Revisiting the Bohr Model

After distracting myself the last two weeks with a copper-cyanide research project, I have returned to reading Helen Kragh’s Niels Bohr and the Quantum Atom. In a previous blog post, I described an inquiry idea I got from the book based on Thomson’s (flawed) atomic model. In today’s post I ponder the difference between Bohr’s original proposed model in 1913 versus the Bohr model as described in textbooks today. In the figure below, I have illustrated the two models using the argon atom.

If you’ve taken a chemistry course, the model on the left should look familiar. The Bohr electron configuration is (2,8,8) with the innermost shell having two electrons. The outermost shell has eight electrons corresponding to the “octet rule” – I have argued previously that one should be careful teaching this topic since students tend to imbibe the ‘happy atom’ story even when you as a teacher make the effort not to spin the tale that way. On the right, you see Bohr’s original 1913 idea. The electron configuration is flipped (8,8,2); and if you drew this on your chemistry exam, your teacher would likely flip out.

I can imagine a teacher (myself included) saying “That’s just wrong! The first shell can only accommodate 2 electrons, then the next two shells can accommodate 8 electrons, blah, blah, blah…” But why, though? You might be tempted to invoke the quantum numbers if you’re teaching general chemistry, but a skeptical student should see them as arbitrary. Why do those quantum numbers have those arbitrary rules? And who’s to say that they translate into the Bohr shell model the way you’ve described? (Unless you recall your own Quantum Chemistry class, you’ll be at a loss to explain any of this.) A much stronger argument can be made using experimental data from photoelectron spectroscopy, and I’ve opted to use this approach the last several years in my general chemistry course even though the standard first-year college chemistry textbook does not.

Bohr was a very, very clever scientist. Is there anything we can learn from his original “wrong” model? Maybe it isn’t so wrong after all. First let’s take a look at the electron configurations for the first twenty-four elements as presented in Kragh’s book (Figure 2.3) shown below.

The first six elements (Hydrogen to Carbon) are what you would expect. But then Bohr proposes Nitrogen is (4,3) instead of (2,5). The argument was based on chemistry, i.e., in its chemical compounds, nitrogen is known to be trivalent – it forms three bonds with other atoms, never five. Phosphorus (#15) is correspondingly (8,4,3) instead of (2,8,5). While phosphorus can be pentavalent, its trivalent compounds are significantly more stable thermodynamically. Bohr takes chemistry seriously and considers the types of stable compounds formed by each element, just as Mendeleev did fifty years prior in his iconic version of the Periodic Table. Oxygen is (4,2,2) since it tends to be divalent; Fluorine is (4,4,1) since it tends to be monovalent. Interestingly H, F and Cl are in the same ‘row’ on the table above indicating that they all just tend to form one bond.

While Neon (8,2) has two outer electrons in the original model, this places it in the same ‘row’ at Helium and Argon – all unreactive noble gases. It doesn’t demand that having two outer electrons corresponds to being divalent. However, we now know that when noble gases do form compounds (as difficult as that might be), the smaller ones tend to be divalent. Krypton difluoride, KrF₂, was synthesized in 1963; and when the divalent H-Ar-F was finally synthesized in 2000, there was cause for celebration! So maybe Bohr’s original idea wasn’t so ridiculous after all.

The naysayer might argue the messiness of having inner shell accommodations vary as atomic number increases. While elements #3-#6 accommodate 2 inner electrons in Bohr’s original model, elements #7-#9 accommodate 4 inner electrons, and then the rest have 8 inner electrons. (And then you see the same pattern of 2,4 and then 8 build up in the second innermost shell.) It’s a “reverse octet rule” except that it progresses in even-numbered stages. It turns out Bohr has some good reasons for the even numbers (see Kragh’s book for more information), but the idea of increasing the number of inner electrons has merit. As the atomic number (# of protons) increases, the electrons should experience a much stronger electrostatic attraction and be increasingly pulled closer to the nucleus. Who’s to say what the limit should be? (Bohr picked 8 as the limit because of periodicity, again appealing to chemistry!) Remember, at this point we don’t know about the four quantum numbers although there is some idea that quantized shells exist and that electrons have angular momentum.

In fact we use this sort of argument when appealing to the transition metals. In General Chemistry you would recognize this as the strange exception where if asked to write the electron configuration of a transition metal cation, you must remove the s-electrons before the d-electrons. For example, neutral titanium atom is 1s²2s²2p⁶3s²3p⁶4s²3d² but the Ti(+1) cation is 1s²2s²2p⁶3s²3p⁶4s¹3d² instead of 1s²2s²2p⁶3s²3p⁶4s²3d¹. Students are flabbergasted by these exceptions. The reason we give them for this reversal of affairs? For transition metal cations, the 3d subshell ‘sinks below’ the 4s subshell in terms of energy. We say this having just taught them the Aufbau principle for writing electron configurations with its weird ‘inter-level’ crossings!

When we discuss trends in the periodic table, how atomic radius or first ionization energy change across a row or down a column, we often appeal to contraction or expansion of the shells. By this we mean that the ‘circle’ representing the shells gets smaller or larger, but not the number of electrons (at least that’s the mental picture we give the students). But having electrons move from outer to inner shells is not unreasonable. If we did not go into orbitals and quantum mechanics, there’s a lot you can do with the original Bohr model that avoids all manner of strange exceptions because Bohr based his ideas on chemical valence.

In 1913, Bohr attempted to conceive molecules. The picture above (Figure 2.4 from Kragh) shows some early sketches of H₂, H₂O, O₂, O₃, CH₄ and C₂H₂. For H₂, the two electrons in the chemical bond are illustrated as rotating in a circle (because: electrodynamics). In O₂, four electrons are involved – in today’s Lewis dot structure parlance we call this a double bond. CH₄ is correctly predicted to be tetrahedral, and C₂H₂ is indeed linear although there should be six electrons in the middle ‘ring’ rather than four. Although H₂O and O₃ are incorrectly drawn as linear, Bohr anticipates the resonance structures of ozone with two diagrams. Lewis dot structures combined with VSEPR Theory would ultimately prove superior, and Bohr being the physicist had very complicated calculations for the electrodynamics of the electrons in his model.

One reason for the success of Bohr’s theory is how it explained the results of spectroscopy – those patterns of light you see in a chemistry textbook. (This previous blog post has an example.) Bohr didn’t know why or how an electron jumped from one level to another. “How does it know where to stop?” is a question my students should ask when they encounter this, but no one has done so the last several years. Pity. I think it’s because I have well-prepared students, who have encountered these models before, and so the strangeness eludes them. What I’ve enjoyed about Kragh’s book is a reminder of the strangeness of the chemistry models of atoms and molecules. Historians of science, please continue to do your good work!

P.S. In case you’re wondering what happened to the copper-cyanide project mentioned in the first line, I’m temporarily stuck. This is a very common state of affairs in research. I usually leave the problem alone for a while before getting back to it later. Is it part of the Creativity cycle? Stay tuned for the next blog post!