Envisioning Electron Wave Properties

[JFS321]

Hi all, I have a few questions regarding electron shells and seeing if they should be intuitively connected to de Broglie's description of electrons as waves. I teach high school level and occasionally get wild questions...if I can ever help a student in the slightest I am inclined to try. So, am I correct in the following?

The 1s subshell can be envisioned as a standing wave wrapped around the nucleus. The waveform has 1 crest. The crest of one wave represents a single electron, and the trough of the same wave might also represent another electron if the shell is filled completely. They must be out of phase to agree with the Pauli exclusion principle. If this is correct, then can it be applied to all remaining subshells?

Thanks in advance.

 

[dextercioby]

Sorry, but I can't advise to teach nonsense to 16-17yr old. It's better to tell them what the textbook already contains and add that the de Broglie 1923-1924 model of pilot/matter waves was very short lived (about 2 years) and is only taught in HS because of its mathematical simplicity and perhaps its important historical value (it certainly meant something for Schrödinger).

 

[JFS321]

So, is it no longer true that the principal quantum number also equals the number of wavelengths found in the standing wave?

 

[dextercioby]

It is true for the model itself, the problem is that the model is a wrong description of nature, that's all.

 

[bhobba]

All I can do is reiterate what Dextercioby said. The De-Broglie model is wrong - it perpetuates the wave-particle duality idea that is at best misleading. It's simple to understand and is an important historical step - but that's all it is. Best to tell your students the truth.

Thanks
Bill

 

[vanhees71]

Already in my high-school times (Germany "Abitur" 1990), we first had to learn all the wrong ideas of "old quantum theory", including the idea the photoelectric effects shows the existence of photons (it does NOT!), the Bohr atomic model (which was known to be wrong already when it was made by the chemists, who knew that hydrogen is not a little disk but more a round ball) and the socalled wave-particle dualism. This is very bad didactics, because you teach outdated and nowadays wrong considered things in a subject which is utmost hard to understand (not the maths is difficult in quantum theory but to get used to the completely new way of thinking about nature and its observation it implies) compared to classical physics. Fortunately we had a very good physics teacher, who then told us the modern picture in introducing the Schrödinger equation for simple cases (infinite square well and the like). You can even discuss Schrödinger's approach of the non-relativistic hydrogen problem in this way.

Unfortunately, I don't have a good idea, how to introduce quantum theory adequately at the high-school level, because you don't have the necessary mathematics available. If I had to teach high-school students about it, I'd also start with some historical introduction to motivate, how wave mechanics came about but always stress that this is only a historical step towards the correct picture established by Heisenberg, Born, and Jordan; Schrödinger; Dirac in 1925/26. Then you have a lot of time to discuss modern quantum mechanics on a level that's understandable to high-school students rather than teaching them outdated models. It's not that these models are bad in themselves. They were indeed very important to find the modern quantum theory which is the most successful theory ever, and the "old quantum theory" was developed by some of the greatest physicists ever (Planck, Einstein, de Broglie, Bohr, Sommerfeld). What makes it, nevertheless, bad didactics wise is that it establishes even qualitatively wrong ideas like "discrete orbits" of the electron in the atom or that photons are something like miniature little billard balls (that's the worst thing ever thought, because as massless spin 1 particles photons are as "unparticle like" as a thing can be in quantum theory).

Another important thing is to stay close to what's really observed, and nowadays a lot is observed which was some decades ago only an "gedanken experiment" and could not be demonstrated then but now. A very good starting point is the Stern-Gerlach experiment, high-precision experiments with neutrons with partiallty very bizarre demonstrations of "quantum weirdness" like the socalle "cheshire cat experiment". With some care you can also refer to photons, but to teach them right, it's really very challenging, because you need very difficult math to establish quantum-field theory. Then you can discuss what's a single-photon state, entangled photons, Bell tests, and all that. That's great fun for the students, I guess.

 

[jtbell]

The crest of one wave represents a single electron, and the trough of the same wave might also represent another electron if the shell is filled completely.

The fact that an orbital can contain two electrons has to do with the electrons' intrinsic angular momentum ("spin") which introduces another quantum number in addition to the three that are associated with the spatial distribution. It doesn't have anything to do with "de Broglie waves" which are a long-superseded historical stepping-stone anyway, as already noted.