Experimental Assignment of Electronic Transitions in Atoms (Grotrian Diagram)

Question

Grotrian diagrams often taught in instrumental methods of chemical analysis to chemists. After a decade, I finally found the original book of 1927 by Grotrian "Graphische Darstellung der Spektren von Atomen und Ionen mit ein, zwei und dreivalenzelektronen" It turned out it is a classical German style handbook with these diagrams for each element. A question which always bothered me as a chemist, is how do we experimentally assign electronic transitions from an atomic spectra for complex atoms. What was the procedure, which seems to be established as early as 1920s? I searched so many texts but nobody talks about experimental procedure of making assignments. For example in this diagram for Cs? How do we experimentally determine or calculate that a spectral line of 894 nm is a transition from 1s to 2p in Cs atom or a 1002 nm is transition from 3d to 4f?

Thanks.

Answer 1

$\let\l=\lambda$ AFAIK 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 $\l$ (or wave numbers $k=1/\l$) to terms, later identified with energy levels. It was Ritz' combination principle: $$k = T_m - T_n.$$ Already at this introductory level a difficulty was to be overcome: the difference between emission and absorption spectra. The former are much richer. This was explained as a consequence of atoms in absorption initially being in 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 $T_n - T_1$ are observable, where $T_1$ is what later would become the ground state energy (divided by $hc$). Note that here $n=1$ means 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 facts were happening.

Answer 2

Here's how I would do it. Pick a high wavenumber transition. That has just set the relative energy difference between two levels. Search through the rest of the transitions for two that add up to the first. You now have three relative energy levels. Continue this for the remainder of the transitions. This process would be relatively easy by cutting out paper with lengths proportinal to the wavenumbers.

Once complete, the lowest level is presumably the 1s level. After this, you might think things get sketchier. For example, naively, one might expect 2s to be the next highest, but it is not. I don't think this would be a problem.

They knew about the Zeeman effect and the multiplicity of lines. I presume they used this to deduce which levels were which. This is consistent with their knowledge of the atomic term symbol at the head of the column.

Edit based on OP comment: First, I made a mistake in my description because I ignored the forbidden transition. So, the first step would have to involve four transitions. For example, they have four transitions between the levels that they call 1$s$, 2$p_1$, 2$p_2$, and 3$s$. By looking at the transition energies, they would see that the sum of the 1$s$-2$p_1$ and 2$p_1$-3$s$ transitions would be the same as the sum of the 1$s$-2$p_2$ and 2$p_2$-3$s$ and transitions. Of course they wouldn't know the labels. This sets the relative levels of these four states. Through the method of deduction, the remainder of the relative energy levels are determined.

The one level farther from the mass of closely spaced levels will be the 1$s$ and will tell you which way to orient the levels. An ionization energy will get you the absolute energy levels.

All that is left is to assign the electron configuration/atomic term symbols ($^{2S+1}L_J$). The quantum numbers would be deduced from multiplicities of levels seen in Zeeman-type experiments.