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 makes it possible to determine only internuclear distances, in other words, the lengths of bonds (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).

Rice. 2.22. Atomic radii, a - van der Waals radius; b - covalent radius; in - metal radius.

Covalent radii. The covalent radius is defined as half the internuclear distance (bond length) between two identical atoms connected to each other by a covalent bond (Fig. 2.22b). As an example, let's take a chlorine molecule whose bond length 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 bond length 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 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, the bond length varies from 0.1070 nm at the trisubstituted carbon atom to 0.115 nm in the compound

Metal radii. The metal 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 the atoms of non-metallic elements, and the term metallic radius to the 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, a - anions are in contact with each other, but cations are not in contact with anions; b - cations are in contact with anions, but the anions are not in contact with each other; c - 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, c. 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

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 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 vary 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 for calculating internuclear distances in ionic crystals 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. Proximity of atomic radii values various metals often serves as an indication of 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 at which two chemically unbonded atoms of different molecules can come together or different groups atoms of the same molecule. 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.

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 an infinitely large 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. A more precise definition is as follows: bond length is the distance between bonded atoms, measured between the centers of mass of two atoms and corresponding to the minimum binding 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 a simple addition law. 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 metal radius is assumed to be equal to half the internuclear distance between neighboring ions in the metal crystal lattice (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. Figure 2.23 shows three possible ways of packing 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.

Comparison of radii of different 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 in size than atoms, and anions are larger in size than atoms of the same elements. For each element of all types of radii, the smallest value always belongs to the cationic 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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See what “Atomic radius” is in other dictionaries:

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

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• 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...

At the end of the article, you will be able to describe- Determination of atomic radius, periodic table trend, Largest atomic radius, Atomic radius diagrams. 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.