Atomic radius periodic variation

Figure 1.46 shows some atomic radii, and Fig. 1.47 shows the variation in atomic radius with atomic number. Note the periodic, sawtooth pattern in the latter plot. Atomic radius generally decreases from left to right across a period and increases down a group. 

The periodic structure of the elements is evident for many physical and chemical properties, including chemical valence, atomic radius, electronegativity, melting point, density, and hardness. Two classic prototypes for periodic behavior are the variations of the first ionization energy and the atomic radius with atomic number. These are plotted in Figs. 9.4 and 9.5. 

Which of the following properties show a clear periodic variation (a) first ionization energy, (b) molar mass of the elements, (c) number of isotopes of an element, (d) atomic radius. 

A Figure 23.22 Variation in atomic radius of transition metals as a function of the periodic table group number. 

The periodic recurrence of analogous groimd state electron configurations as the atomic number increases accounts for the periodic variation in the properties of atoms. Here we concentrate on two aspects of atomic periodicity—atomic radius and ionization energy—and see how they can help to explain the different biological roles played by different elements. 

Fig. 9.54 The variation of atomic radius through the periodic table. Note the contraction of radius following the lanthanoids in Period 6 (following lutetimn, Z=71).

The variation of the first ionization energy through the periodic table is shown in Fig. 9.55, and some numerical values are given in Table 9.3. The ionization energy of an element plays a central role in determining the ability of its atoms to participate in bond formation (for bond formation, as we shall see in Chapter 10, is a consequence of the relocation of electrons from one atom to another). After atomic radius, it is the most important property for determining an element s chemical characteristics. 

In the expression above, is the effective nuclear charge for the electron of interest and aq is the Bohr radius. For each atom, we expect the least strongly bound electron to be, on average, farthest from the nucleus. Let s use Zeff for that electron in equation (9.5) to obtain an estimate of the radius of each atom. The results are shown in Figure 9-9. Notice that the variation of with Z is very similar to that of atomic radius (Fig. 9-4), and thus it seems reasonable to use equation (9.5) to rationalize the variation of atomic radius across a period and down a group. 

The variation of polarizability with atomic number (solid black line) closely resembles that of atomic volume (dashed red line). The atomic volume is calculated as (4/3)7rf, where r is the atomic radius as defined in Figure 9-4. Both polarizability and atomic volume decrease from left to right across a period and increase from top to bottom in a group. 

A The general trend to more exothermic values with increasing atomic number is attributable to the decrease in ionic radius across the period because, as the anion-cation separation becomes smaller, the lattice enthalpy increases (equation 3.3). Superimposed on this trend is the effect of CFSE values. These are small in comparison to the overall magnitude of A// , but nonetheless have a significant effect. The double dip in the plot may be accounted for in terms of the variation in high-spin CFSE values across the first-row d-block. as shown in Figure 6.3. This shows respective CFSE contributions to of -(YsfA j for Ti-", -(V Aq for... 

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