Hi Pete,
I apologize for the delay in replying to your post. I have a couple of thoughts for you.
First, I take issue with a number of points in the email/message you quoted, in which it was stated that Bohr's model was "thrown out 100 years ago". I wouldn't say Bohr's model was thrown out. Such a statement shows a disregard for the historical context of Bohr's work in this area. Bohr was a smart guy and clearly understood that his model didn't solve every problem with the classical approach to atomic structure. What Bohr was after was the solution of one particular problem: atomic spectral lines. Rydberg was the first to identify a mathematical pattern to the various sets of spectral lines (Balmer, Paschen, etc.) that had been known for some time, but although Rydberg found this pattern, nobody could explain its origin. Certainly not with a classical model of the hydrogen atom. Bohr found a "solution" by restricting electrons to certain orbital distances from the nucleus. Using classical Coulombic energy differences and rigid circular orbits, he was able to show that the resulting energy differences matched the Rydberg formula. This aspect of quantization of electron position was an important step toward full-blown quantum mechanics. But Bohr's model was still fundamentally based on classical physics - that electrons behave like waves was not incorporated into the model at all - and thus it violates many of the principles of QM as we know them today. As such it fails pretty dramatically to give a true picture of atomic structure and - more importantly - doesn't even do a good job of predicting spectral lines in atoms other than hydrogen.
The email/message you quoted also appears to be incorrect in a few places - although maybe I'm missing some of the context. For example: "Since the 2s orbital shows greater density near the nucleus, the energy of the orbital is lower than that of a 2p." This is not true. The energy of hydrogen atomic orbitals depend only on n, the principle quantum number. The 2S and 2P orbitals have exactly the same energy in the hydrogen atom. It is only in a multielectron system where the 2S orbtial becomes lower in energy than the 2P orbital, the so-called shielding effect. (If you want to be really correct, in hydrogen the 2P is actually slightly lower in energy than the 2S due to the Lamb effect, but this has nothing to do with penetration and the effect is quite small - <5 micro-eV - so for all purposes the hydrogen 2S and 2P have exactly the same energy, and this is what is predicted by most elementary QM models.)
Second, the Bohr model correctly predicts the spectral lines of hydrogen, and also correctly predicts the most probable distance of the electron from the nucleus... but, for transitions originating from the lowest energy states, anyway, only in orbitals involved in the allowed spectral transitions of the atom. This latter point is a bit historically fortuitous, admittedly, but it is important to point this out to fully understand what's going on. Consider: the Bohr model predicts electron-nuclear distances in hydrogen for the n = 1, 2, and 3 states to be 1, 4 and 9 in units of the Bohr radius. This n^2 dependence is mirrored in the energies of these states as well. However, as you've pointed out with your plot above, an electron in the 2S differs in its most probable distance (obtained by finding the roots of the derivative of the radial probability distribution) from an electron in the 2P. In fact, if we calculate these, we get the following for the maxima of the n = 1, 2 and 3 levels/sublevels*:
| n | Orbital | Rmax | | | <r> |
| 1 | S | 1.0 | | | 1.5 |
| 2 | S | 5.24 | 0.76 | | 6.0 |
| | P | 4.0 | | | 5.0 |
| 3 | S | 13.07 | 4.19 | 0.74 | 13.5 |
| | P | 12.0 | 3.0 | | 12.5 |
| | D | 9.0 | | | 10.5 |
For completeness I also calculated the mean distance or expectation value, <r>. All distances are in units of the Bohr radius.
What do we notice here? As already stated above, the energy is the same for the 2S and 2P levels, and for the 3S, 3P and 3D levels. The Bohr model correctly predicts these. The Bohr model also correct predicts the most probable distances for the 1S, 2P and 3D levels. But not the 2S, 3S and 3P levels. As you may have correctly guessed, what the 1S, 2P and 3D level probability distributions have in common is that they have no nodes - only a single maximum value where the Bohr model predicts it should be (1, 4, and 9 Bohr radii). Not coincidentally, these are also some of the primarily levels between which spectral transitions are allowed.
Here's what I mean. Take only the first two levels for simplicity. 1S, 2S and 2P. 1S and 2P have electron-nuclear most probable distances predicted perfectly by the Bohr model and 2S does not. The Bohr model was formulated primarily to match hydrogen spectral transitions. The 1S --> 2P transition is allowed. The 1S --> 2S transition is not allowed. Granted, the latter would have the same energy as the former, so it's seemingly a trivial point, but because the Bohr model doesn't incorporate the wave properties of electrons at all, it should be no surprising that the model's predictions of distance only match those orbitals which have no nodes. Same can be said for the n = 2 to n = 3 levels. The 2P --> 3D transition is allowed and both orbitals have no nodes, so this transition is correctly predicted in both energy and most probable electron distance by the Bohr model. 2P --> 3P transition is not allowed. The 2P --> 3S transition is allowed, but its energy is the same as the 2P --> 3D transition, so Bohr's correct prediction of this energy gap is coincidental, and it does not correctly predict the most probable distance(s) of electrons in the 3S orbital. For each primary shell (n value), there is one orbital that has no nodes, and so there is always an orbital in each shell that conforms to both the energy and most probable distance predicted by the Bohr model.
I hope that maybe clarifies some of the strengths and weaknesses of the Bohr model. It certainly isn't right, but it does offer a correct "scaffold" for the energy level structure of the hydrogen atom, it is useful for students as an introductory model and it also has profound historical significance. Therefore to say it has been "thrown out" seems like something of an unfair statement to my mind.
Third, you do seem to have some area of confusion about atomic and molecular structure. Hybridization is a bonding concept related to molecular orbital theory and as such it is no replacement for atomic structure models, even an obsolete one like the Bohr model. Hybridization as a molecular model has itself come into question in many circumstances and atomic orbitals certainly don't hybridize without some energetic payoff in the form of a molecular bond. So it's not really relevant here at all. Atomic spectral lines are completely and quantitatively explained - including fine and hyperfine structure - by a full quantum mechanical treatment (in the case of hydrogen, without the need of approximations). At this point improvements will likely only come in the form of better approximations, but in the case of atomic spectra the models are so good that instrumental measuring limitations are probably a more likely source of line position ambiguity (I could be wrong here). Certainly models are good enough to be able to specify the composition of stars light years away, so it's hard to see what the need is of further improvement.
Finally,
I had been trying to place the Bohr atom in context. If you compare atomic emissions, longer wavelength emissions correspond with larger quantum number transitions. I understand that to indicate that as an element cools, it cools to higher and higher quantum numbers. Seems wrong to me.
Here you seem to be confusing black body radiation with an emission spectrum of a dilute, pure gas. A container of hydrogen gas would obey statistical mechanics: the strength of an emission line would be proportional to the fraction of hydrogen in the origin state at the time of the experiment, which would be dependent on temperature. At higher temperatures, higher energy states tend to be populated, so emission will occur from these states to lower energy states, and these transitions, as you've noted, would tend to have longer wavelength emission. As the temperature decreases, only lower lying states would be populated, and emission from these states would have shorter wavelengths. Therefore as the temperature cools, you would tend to see higher frequency (bluer) emission from the gas. This is different from a black body radiator, where there is a continuum of allowed states. When you cool a black body, the mean radiation frequency red-shifts to lower frequencies.
*I couldn't find these anywhere so I had to calculate them myself. It's been a while since I did this. Errors may therefore be present.
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