Is Bohr’s model of the atom still up to date?
The question arises why Bohr’s model of the atom from 1913 – even after the 100th anniversary of quantum mechanics – still holds such a prominent place in school physics.
G. Sauer has provided a didactically very rewarding discussion of the arguments for treating Bohr’s model of the atom in school, which we quote here: G. Sauer, “Didaktische Aspekte der Bohrschen Atomtheorie” [Didactic aspects of the Bohr theory of the atom], in: H. Fischler (ed.), Quantenphysik in der Schule, IPN Kiel (1992), p. 69:
* Presenting Bohr’s model of the atom gives insight into a chapter in the history of quantum mechanics.
The only critical remark to make regarding this function is that the planetary model from 1913 should be regarded as a rather short-lived precursor of quantum theory, whose significance in the history of physics should not be overestimated. For a presentation of the history of physics, an essentially verbal treatment is already sufficient. If the hydrogen atom is only considered at a more advanced level, after the introduction of elementary quantum mechanics, as in BADER (1972), the model can be classified, through critical commentary, within the later development of quantum theory. From a historical point of view, it seems to me hardly worthwhile to address the further development toward the BOHR–SOMMERFELD model with elliptical orbits in class. In any case, less time is available in class for the history of physics than one would wish, so that this limited amount of time must be allocated carefully.
* The model of electrons moving on certain, allowed “planetary orbits” around the atomic nucleus offers a simple, intuitive way “to describe and interpret a wealth of empirical facts” (Höfling 1976).
In fact, the model can only describe the energy levels, and even that, in quantitative terms, only for the hydrogen atom. The regularities of the hydrogen spectrum are thereby traced back to the quantization of energy, and the RYDBERG constant can be calculated, i.e. expressed in terms of universal natural constants. As far as an actual explanation of the empirical facts described is concerned, the planetary model is further removed from it than, say, KEPLER was from NEWTON’s mechanics. The degree of understanding of the physics of atoms that Bohr’s model can convey to students is not, by itself, enough to justify the special role that is evidently granted to it in school teaching.
Of course, students can also learn a great deal from a purely phenomenological description of atomic physics, without any underlying theory. Didactically, however, it seems important to me to clearly distinguish a phenomenological description from a model-based explanation or a theory.
* Presenting Bohr’s model provides one motivation (among others) for introducing quantum mechanics.
What can be motivating here is the very deficit in justifying the postulates that are introduced, and the unresolved coexistence of classical physics and quantum conditions. The presentation should accordingly bring out, critically, the unsatisfactory status of the model.
A presentation that first stretches the model too far and then, in the end, cites the limitations of the supposedly so successful model as the reason for better atomic models will tend to obscure the need for a fundamental revision of classical physics rather than bring it out clearly.
The step that is probably most essential for students in moving from classical mechanics to quantum mechanics – namely, giving up the idea of motion along classical trajectories – cannot be convincingly justified in school by using the atom. The main motivation for this step comes instead from discussing the directly observable wave properties of matter (diffraction, slit experiments). Here, the electron diffraction tube is the most important experiment in school for demonstrating wave-like properties of electron beams.
In many approaches, experiments from wave optics are considered in parallel with analogous experiments using electrons, with the observations made with light interpreted using the photon hypothesis. As an example, one may cite the optical biprism experiment in analogy to the MÖLLENSTEDT experiment with electrons.
* In school, Bohr’s theory has to substitute for a quantum-mechanical description of the atom, because the latter is regarded either as too difficult or as too time-consuming.
Insofar as the physics of atoms must be regarded as a necessary part of school physics at all, it is difficult to argue against this reasoning as long as one has no alternative quantum mechanics of atoms suitable for the majority of students to offer instead. This does not necessarily mean that the basic ideas leading up to quantum mechanics have to be abandoned. There are, however, simpler physical systems, far better suited didactically, for introducing and explaining the basic concepts of quantum mechanics than treating even the simplest atom.
For school physics, it is probably already a significant success if a few basic ideas of quantum mechanics can be used to make the stability of the atom and the quantization of energy as such plausible. Deriving the energy ranges of the hydrogen atom is, at any rate, not a primary goal here.
* Treating Bohr’s model of the atom in physics lessons can mislead students.
If the allowed circular and elliptical orbits play a central role in the presentation, students can easily end up with “intuitive” pictures of the atom that, according to our present state of knowledge, certainly have little to do with reality. For instance, the quantization of energy and the radiative transitions that give rise to the spectra are usually represented in an energy-level diagram. A graphical representation of the corresponding circular orbits, or even of the transition itself in such a picture, contains no more information than the level diagram, yet unnecessarily suggests a misleading picture.
Quantum physics, which after all requires letting go of entrenched ideas and habits of thought, will always find it very difficult to displace such pictures once they have taken hold. The possibility of associating intuitive orbits with energy levels is also a didactic dead end. Must we not assume that, for students less interested in physics, the only thing from atomic physics that will outlast the school years is the picture of orbiting electrons?
In summary, I draw the conclusion that the didactic value of Bohr’s model of the atom, if understood as the planetary model from 1913, should be assessed as being hardly greater than the model’s scientific value. On the other hand, we are today still so far from an elementarization suitable for schools that the need for an “atomic theory without quantum mechanics” is understandable. This negative motivation seems to be the only convincing justification for all quasi-classical atomic theories in teaching.
The following advantages and disadvantages of treating Bohr’s model of the atom can be summarized:
Advantages:
* Easy for students to follow and to visualize.
* Bohr’s postulates can be used to explain the further development of atomic structure, thereby also showing the limits of the model.
* The formula for calculating the energy levels can be justified intuitively in terms of “shells”.
Disadvantages:
* Misconceptions about the atom become entrenched in students’ minds.
* There is a discrepancy between school and university textbooks.
* The model is not suited to giving a concise, simple overview of quantum mechanics (the model predates the emergence of quantum mechanics).
* It remains unclear whether, and why, an atom is stable.
* This model does not correspond to the one used in chemistry.
* In addition, a criticism of Bohr’s model of the atom is that in the formula for the angular momentum, L = n · h/2π, with n = 1, 2, 3, …, the result is always nonzero. In this model, therefore, there should be no s states.