6.5 Atomic & Ionic Radii Trend
Periodic trends in atomic and ionic radii
The original purpose of the periodic table was to organize the chemical elements in a manner that would make sense of the ways in which the observed physical and chemical properties of the elements vary with the atomic number.
In this section, we look at some of these trends and try to understand the reasons for them based on the electron structures of the elements.
Periodic trends in the sizes of atoms
What do we mean by the “size” of an atom?
The concept of “size” is somewhat ambiguous when applied to the scale of atoms and molecules. The reason for this is apparent when you recall that an atom has no definite boundary; there is a finite (but very small) probability of finding the electron of a hydrogen atom, for example, 1 cm, or even 1 km from the nucleus. It is not possible to specify a definite value for the radius of an isolated atom; the best we can do is to define a spherical shell within whose radius some arbitrary percentage of the electron density can be found.
Figure 6.49 Size of an Atom
When an atom is combined with other atoms in a solid element or compound, an effective radius can be determined by observing the distances between adjacent rows of atoms in these solids. This is most commonly carried out by X-ray scattering ex
periments. Because of the different ways in which atoms can aggregate together, several different kinds of atomic radii can be defined.
Distances on the atomic scale have traditionally been expressed in Ångstrom units (1Å = 10–8 cm = 10–10 m), but nowadays the picometer is preferred;
1 pm = 10–12 m = 10–10 cm = 10–2 Å, or 1Å = 100 pm. The radii of atoms and ions are typically in the range 70-400 pm.
A rough idea of the size of a metallic atom can be obtained simply by measuring the density of a sample of the metal. This tells us the number of atoms per unit volume of the solid. The atoms are assumed to be spheres of radius r in contact with each other, each of which sits in a cubic box of edge length 2r. The volume of each box is just the total volume of the solid divided by the number of atoms in that mass of the solid; the atomic radius is the cube root of r.
Although the radius of an atom or ion cannot be measured directly, in most cases it can be inferred from measurements of the distance between adjacent nuclei in a crystalline solid.
Figure 6.50 Diameter of an Atom
Because solids fall into several different classes, several kinds of atomic radius are defined. Many atoms have several different radii; for example, sodium forms a metallic solid and thus has a metallic radius, it forms a gaseous molecule Na2 in the vapor phase (covalent radius), and of course it forms ionic solids such as NaCl.
- Metallic radius is half the distance between nuclei in a metallic crystal.
- Covalent radius is half the distance between like atoms that are bonded together in a molecule.
- van der Waals radius is the effective radius of adjacent atoms which are not chemically bonded in a solid, but are presumably in “contact”. An example would be the distance between the iodine atoms of adjacent I2 molecules in crystalline iodine.
Many atoms have several different radii; for example, sodium forms a metallic solid and thus has a metallic radius, it forms a gaseous molecule Na2 in the vapor phase (covalent radius), and of course it forms ionic solids as mentioned above.
Periodic trends in atomic radius
We would expect the size of an atom to depend mainly on the principal quantum number of the highest occupied orbital; in other words, on the “number of occupied electron shells”. Since each row in the periodic table corresponds to an increment in n, atomic radius increases as we move down a column. The other important factor is the nuclear charge; the higher the atomic number, the more strongly will the electrons be drawn toward the nucleus, and the smaller the atom. This effect is responsible for the contraction we observe as we move across the periodic table from left to right.
Figure 6.51 Covalent Radii Trend
The figure shows a periodic table in which the sizes of the atoms are represented graphically. The apparent discontinuities in this diagram reflect the difficulty of comparing the radii of atoms of metallic and nonmetallic bonding types. Radii of the noble gas elements are estimates from those of nearby elements.
How ionic radii are estimated
The size of an ion can be defined only for those present in ionic solids. When an ion dissolves in water, it acquires a hydration shell of loosely-attached H2O molecules that increase its effective radius in ways that are difficult to define in a systematic way.
By observing the diffraction of X-rays by an ionic crystal, it is an easy task to measure the distance between adjacent rows of Na+ and Cl– ions, but there is no unambiguous way to decide what portions of this distance are attributable to each ion. The best one can do is make estimates based on studies of several different ionic solids (LiI, KI, NaI, for example) that contain one ion in common. Many such estimates have been made, and they turn out to be remarkably consistent.
For example, the lithium ion is sufficiently small that in LiI, the iodide ions are in contact, so I-I distances are twice the ionic radius of I–. This is not true for KI, but in this solid, adjacent potassium and iodide ions are in contact, allowing estimation of the K+ ionic radius.
Comparing the radii of atoms and their ions
Figure 6.52 Comparison of atomic vs. Ionic Radii
A positive ion is always smaller than the neutral atom, owing to the diminished electron-electron repulsion. If a second electron is lost, the ion gets even smaller; for example, the ionic radius of Fe2+ is 76 pm, while that of Fe3+ is 65 pm. If formation of the ion involves complete emptying of the outer shell, then the decrease in radius is especially great.
The hydrogen ion H+ is in a class by itself; having no electron cloud at all, its radius is that of the bare proton, or about 0.1 pm— a contraction of 99.999%! Because the unit positive charge is concentrated into such a small volume of space, the charge density of the hydrogen ion is extremely high; it interacts very strongly with other matter, including water molecules, and in aqueous solution it exists only as the hydronium ion H3O+.
Negative ions are always larger than the parent ion; the addition of one or more electrons to an existing shell increases electron-electron repulsion which results in a general expansion of the atom.
Figure 6.53 Ionic Radii
Periodic trends in ionic radii
The best way of visualizing these trends is to compare the radii of an isoelectronic series — a sequence of species all having the same number of electrons (and thus the same amount of electron-electron repulsion) but differing in nuclear charge. Of course, only one member of such a sequence can be a neutral atom (neon in the series shown below.) The effect of increasing nuclear charge on the radius is clearly seen.
Figure 6.53 Periodic Trend in Ionic Radii