Lanthanoid Contraction and Its Consequences

Lanthanoid contraction is the name given to the steady, small, but strictly cumulative decrease in atomic and ionic radius observed across the fourteen lanthanoid elements, from lanthanum to lutetium.

Cause. As one moves across the lanthanoid series, one additional proton is added to the nucleus at each step, and (in the great majority of cases) one additional electron is added to the 4f subshell. The 4f orbitals, however, are unusually diffuse and radially poorly defined compared with $s$, $p$ or even $d$ orbitals of the same principal shell, so a 4f electron is a comparatively poor shield against the nuclear charge for another electron in the same 4f subshell (this is called poor 4f-4f shielding, or poor mutual shielding). As a direct consequence, the effective nuclear charge felt by the outer $6s^2$ electrons (and by the $5d$, $5p$, $5s$ core beneath them) rises steadily across the series, pulling the outer electron cloud in a little more tightly at every step -- so both the atomic radius and the ionic radius of the $\text{Ln}^{3+}$ ion decrease steadily and (unlike the more complex fall-then-rise pattern seen in the d-block) essentially monotonically from La to Lu.

Magnitude. The ionic radius of $\text{La}^{3+}$ is about $106\ \text{pm}$; by the end of the series, the ionic radius of $\text{Lu}^{3+}$ has fallen to about $85\ \text{pm}$ -- a net contraction of roughly $21\ \text{pm}$ spread across fourteen elements, i.e. only about $1$-$2\ \text{pm}$ per element on average. Individually, this per-element contraction is smaller than the corresponding contraction seen at the start of the d-block (where, as covered earlier in this chapter, the radius falls by several picometres per element over just the first three or four elements); the significance of lanthanoid contraction lies not in its size per element but in its being steady and cumulative over fourteen consecutive elements with essentially no reversal, which is what makes its downstream consequences so pronounced.

Consequences. Because lanthanoid contraction operates across the entire block of fourteen elements sitting between lanthanum (the last element before the f-block) and hafnium (the first element of the third-row d-block, immediately after the lanthanoids), the cumulative contraction very nearly offsets the size increase that would otherwise be expected on descending a d-block group from its second-row (4d) member to its third-row (5d) member. The result is that pairs of elements in the same group across the second and third transition series -- zirconium/hafnium, niobium/tantalum, molybdenum/tungsten -- end up with almost identical atomic and ionic radii, and consequently very similar chemical properties. This near-identity makes these pairs of elements unusually difficult to separate from one another chemically, a genuine practical problem in the extraction and purification of zirconium and hafnium in particular (which typically occur together in the same ores). …