# Empirical Evidence and Assignment of Orbital Energies (Electron Filling)

I see a lot of questions on electron configurations from students at various levels here. Students mechanically remember how to fill orbitals and sorry to say many teachers do the same. Not a single general chemistry or even undergraduate physical chemistry book discusses the "why" part of orbital filling and what is the experimental evidence behind the electron configurations? Yes, hand-waving discussion is always present. It all comes from spectroscopy and so on.

A long time ago I asked a question here, on the physics forum and ResearchGate as how one would come up with an electron configuration from the raw spectrum of a non-hydrogen element. Experimental Assignment of Electronic Transitions in Atoms (Grotrian Diagram) However, even trained atomic spectroscopists did not have an answer. Is it an art which has been lost and all we have now are tables?

The question is that what is the point in arguing and teaching that electronic configuration of copper is [Ar] 3d10 4s1 or [Ar] 3d9 4s2? What difference does it make in the world when the teacher and the student have no clue of experimentally verifying it except both are memorizing the rules and exceptions like a parrot? Suppose a very good undergraduate asks this question that how do we experimentally know that configuration of copper is [Ar] 3d10 4s1 or [Ar] 3d9 4s2 vice versa? Most of us may not have an answer.

I would be very happy to know a resource that talks about the experimental evidence and determination of electron configurations of heavier metals. So far my efforts have not been very fruitful.

A similar question has been asked here Evidence of orbitals but it does not fully address my old query.

• Your particular example of Cu (and many others) can be verified by a measurement of the Zeeman effect and the Landé $g$ factor. Since the ground state has a $^2S$ configuration and the excited state has a $^2D$ configuration the $g$ factors are rather different. Also by measuring fine- and hyperfine splittings one can tell a lot about the angular momenta and therefore the electronic configuration. In a similar way, spectroscopy of excited electronic states (e.g. via Rydberg series) also provides a wealth of information. – Paul Oct 31 '19 at 20:06
• Is there any solved example for the determination of electron configuration using Zeeman effect confirming that copper is [Ar] 3d10 4s1 or [Ar] 3d9 4s2 vice versa? I am basically looking for an example (from historical point of view as well) that how electron configurations of heavier elements were determined. Thanks. – M. Farooq Oct 31 '19 at 22:04
• You can have a look at the paper by Sommer (Z. Phys. 39, 711, 1926), which is unfortunately in German. In his Table 1, he looks at the $g$ factor of Zeeman lines and compares that with predictions based on the $g$ factor for each level in the transition in order to determine the configuration of the term. He writes on page 729 (translated from German): "From the table of Zeeman effect measurements it is immediately apparent to what extent each term is supported by the observation of the Zeeman effect." – Paul Oct 31 '19 at 23:22
• Thanks, I will try go thru it. DeepL translator is pretty good and I can find the relevant paragraphs. – M. Farooq Oct 31 '19 at 23:52
• I do believe I saw some explanation of this in, "Inorganic Chemistry: 5th Edition" by Gary L. Miessler. It's been quite a while since I took the course, but the content of that book seems fairly relevant to your question. I hope that helps. – Melanie Feb 29 '20 at 8:04

As far as I know, it was a long and complex undertaking. You can't look at a single atomic species by itself. The understanding of level assignments to series slowly grew starting from the simplest cases.

Of course the first was hydrogen, where - at least initially - no series are discernible but one - there is almost perfect degeneration on l . But that helped, as it allowed the first step, the one from wavelengths λ (or wavenumbers k=1/λ) to terms, later identified with energy levels. It was Ritz' combination principle: k=Tm−Tn. Already at this introductory level, a difficulty was to be overcome: the difference between emission and absorption spectra. The former is much richer. This was explained as a consequence of atoms in absorption initially being in the ground state alone, whereas in emission photons are emitted by excited atoms jumping to a lower state, not necessarily the ground one. For hydrogen this is especially notable, as there are no absorption lines in the visible region - the Balmer series has n=2

.

Then alkaline spectra were explored. In absorption spectra only lines Tn−T1 are observable, where T1 is what later would become the ground state energy (divided by hc). Note that here n=1, meaning the ground state, but this is not the principal quantum number of hydrogen-like classification, which is 2 for Li, 3 for Na, etc...

The main difference between hydrogen and alkaline spectra is that in the latter l degeneracy is broken. This required to separate terms in several series. Surely you know the origin of symbols S, P, D,... related to a different appearance of lines starting from different series towards the same final term. An instance is transitions S-P and D-P (in emission), In absorption only S-P transition is visible, giving rise to the principal series (therefrom P-terms).

But a second feature appears in alkaline spectra: the so-called "fine structure". It exists in hydrogen lines too, but is much less prominent, whereas the famous sodium doublet requires a modest resolving power to be seen. Its interpretation required the discovery of electron spin and of L-S coupling. The effect was a doubling of columns for all series, S excepted.

Well, this is a rough history, as I'm able to follow. Maybe a book could be of help: G. Herzberg, "Atomic Spectra and Atomic Structure". It's outdated as far as theory is concerned, but thanks to its publication date (first edition 1936) is nearer to the times when the studies were carried out.

• Thanks for comments. Although Herzberg's Atomic Spectra is a lovely book, unfortunately he never discussed about spectral assignments of lines nor talked about electron configurations. I am waiting for other expert opinions as well. – M. Farooq Nov 1 '19 at 4:56