Atomic and ionic radii

Key points: Atomic radii increase down a group and, within the s and p blocks, decrease from left to right across a period. The lanthanide contraction results in a decrease in atomic radius for elements following the f block. All monatomic anions are larger than their parent atoms and all monatomic cations are smaller.

One of the most useful atomic characteristics of an element is the size of its atoms and ions. As we shall see in later chapters, geometrical considerations are central to explaining the structures of many solids and individual molecules. In addition, the average distance of electrons from the nucleus of an atom correlates with the energy needed to remove it in the process of forming a cation. An atom does not have a precise radius because far from the nucleus the electron density falls off only exponentially (but sharply). However, we can expect atoms with numerous electrons to be larger, in some sense, than atoms that have only a few electrons. Such considerations have led chemists to propose a variety of definitions of atomic radius on the basis of empirical considerations. The metallic radius of a metallic element is defined as half the experimentally determined distance between the centres of nearest-neighbour atoms in the solid (Fig. 1.23a, but see Sec tion 3.7 for a refinement of this definition). The covalent radius of a nonmetallic element is similarly defined as half the internuclear distance between neighbouring atoms of the same element in a molecule (Fig. 1.23b). We shall refer to metallic and covalent radii jointly as atomic radii (Table 1.3). The periodic trends in metallic and covalent radii can be seen from the data in the table and are illustrated in Fig. 1.24. As will be familiar from introductory chemistry, atoms may be linked by single, double, and triple bonds, with multiple bonds shorter than single bonds between the same two elements. The ionic radius (Fig. 1.23c) of an element is related to the distance between the centres of neighbouring cations and anions in an ionic compound. An arbitrary decision has to be taken on how to apportion the cation anion distance between the two ions. There have been many suggestions: in one common scheme, the radius of the O2 ion is taken to be 140 pm (Table 1.4; see Section 3.7 for a re f inement of this definition). For example, the ionic radius of Mg2 is obtained by subtracting 140 pm from the internuclear distance between adjacent Mg² and O^2- ions in solid MgO. The data in Table 1.3 show that atomic radii increase down a group, and that they de crease from left to right across a period. These trends are readily interpreted in terms of the electronic structure of the atoms. On descending a group, the valence electrons are found in orbitals of successively higher principal quantum number. The atoms within the group have a greater number of completed shells of electrons in successive periods and hence their radii increase down the group. Across a period, the valence electrons enter orbitals of the same shell; however, the increase in effective nuclear charge across the period draws in the electrons and results in progressively more compact atoms. The general increase in radius down a group and decrease across a period should be remembered as they correlate well with trends in many chemical properties. Period 6 shows an interesting and important modification to these otherwise general trends. We see from Fig. 1.24 that the metallic radii in the third row of the d block are very similar to those in the second row, and not significantly larger as might be expected given their considerably greater numbers of electrons. For example, the atomic radii of Mo (Z=42) and W (Z=74) are 140 and 141 pm, respectively, despite the latter having many more electrons. The reduction of radius below that expected on the basis of a simple ex-trapolation down the group is called the lanthanide contraction. The name points to the

Figure 1.23 A representation of (a) metallic radius, (b) covalent radius, and (c) ionic radius.

Table 1.3 Atomic radii, r/pm*

Figure 1.24 The variation of atomic radii through the periodic table. Note the contraction of radii following the lanthanoids in Period 6. Metallic radii have been used for the metallic elements and covalent radii have been used for the nonmetallic elements.

origin of the effect. The elements in the third row of the d block (Period 6) are preceded by the elements of the first row of the f block, the lanthanoids, in which the 4f orbitals are being occupied. These orbitals have poor shielding properties and so the valence electrons experience more attraction from the nuclear charge than might be expected. The repulsions between electrons being added on crossing the f block fail to compensate for the increasing nuclear charge, so Zeff increases from left to right across a period. The dominating effect of the latter is to draw in all the electrons and hence to result in a more compact atom. A similar contraction is found in the elements that follow the d block for the same reasons. For ex ample, although there is a substantial increase in atomic radius between C and Si (77 and 118 pm, respectively), the atomic radius of Ge (122 pm) is only slightly greater than that of Al. Relativistic effects, especially the increase in mass as particles approach the speed of light, have an important role to play on the elements in and following Period 6 but are rather subtle. Electrons in s and p orbitals, which approach closely to the highly charged nucleus and experience strong accelerations, contract whereas electrons in the less penetrating d and f orbitals expand. One consequence of the latter expansion is that d and f electrons become less effective at shielding other electrons, and the outermost s electrons contract further. For light elements, relativistic effects can be neglected but for the heavier elements with high atomic numbers they become significant and can result in an approximately 20 per cent reduction in the size of the atom. Another general feature apparent from Table 1.4 is that all monatomic anions are larger than their parent atoms and all monatomic cations are smaller than their parent atoms (in some cases markedly so). The increase in radius of an atom on anion formation is a result of the greater electron–electron repulsions that occur when an additional electron is added to form an anion. There is also an associated decrease in the value of Zeff. The smaller radius of a cation compared with its parent atom is a consequence not only of the reduction in electron–electron repulsions that follow electron loss but also of the fact that cation formation typically results in the loss of the valence electrons and an increase in Zeff. That loss often leaves behind only the much more compact closed shells of electrons. Once these gross differences are taken into account, the variation in ionic radii through the periodic table mirrors that of the atoms.

Although small variations in atomic radii may seem of little importance, in fact atomic radius plays a central role in the chemical properties of the elements properties of the elements.

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