fluorescence
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Echo Sphere and Hydrogen Atom
Hi,
I recentely watched that Video with Cliff Stoll where he talks about
Science and on one scene he mentions that the way sound is distorted in a spehere could be used to demonstrate Electrons moving around a nucleus in a
hydrogen atom. Now I had theoretical Chemistry which is full of Quantum Mechanics and we discussed the basic equations, calculated simple molecules
and had the Approximations but I can't remember anything that would resemble that specific example. I tried to google it but Echo Spehre or Sound
Spehre, those are all sort of brand names, and then there are Spin Echoes and stuff like that. Dozens of similar names that hide what I am looking
for. Does anyone have a simple answer to what he is referring to or can give me a hint what to look for ?
Thank you 
Here is the video:
https://www.youtube.com/watch?v=xHEIOgONq6A
At 3:20
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blogfast25
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I believe he may be referring to the older wave-mechanical view of the electron in a hydrogen atom as forming a standing matter wave. Sound waves of
the right wavelength would do that in a spherical cavity.
But it's a poor analogy: the electron isn't really a matter wave and it doesn't bounce off the boundary because the atom doesn't have a well defined
boundary anyway.
[Edited on 9-9-2015 by blogfast25]
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fluorescence
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Mhm you're probably right, I didn't think of that. You are referring to the model where the electron is a wave
that must perfectely close without creating a destructive interference ? Could be it.
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Fulmen
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All analogies fail if you examine them close enough. That doesn't mean they are useless, just limited.
We're not banging rocks together here. We know how to put a man back together.
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blogfast25
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Quote: Originally posted by fluorescence  | Mhm you're probably right, I didn't think of that. You are referring to the model where the electron is a wave
that must perfectely close without creating a destructive interference ? Could be it. |
Take a look at the radial probability densities of the ns orbitals of hydrogen:
http://hyperphysics.phy-astr.gsu.edu/hbase/hydwf.html#c1
The peaks and troughs for 2s, 3s etc represent the 'nodes' of the 'standing wave' but as you can see the 'wavelengths' (if you can call 'em that!)
vary from one node to another! Standing sound waves in a spherical cavity would look very different.
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annaandherdad
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| Quote: Originally posted by fluorescence | Mhm you're probably right, I didn't think of that. You are referring to the model where the electron is a wave
that must perfectely close without creating a destructive interference ? Could be it. |
Yes, that's right. The quantization of energy levels of atoms was known well enough after Bohr's work in 1911, but the Schro"dinger equation didn't
come until 1926. When it did, the realization that energy levels were eigenvalues of a wave operator came as a great revelation. People at the
time drew the analogy with the quantization of frequencies of modes of waves in a resonant cavity.
Actually the Bohr quantization conditions are equivalent to the idea that an integral number of wavelengths has to fit around a classical orbit. As
blogfest notes, the wavelength is not constant, rather it's a function of position on the orbit, so the quantization condition involves an integral.
Sommerfeld improved on Bohr's quantization condition, realizing that an integral number of wavelengths had to fit in each of the 3 directions in space
(one radial and two angular, in the case of a spherically symmetric problem like the hydrogen atom or the waves in a spherical cavity).
The main difference between a cavity (for sound waves, for example) and the hydrogen atom is that the walls of the cavity, which confine the waves,
are replaced by the electrostatic attraction of the nucleus, which confines the electron. I would not dismiss the analogy too quickly, it is quite
apt. For example, both in the case of the hydrogen atom and the waves in a cavity the radial eigenfunctions are oscillating functions (waves) whose
wavelength depends on position, and the radial part of the Bohr-Sommerfeld quantization condition provides an excellent approximation to the
eigenvalues (exact, in the case of hydrogen). Also, the angular parts of the waves are the same in both cases.
Any other SF Bay chemists?
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fluorescence
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Eww... I remember these diagrams from the link those were usually exam questions.
So far thanks for all the ideas. I wasn't even sure what how a wave behaves in a spehre or how he
wanted to compare it to an atom but that sounds quite logic now.
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