Atomic Sizes

Submitted by ChemPRIME Staff on Thu, 12/16/2010 - 12:31

The sizes of atomsThe smallest particle of an element that can be involved in chemical combination with another element; an atom consists of protons and neutrons in a tiny, very dense nucleus, surrounded by electrons, which occupy most of its volume. and ions are important in determining the properties of both covalent and ionic compounds. You should already have some appreciation of the factors which govern atomic sizes from the color-coded dot-densityThe ratio of the mass of a sample of a material to its volume. diagrams of Hydrogen, Helium, and Lithium and of Beryllium, Boron and Carbon.

By far the largest atom illustrated in these color plates is Li. Because Li has an electron in the n = 2 shell, it is larger than H or He whose 1s electron clouds are much closer to the nucleusThe collection of protons and neutrons at the center of an atom that contains nearly all of the atoms's mass.. Li is also larger than Be, B, or C. In the latter atoms, the 2s and 2p electron clouds are attracted by a greater nuclear charge and hence are held closer to the center of the atom than the 2s cloud in Li. Thus two important rules may be applied to the prediction of atomic sizes.

1 As one moves from top to bottom of the periodic tableA chart showing the symbols of the elements arranged in order by atomic number and having chemically related elements appearing in columns., the principal quantum numberOne of a set of numbers that specifies the state of an electron in an atom; the set of quantum numbers summarize results from quantum mechanics. n increases and electrons occupy orbitals whose electron clouds are successively farther from the nucleus. The atomic radii increase.

2 As one moves from left to right across a horizontal periodThose elements from a single row of the periodic table., then n value of the outermost electron clouds remains the same, but the nuclear charge increases steadily. The increased nuclear attraction contracts the electron cloud, and hence the atomic size decreases.

It is difficult to measure the size of an atom very exactly. As the dot-density diagrams show, an atom is not like a billiard ball which has a definite radius. Instead of stopping suddenly, an electron cloud gradually fades out so that one cannot point to a definite radius at which it ends. One way out of this difficulty is to find out how closely atoms are packed together in a crystal latticeAn orderly, repeating arrangement of points in 3-D space in which each p;oint has surroundings identical to every other point. A crystal's constituent atoms, molecules, and ions are arranged about each lattice point.. Fig. 1 illustrates part of a crystalA solid with a regular polyhedral shape; for example, in sodium chloride (table salt) the crystal faces are all at 90° angles. A solid in which the atoms, molecules, or ions are arranged in a regular, repeating lattice structure. of solidA state of matter having a specific shape and volume and in which the particles do not readily change their relative positions. Cl2 at a very low temperatureA physical property that indicates whether one object can transfer thermal energy to another object.. The distance AA′ has the value of 369 pm. Since this represents the distance between adjacent atoms in different Cl2 molecules, we can take it as the distance at which different Cl atoms just “touch.” Half this distance, 184 pm, is called the van der Waals radius of Cl. The van der Waals radius gives an approximate idea of how closely atoms in different molecules can approach each other.

Figure 1 The relationship between van der Waals radii and covalent radii for Cl2(s). In solid chlorine the molecules pack together so that the shortest distance between chlorine nuclei in different molecules (AA′ or BB′) or is 369 pm. The van der Waals radius of chlorine is defined as half that distance or 184 pm. The covalent radius of chlorine is half the distance (one-half AB or A′B′) between two chlorine nuclei in the same molecule. This is smaller than the van der Waals radius because of the covalent bond in each Cl2 molecule.

Commonly accepted values of the van der Waals radii for the representative elements are shown in the Fig. 2. Note how these radii decrease across and increase down the periodic table.

Figure 2 Sizes of atoms of the representative elements as a function of their position in the periodic table. Outer (lightly shaded) circles indicate van der Waals radii, while inner (darkly shaded) circles represent covalent radii. Colored numbers are van der Waals radii, and black numbers are covalent radii, both expressed in picometers.

Also given are values for the covalent radius of each atom. Returning to the figure of Cl2, we see that the distance AB between two Cl atoms in the same molecule (i.e., the Cl—Cl bondlength) has a value of 202 pm. The covalent radius is one-half of this bond lengthThe distance between the nuclei of two bonded atoms., or 101 pm. Covalent radii are approximately additive and enable us to predict rough values for the internuclear distances in a variety of molecules. For example, if we add the covalent radius of C (77 pm) to that of O (66 pm), we obtain an estimate for the length of the C―O bond, namely, 143 pm. This is in exact agreement with the measured value in ethyl alcoholAn organic compound containing the functional group -OH. and dimethyl ether seen previously.