Variation of Atomic and Ionic Size

The generally expected pattern across any period of the periodic table is a steady decrease in atomic radius as one moves left to right, driven by the rising nuclear charge pulling the (constant-shell) electron cloud progressively inward. The 3d transition series follows this expectation only for its first few members: the anticipated decrease in atomic radius is indeed observed moving from scandium to vanadium. But thereafter, from vanadium all the way through to copper, the atomic radius levels off and remains nearly constant rather than continuing to shrink.

The explanation lies in a tug-of-war between two competing effects as electrons are added to the 3d sub-shell moving across the series. On one hand, the added 3d electrons only partially shield the increasing nuclear charge from the outer 4s electrons (d electrons are relatively poor shields compared with s or p electrons in the same or an outer shell), so the effective nuclear charge experienced by the valence electrons rises slightly as atomic number increases. On the other hand, those same additional 3d electrons strongly repel the 4s electrons that sit further out, an effect that tends to push the atom's outer boundary outward. These two forces -- the slowly rising effective nuclear charge pulling inward, and the growing 3d-4s electron repulsion pushing outward -- operate in opposite directions and, across most of the series, very nearly cancel each other out, producing the observed near-constancy in atomic radii from V through Cu.

At the very end of the series, at zinc, the d-orbitals hold their full complement of 10 electrons. Here, the mutual repulsive interaction among these ten d electrons outweighs the (by-now only modestly higher) effective nuclear charge, so the d-orbitals slightly expand and the atomic radius correspondingly increases a little at zinc relative to its immediate neighbours -- the small uptick visible at the right-hand end of Figure 4.4(a). …