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The valence shell of an atom, is the set of orbitals which are energetically accessible for accepting electrons to form chemical bonds. For various atoms, the valance electrons are submerged beneath filled shells with a higher principal quantum number [1]. This type of electronic configuration is called a submerged-shell [2].

Before I learnt about submerged shells, I was under the impression that valance electrons were always in the shell with the highest principal quantum number $n$, since it denotes the distance of a shell from the nucleus. However the literature I have read today indicates that this is not always the case, and I was wondering why. I expected that the outermost electrons would fill the lower shells first, and that if they did not, then they would get in the way of chemical bonds, shielding electrons in lower orbits in some way.

Why is it that the valance electrons of some atoms are not in the outermost shell, with the highest principle quantum number?

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    $\begingroup$ The valence electrons of the RE elements are mainly their outermost electrons: $6s^2$. Only one 'submerged' electron (from $6f^x$) contributes to their most probable oxidation state ($+3$). $\endgroup$
    – Gert
    Commented Jun 14, 2021 at 6:09
  • $\begingroup$ @Gert Thank you for the comment. I have removed the phrase “various rare earth elements” before any answers get posted, since I didn’t intend to place particular emphasis on them. $\endgroup$
    – user400188
    Commented Jun 14, 2021 at 6:32

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The electron shells surrounding an atom possess progressively higher energy levels as their corresponding quantum numbers are indexed upwards. Roughly speaking, as you add build larger and larger nuclei, the bigger the nucleus (that is, the more protons you populate it with), the larger the the resulting electron cloud becomes and the more oddly-shaped and "ornate" the probability distributions become for the outermost orbitals. But there are exceptions.

This effect eventually produces a peculiarity: a class of atoms where the outermost-orbitals are the same across the range of atomic weights in the family. In this special case, the extra electron that balances the successively increasing nuclear charge as the number of protons increases in the family lies inside the outermost orbitals and as a result all the members of that family have such similar chemical properties that they are almost impossible to separate by the usual chemical reactions used for other elements. These are the so-called rare earths.

This is a simplified picture of a complicated topic and I invite the experts here to furnish more information on it.

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