Clear Notion
Login

Concepts

Read through concept notes with worked explanations and diagrams, chapter by chapter.

Concept 04 / 05Classification of Elements and Periodicity

Atomic and Ionic Radii: Trends, Effective Nuclear Charge and Isoelectronic Species

Covalent, metallic and van der Waals radii, effective nuclear charge and shielding, the decrease across a period and increase down a group, cation and anion sizes compared with parent atoms, isoelectronic series, and the lanthanoid contraction.

Figure 1
An atom has no sharp boundary, so its size is defined operationally. The covalent radius is half the distance between the nuclei of two identical atoms joined by a single covalent bond (Cl2\mathrm{Cl_{2}}: 198198 pm bond, 9999 pm radius). The metallic radius is half the internuclear distance in a metal crystal. The van der Waals radius is half the distance between non-bonded atoms of neighbouring molecules in the solid; it is the largest of the three. Effective nuclear charge. An outer electron does not feel the full nuclear charge ZZ, because inner electrons shield it. It feels Zeff=Z−σZ_{\text{eff}} = Z - \sigma, where σ\sigma is the shielding constant (estimated by Slater's rules). Inner shells shield strongly; electrons in the same shell shield each other only weakly; and d and f electrons shield poorly. Across a period (left to right) the number of shells is constant but ZZ increases by one each step while shielding by same-shell electrons increases only slightly. ZeffZ_{\text{eff}} rises, the outer electrons are pulled in, and the radius decreases, as the figure shows for periods 22 and 33. (Noble-gas radii are van der Waals radii and appear anomalously large if compared with the covalent radii of their neighbours.) Down a group, a new shell is added each period, and the increase in distance outweighs the increase in ZeffZ_{\text{eff}}, so radius increases: Li 152152, Na 186186, K 231231 pm. Ionic radii. A cation is smaller than its parent atom: it loses its outer shell (often completely) and the remaining electrons feel a greater effective charge. Na\mathrm{Na} 186186 pm, Na+\mathrm{Na^{+}} 9595 pm. Higher charge means smaller size: Fe3+<Fe2+\mathrm{Fe^{3+}} < \mathrm{Fe^{2+}}. An anion is larger than its parent atom: added electrons increase repulsion and the same nuclear charge holds more electrons. Cl\mathrm{Cl} 9999 pm, Cl−\mathrm{Cl^{-}} 181181 pm. Isoelectronic species have the same number of electrons, so the only difference is nuclear charge; size decreases as ZZ increases: N3−>O2−>F−>Na+>Mg2+>Al3+\mathrm{N^{3-}} > \mathrm{O^{2-}} > \mathrm{F^{-}} > \mathrm{Na^{+}} > \mathrm{Mg^{2+}} > \mathrm{Al^{3+}} (all with 1010 electrons). Lanthanoid contraction. Across the lanthanoids (Ce to Lu), electrons enter the 4f4f subshell, which shields very poorly. ZeffZ_{\text{eff}} on the outer electrons rises steadily and the radii shrink more than expected. As a result, the elements following the lanthanoids are almost the same size as the elements above them: Zr (160160 pm) and Hf (159159 pm), Nb and Ta, Mo and W are nearly identical in size and very similar chemically, which makes them hard to separate. Key Takeaways: - van der Waals radius > metallic radius > covalent radius for a given element. - Zeff=Z−σZ_{\text{eff}} = Z - \sigma; d and f electrons shield poorly. - Radius decreases across a period, increases down a group. - Cation < parent atom < anion; higher positive charge, smaller ion. - Isoelectronic: larger ZZ, smaller size. - Lanthanoid contraction makes Zr and Hf nearly the same size. - Pitfall: comparing a noble gas's van der Waals radius with covalent radii of its neighbours. Brain-Teaser 1: Arrange S2−\mathrm{S^{2-}}, Cl−\mathrm{Cl^{-}}, K+\mathrm{K^{+}}, Ca2+\mathrm{Ca^{2+}} and Ar in order of size. Solution: All have 1818 electrons. Nuclear charges are 16,17,19,2016, 17, 19, 20 and 1818. Size decreases with nuclear charge: S2−>Cl−>Ar>K+>Ca2+\mathrm{S^{2-}} > \mathrm{Cl^{-}} > \mathrm{Ar} > \mathrm{K^{+}} > \mathrm{Ca^{2+}}. For isoelectronic species, only ZZ matters. Brain-Teaser 2: The metallic radius of aluminium is 143143 pm, but that of gallium, one period lower, is about 135135 pm. Explain why gallium is not larger. Solution: Going from Al to Ga, a new shell is added, which would normally increase the radius. But in between, the ten 3d3d electrons of the transition series were added. They shield the outer electrons poorly, so Ga's valence electrons feel a much higher ZeffZ_{\text{eff}} than expected, and the radius does not increase (it slightly decreases). This 'd-block contraction' also explains why Ga's ionisation energy is higher than Al's. Brain-Teaser 3: Why are the chemical properties of Zr and Hf so similar that they occur together in nature? Solution: Hf follows the lanthanoids. The lanthanoid contraction cancels the size increase expected from the extra shell, so Zr and Hf have almost the same atomic and ionic radii (Zr4+\mathrm{Zr^{4+}} and Hf4+\mathrm{Hf^{4+}} are nearly identical). With the same size, charge and valence configuration, their chemistry is almost identical. Size, more than any other factor, controls how similar two elements of the same group are.

Practice this concept

Free · no account required · instant solutions

Atomic and Ionic Radii: Trends, Effective Nuclear Charge and Isoelectronic Species — DPP

10 questionsSee the solution the moment you answer

Practice