For a little bit of context, my background is in physics and my understanding of chemistry doesn't go past, say, middle school level. Recently, I decided to self-study chemistry and picked up "Inorganic Chemistry (Housecroft & Sharpe)" but I couldn't get past the first chapter because of the following question:

In the advent of quantum mechanics, our understanding of electron orbital underwent a paradigm shift; they are no longer always in spherical orbit, but their boundary surface take on awkward shapes like "dumbbell" shape or have "rings" around the nucleus.

With this in mind, how then does the idea of valence electron still fit into this picture? How do we define "outer electrons" if the "shells" are no longer nested like Russian dolls? Why do we say that Co ([Ar]$4s^2 3d^7$) has 9 valence electrons but Br ([Ar]$4s^2 3d^{10} 4p^5$) only has 7? Is there a single, consistent definition for valence electron that does not differentiate between s-block, p-block, d-block and f-block of the periodic table?

  • $\begingroup$ @Poutnik That was what I am perplexed about. If we go by "top total energy", then we should have said that Co has 7 valence electrons and Br has 5. Why do we consider electrons in both $4s^2 3d^7$ as valence for Co but totally ignore the $d$-shell for Br and only say that electrons in $4s^2 4p^5$ is counted? Using spatial extend as an "indicator" is also problematic since the irregular shape of the orbitals makes it hard to properly quantify this. $\endgroup$
    – Tham
    Oct 17 at 12:37
  • $\begingroup$ @Poutnik Hmm.... So why is $3d^{10}$ not counted towards to valance electron of Br since $3d$-orbital has a higher energy than $4s$-orbital? $\endgroup$
    – Tham
    Oct 17 at 12:49
  • $\begingroup$ @Poutnik Ohhhh... That makes much more sense now! Do you think you can point me to any textbooks/monographs/resources that discusses how energy level changes as the electron count increases? $\endgroup$
    – Tham
    Oct 17 at 12:56
  • $\begingroup$ Moved my comments in the answer. $\endgroup$
    – Poutnik
    Oct 17 at 14:37

Valence / outer electrons in context of quantum atomic models are those orbital groups(1) with the top total energies, involved or being able to be involved in interatomic bonds. It usually involves orbitals with the most spatially outstretched electron probability density. Usually ns, np, (n-1)d, (n-2)f, mostly just 2 of these 4. See also the (*) orbital footnote in this answer

See also wikipedia: Valence_electron

The chart overview of orbital energies from Sciencedirect Orbital energies

and the 4th period details from QM class 4th period details from

(1) I meant it as the group, not necessarily the very top only.. Spacial extent is not the indicator, there is just the correlation. The energy order rules becomes complicated, starting with the 4th period of elements.

Electrons in folly occupied 3d orbitals have lower energy than 4s electrons. Orbital energy depends on electron configuration and the order frequently switches.


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