Why does Europium and Ytterbium show an anomaly when considering the trends of Lanthanide atomic radius across the group?

Answer 1

lanthanide contraction, or f-block contraction.

Source:
http://facultyfp.salisbury.edu/dfrieck/htdocs/212/rev/table/size.htm
In the data given for group 13 there is an interesting deviation from the expected trend for atomic radius. At first, we might expect that an atom of Ga would be larger than an atom of Al based on their positions in group. Gallium, however, is considerably smaller than Al due to a phenomenon known as the d-block contraction. As explained above, atoms get smaller as we progress from left to right across a given period, thus in period three Na is larger than Mg, Mg is larger than Al, Al is larger than Si, etc., until we arrive at Ar, the smallest atom in row. The next element, K, is in period four and is, as expected, larger than any period three atom. Again, as we progress to the right atomic radius decreases due to increasing Zeff. It is in period four, however, that we first encounter the transition elements. Atomic radius decreases as we move from Sc to Ti to V, etc., as electrons are added to the d-subshell. By the time we completely fill the d-subshell and reach the p-block elements, the atomic radius has decreased so much that Ga is actually smaller than Al. Because of the d-block contraction, the post transition elements of period four are about the same size as their period three congeners. Similarly, the occurrence of the f-block elements between the period six s- and p-blocks causes the period six p-block elements to be about the same size as their period five congeners. This effect is called the lanthanide contraction, or f-block contraction.

Answer 2

Whereas the other lanthanide elements adopt the Ln3+ oxidation state while Eu and Yb take on the Ln2+ state (as the 2+ state gives Eu and Yb a half filled [4f7] and a full [4f14] f shells respectively) thus giving them higher atomic radii than the rest of the lanthanide series.

Answer 3

Europium and Ytterbium exhibit anomalies in atomic radius because they have stable half-filled or fully filled inner f electron shells, leading to a contraction in atomic size. This phenomenon is known as the "lanthanide contraction" and causes these two elements to have smaller atomic radii than predicted based solely on their position in the Periodic Table.