Chemistry · Ch 7 — Modern Periodic Table
Atomic Radius
Atomic Radius
The quantum mechanical model describes an atom's extranuclear region as a fuzzy electron cloud with no sharply-defined outer boundary, so 'atomic radius' cannot be measured directly — it has to be ESTIMATED from internuclear distances under different circumstances. For nonmetals (other than the noble gases), atoms are joined to their neighbours by covalent bonds, and the bond length of a single bond is taken as the sum of the two bonded atoms' radii — this half-of-bond-length value is called the covalent radius. For example, the C-C single bond in diamond measures 154 pm, giving carbon a covalent (atomic) radius of 77 pm; the Cl-Cl bond in a Cl2 molecule measures 198 pm, giving chlorine a covalent radius of 99 pm. For metals, instead, the distance between two adjacent atoms in a bulk metallic sample is measured, and half of that distance is taken as the metallic radius. Either way, atomic radius is defined as one-half of the internuclear distance between two adjacent atoms — whether two metal atoms in a metallic lattice, or two single-bonded atoms of a nonmetal. Table 7.2 shows that, reading across period 2 or period 3 (up to group 17), atomic radius steadily DECREASES, because the screening from core electrons stays essentially constant across a period while the effective nuclear charge keeps rising (section 7.5.1) — pulling the valence electrons in more tightly as you m …
What this figure shows. Two worked diagrams illustrating the two measurement methods side by side. For the metal beryllium: a cluster of nine Be atoms packed together (representing the bulk metal) with the centre-to-centre distance between two adjacent atoms marked as 224 pm; the atomic (metallic) radius is taken as half of this, 224/2 = 112 pm. For the nonmetal chlorine: a single Cl2 molecule with its Cl-Cl bond length marked as 198 pm; the atomic (covalent) radius is taken as half the bond length, 198/2 = 99 pm. Fidelity note: the source page prints this figure's own label as 'Fig 6.3', evidently a leftover caption number from an earlier edition of the chapter (it is the chapter's third figure, positioned after Fig. 7.1 and Fig. 7.2, and every numeric value in it — 224 pm for Be, 198 pm for Cl2 — matches standard reference values, so only the capti …
Worked out. A supplementary note: since the electron cloud fades out gradually rather than stopping at a hard edge, atomic radius is conventionally estimated as the radius of the surface that encloses a fixed, high proportion (typically about 95% or more, the exact cutoff being a matter of convention) of the total electron density around the nucleus. …
Table 7.2 — atomic radius by group and period (values in pm):
Period 2: Li 152, Be 111, B 88, C 77, N 74, O 66, F 64.
Period 3: Na 186, Mg 160, Al 143, Si 117, P 110, S 104, Cl 99.
Period 4 (group 1 and group 17 only, as printed): K 231, Br 114.
Period 5 (group 1 and group 17 only): Rb 244, I 133.
Period 6 (group 1 and group 17 only): Cs 262, At 140. …
Worked out. Worked example: which species has the larger radius — (i) Na or Na⁺; (ii) Na⁺ or Mg²⁺? (i) Na and Na⁺ share the same nuclear charge, but Na⁺ has fewer electrons and fewer occupied shells (two shells in Na⁺ versus three in neutral Na), so Na is larger. (ii) Na⁺ and Mg²⁺ are isoelectronic (both have 10 electrons), but Mg²⁺ has the larger nuclear charge, so it pulls its electron cloud in more tightly — therefore Na⁺ has the larger radiu …