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Re: [Phys-L] the Bohr atom, or not



On 04/25/2013 06:55 PM, Aburr@aol.com wrote:
"What am I missing?"
You are missing a familiar (solar system) simple visual model which
illustrates (notice I did not say explain) many features of an atomic model.

OK, that's exactly the sort of answer I needed. Let me see if I can
boost myself into a place where I can see both sides of the argment.

Arguments *for* the Bohr model:

++1) It's a model. Any model is better than nothing.

++2) It makes some correct predictions.

++2a) In particular, predicting the hydrogen energy spectrum is an
impressive feat.

++2b) Not surprisingly, it also works for He^++ and similar "hydrogenic"
atoms.

++2c) Not surprisingly, it also works for the muonic analogs for all
of the above.

++2d) It also works for so-called Rydberg atoms, where one of the electrons
is in a state with very high angular momentum, just a gnat's eyelash away
from being unbound.

++3) It connects the quantization of energy to the quantization of angular
momentum.


Arguments against:

--1) At no relevant point in the story has there been a choice between
"model" and "no model". It as always been a choice between better models
and worse models. A hundred years ago the Bohr model was /better/ than
everything else ... but it's not anymore. For 85 of those 100 years,
vastly better models have been available.

--2) For every correct prediction, it makes several incorrect predictions.

--2a) The fact that it "mostly" gets the right answer for hydrogenic
atoms is fortuitous. It depends on an amazing symmetry, a hidden
dynamical symmetry of the 1/r potential. The same symmetry that leads
to conservation of the Laplace-Lenz-Runge vector leads to a degeneracy
in the energy spectrum, so that the 2s and 2p states have the same
energy, the 3s, 3p, and 3d states have the same energy, and so forth.

--2b) This degeneracy is broken by the hyperfine interaction and grossly
broken by an applied magnetic field (Zeeman splitting). The Bohr model
cannot begin to account for this. This is basic spectroscopic data that
has been know for at least 150 years.

--2c) It does even get hydrogen completely right. The 1s state has zero
orbital angular momentum, which is rather hard to account for in terms
of Bohr orbits.

--2d) Even for hydrogen, it gets the transition selection rules all wrong.

--2e) The Bohr model cannot be extended to describe even the most basic
features of multi-electron atoms. If you look at 92 different elements,
you get 91 wrong predictions.

--2f) If we take it literally, it predicts that atoms are little flat
disks, flat like the solar system ... which is inconsistent with
everything we know about the mechanical properties of solids.

--2*) et cetera

--3) Most of what the introductory textbooks say about the quantization
of energy is wrong anyway, so connecting it to something else is just
connecting one error to another ... thereby making both of them much
harder to unlearn.

Circa 1900 Planck considered quantization to be a dirty trick, little
more than numerology that fortuitously produced an answer that agreed
with experiment.

In 1905 Einstein considered it a hypothesis, in connection with the
photoelectric effect. By 1907, Einstein was arguing that quantization
was actually /proven/ by the success of his calculation of the heat
capacity of phonons.

However, as with a number of other things, just because Einstein said
it doesn't make it true. All of the thermodynamic calculations, including
Planck's black-body calculation and Einstein's heat-capacity calculation,
depend not on the number of states, but rather on the number of *basis*
states.

As I like to emphasize, the definite-energy states are not the only
states; they are not even the only basis states! You could choose
any other basis and get the same answer. For more about the non-
quantization of energy, see
http://www.av8n.com/physics/coherent-states.htm

On 04/25/2013 08:28 PM, Bruce Sherwood wrote:

I'm not
sure it makes sense to denigrate models that working physicists use
productively.

I don't see how that earns the model a place in the introductory
discussion.

Working physicists know that the predictions of the Bohr model are
nothing more than numerological mnemonics. They model doesn't explain
anything. You know the one-lepton atom is going to have a Rydberg
spectrum; you know that even without mentioning the Bohr model, so
mentioning it doesn't actually help at all.

In addition, precisely because the model explains some of the key features
of the phenomena yet is inadequate in ways that can be talked about, it
provides another useful opportunity to talk about the role of models in
physics, a topic that alas is nearly absent from most physics instruction
at all levels yet is absolutely central to the discipline of physics, and
the aspect which is arguably the most important thing we have to offer to
STEM students.

Here's how that scheme works in this case: It makes the instructor feel
good, insofar as he can say he didn't deceive the students. However, the
students don't feel nearly so good. They've got a model they can't use
... and nothing they can use!

To be constructive, one must show how to replace the worse model with a
better model.

On 04/25/2013 06:55 PM, Aburr@aol.com wrote:

However a quicker solution might be to, at every level, decide what
features of the atomic model should be taught. Then make a large effort to create
a good, widely applicable, visual image illustrating those features (at
every level), Publicize your results.
Another difficulty is that introductory students are more familiar with
particles than they are with waves.

Amen, brother! That is the constructive approach!

I've tried to take a few modest steps in that direction. There are a lot of
different ways to visualize what atoms are doing. No single visualization
gives the whole picture, but given enough partial pictures you can begin to
piece together some genuine understanding.
http://www.av8n.com/physics/wavefunctions.htm

There are a bunch of pictures there, including several different types of
animations. (Some of the pictures that "should" be animated are not,
because I haven't got around to it yet. Making decent physics diagrams
is a major time-sink, and animations are even worse.)

Perhaps the best advice is to get a circular tub or pool of water and practice
setting up various wavefunctions. I spent hours and hours doing this when I
was a little kid. We had a backyard pool that was round, 25 feet in diameter
and 4 feet deep, which is just about perfect for this application. In a big
pool, the Q is large and the coupling to the kid is small, so it might take
a minute or so build up a big amplitude. I knew how to set up N=1, N=2, N=3
et cetera. I knew how to set up px and py waves. I could even set up the
rotating p+ and p- waves. I noticed that it was possible to create a wave
such that the middle was considerably higher than the rim of the pool ...
without sloshing any water over the edge. Of course I didn't know the names
these things, and I had no clue that they were connected to physics (let alone
modern physics) but that didn't stop me from making them. The sad thing is,
when I started reading about chemistry and physics, everything they said about
orbitals was hopelessly confusing. It took me forever to realize, hey wait a
minute, I've seen those things before. I know exactly what those things look
like.
http://www.av8n.com/physics/wavefunctions.htm#sec-ylm-water

For classroom work, a much smaller round tub works fine.

Somebody should make a brief movie of this.

=============================

On 04/25/2013 09:08 PM, Ian Sefton wrote:

Although I agree with John Denker here is a reference for a counter-argument.

McKagan, S. B.; Perkins, K. K.; Wieman, C. E. (2008)
Why we should teach the Bohr model and how to teach it effectively
Physical Review Special Topics – Physics Education Research
Volume: 4, Number: 1, Pages: 010103
URL: http://link.aps.org/abstract/PRSTPER/v4/e010103

Thanks for that.

Those authors say in part:
"we find that comparing and contrasting different models is a key feature of
a curriculum that helps students move beyond the Bohr model and adopt
Schrödinger’s view of the atom."

Surely we all agree that comparing and contrasting different models is a good
thing ... but that doesn't mean that the Bohr model needs to be part of the
mix. One can compare and contrast
-- models using waves on a string
-- models using waves in a pool of water
-- computer animations using dot-density plots
-- computer animations using amplitude and color-coded phase
-- lots of other things, each of which involves more sense and less
nonsense than the Bohr model.

Bottom line: What really bugs me is the messed-up sense of priorities, i.e.
spending time on the Bohr model to the exclusion of so much other stuff that
would be in every way better.