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Is there a justification for why are the $4f$ electrons strongly localized about the nucleus in rare-earth atoms but the $3d$ electrons in transition metals extend further out from the nucleus? I have hit upon this question while reading about magnetism. Here is a reference from Blundell's Magnetism in Condensed Matter Sec.4.2.2 second paragraph.

A slightly different quote can be found in Kittel's Solid State Physics book which says,

The difference in the behaviour of the rare earth and the iron group salts is that the $4f$ shell responsible for paramagnetism in the rare earth ions lies deep inside the ions, within the $5s$ and $5p$ shells, whereas the iron group ions in the $3d$ shell responsible for paramagnetism is the outermost shell.

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  • $\begingroup$ Well, the 4$f$ electrons are shielded by a closed 5$s$ shell. Look at the electronic configuration of the various elements of interest. $\endgroup$
    – Jon Custer
    Commented Jun 10, 2019 at 16:46
  • $\begingroup$ @JonCuster That's true. But that doesn't work to explain why $3d$ electrons are the outermost. $\endgroup$ Commented Jun 10, 2019 at 17:03

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The crystal field splittings are much larger in transition-metal salts (mostly due to covalency, the ligand-field effect), of the order of electronvolts. In rare-earth salts, crystal field splittings are two orders of magnitude smaller.

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