# What does valence electron mean (in the context of spdf orbitals)?

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?

• @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.
– Tham
Oct 17 at 12:37
• @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?
– Tham
Oct 17 at 12:49
• @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?
– Tham
Oct 17 at 12:56