Radii the sizes of atoms and ions

of course, impossible to measure the absolute size of an isolated atom its electron cloud extends to infinity. It is possible to calculate the radius within which (say) 95% of its total electron cloud is confined but most measures of atomic/ionic size are based upon experimental measurements of internuclear distances in molecules and crystals. This means that the measurement is dependent on the nature of the bonding in the species concerned, and is a property of the atom or ion under scrutiny in a particular substance or group of substances. This must always be borne in mind in making use of tabulated radii of atoms or ions. The most important dictum to remember is that radii are significant only insofar as they reproduce experimental internuclear distances when added together. The absolute significance of a radius is highly suspect, 

The atomic radius of the atom X is defined as half the length of an X-X single bond. This can be obtained experimentally from the structures of elemental substances containing molecules X where the X-X bond order is believed to be unity, e.g. Cl2, P4, S8. It may also be obtained from the X-X distances found in molecules such as HO—OH, H2N—NH2 etc. for atoms which form multiple bonds in the elemental substance. Such atomic radii may be termed covalent radii. For atoms which form metallic elemental substances, metallic radii are obtained. These are usually standardised for 12-coordination of each atom, which is the most common situation in metals. Corrections can be made in the cases of metals which adopt other structures. 

Some writers feel it important to distinguish carefully between covalent and metallic radii. Others suggest that a self-consistent set of atomic radii - some covalent, others metallic - can be devised. Such a collection is presented in Table 4.1. In cases where both a covalent and a metallic radius can be obtained, the agreement is variable. For example, the metallic radii of atoms of the Group 1 elements are 20-30 pm greater than the corresponding covalent radii, taken from the M-M distances in M2(g). The Mn-Mn distance in (CO)5Mn—Mn(CO)5 is 293 pm, which compares with 274 pm calculated from the metallic radius of Mn. The electronic environment of the Mn atom in the carbonyl complex is, of course, very different from that in the elemental substance. 

It will be noted in Table 4.1 that the metallic radii along the 5d series are very close to the values for the corresponding atoms in the 4d series. This observation is related to the remarkable chemical similarities between Zr and Hf. The effect of the lanthanide contraction on metallic radii persists to the end of the 5d series, but its chemical consequences become less marked as we pass from left to right. It is important not to make too much of similarities in metallic radii in chemical arguments, however. For example, the triad Mn, Tc and Re all have practically equal metallic radii, but their chemical behaviour shows dramatic differences. The near-equivalence of their metallic radii is less marked when we look at bond lengths in molecules. For example, the M-M distances in (CO)5M—M(CO)5 are respectively 293, 304 and 302 pm for M = Mn, Tc and Re. 

Towards the end of each of the three series which constitute the d block, we observe a marked increase in radius. For reasons discussed in more detail in Section 7.5, the filled nd subshell tends to weaken the bonding in metallic elemental substances, leading to longer internuclear distances. 

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