalent radius.
• For example, the van der Waal strength of chlorine is 180 m, and the covalent radius is 99 pm (picometer).

Metal radius

because metal bond is weaker than covalent bond internuclear molecular distance between two atoms in metal connection makes up more covalent bonds.

• A metal bond is more than a covalent bond.

Periodic Atomic Radius Table Trend

During the study, Scientists discovered the smallest particle of matter and named it as an atom. Different atoms of different elements show different chemical and physical properties. This can be seen when atomic radius changes in the periodic table trends. Changing atomic radii has a great influence on the behavior of atoms in the process chemical reaction. This is because it affects ionization energy, chemical reactivity, and many other factors.

It should be noted that the atomic radius of the last element in each period is quite large. Because noble gases are considered to have a van der Waal radius, which always has a higher value than the covalent radius. When we compare three atomic radii the order of forces

• Van der Waal >Metallic radius>Covalent

Atomic Radius Trend

During the period the number of shells remains unchanged, but the nuclear charge increases. This is a consequence of an increase in the force of attraction to the nucleus, which causes a reduction in size.

• Nuclear attractionα 1/ Atomic radii.
• Principal quantum number( N) α Atomic radii.
• Screening effect α Atomic radii.
• Number of bondsα 1/ Atomic radii.

Note: Atomic Radium is plural from the radius of the atom.

In a group, as you move from the top to the bottom in a group, the atomic radii increase with increasing atomic number, this is due to the fact that the amount of energy of the shells increases.

Largest atomic radius

• Hydrogen is the smallest size.
• Francium, having atomic number 87, has a larger covalent and van der Waals radius than cesium.
• Since Francium is an extremely unstable element. Thus, Cesium has the highest atomic number.

This is all about the basics Determination of atomic radius, periodic table trend, Largest atomic radius, Atomic radius chart.