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Atom model wrong?

  1. Apr 20, 2004 #1
  2. jcsd
  3. Apr 21, 2004 #2

    arivero

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    ¿hmm? The currently accepted model of atom is that each electron is a standwave around a central potential. It is so since Bohr and Sommerfeld. Or, better, since De Broglie.
     
    Last edited: Apr 21, 2004
  4. Apr 21, 2004 #3

    ZapperZ

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    Actually, the Bohr-Sommerfeld model isn't quite right either. The Bohr Atom was part of what is now known as the Old Quantum Mechanics. The naive picture of "standing wave" can only be loosely applied to maybe the angular component of the atomic wavefunction. The radial part has no "standing wave" in the traditional sense.

    There is a related string in the General Physics section (of all places) under the topic "Protons and electrons" where I tried to discuss extensively the H-atom model. So maybe the originator of this string may want to read that.

    Zz.
     
  5. Apr 21, 2004 #4

    Njorl

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    Models are always wrong.

    There are many atomic models from which you can choose. You will never be "right". The question is, how wrong are you willing to be, and how much time are you willing to spend increasing your accuracy.

    You can't very well teach grade school kids quantum mechanics, but you can teach them that electrons orbit a positively charged nucleus.

    The latest models accurately predict just about any measurement we can make, but they are not perfect. We do not have an agreed upon model for gravitational effects in quantum mechanics, nor could we measure those effects if we did. Someday, naive but well educated physcics students will point to our models and say, "They were wrong. They ignored such-and-such."

    Njorl
     
  6. Apr 21, 2004 #5

    ZapperZ

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    Oy.. I hate to think that I was trying to convey the idea that there is a "correct" model. In my other posting in that string that I cited, I mentioned that we have no exact solution even with our current "model" for anything beyond the simple He atom. So far be it from me to insist of such things.

    I have no idea the educational background of the person who asked this question. So I didn't make any guess as to what level of sophistication that an answer should be restricted to. However, having said that, I also do not think it is too much to refrain from telling high school kids, for example, that electrons orbit the nucleus. This is because once we tell them that, it seems to stick in their heads of such a picture, and it takes years to get that out of their systems. And that is if they're lucky enough to actually continue studying physics. Most don't and graduate with college degrees continuing to believe in such a picture.

    So while I agree that there's only so much we can tell the students at the elementary level (re: my discussion on buoyancy for 8th graders in another string), we must also try to minimize doing any "damage".

    Cheers!

    Zz.
     
  7. Apr 21, 2004 #6

    arivero

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    Still, the whole wavefunction, combining radial and angular parts, is a standing wave. Ok, It has two peculiarities:
    -it is not a free wave, but a wave under the influence of a central potential.
    -it is not a real valued wave, but a complex valued one.
    But the main peculiarity of standing waves remains: it is the result of constructive interference.

    A kind of free wave can be seen by using a 3D spherical infinite well instead of a central potential. There, the wave moves freely, bouncing in the spherical wall. The eigenfuncions are the resulting standing waves, and you can label them with angular momenta, decompose them on radial and angular parts, etc all the same that with atomic wavefunctions.
     
  8. Apr 21, 2004 #7

    TeV

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    I haven't heard of such presentation.
    Any refferences,informational links?Thanks.
     
  9. Apr 21, 2004 #8

    arivero

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    TeV, do you agree in that the energy eigenfunctions of the one dimensional infinite well are standing waves "moving" (er, freezing?) according schroedinger wave equation?

    If so, which problem do you forsee for higher dimensional wells?
     
  10. Apr 21, 2004 #9

    TeV

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    I was asking wether the mathematical representation in 3 D spherical well you 're reffering to have some advantage (like simplycity) over model of standingwave around central potential resulting from application of wavefunction?
     
  11. Apr 21, 2004 #10

    ZapperZ

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    I didn't reply immediately to this because I had to think a little bit on what you were trying to say. I have a feeling that we have have a slight language/semantics problem. I am not quite sure what you mean by "free wave". If you mean this as the wavefunction for a "free particle", then this is self-contradictory because by being in an infinite well, the particle does not have a wavefunction of a free particle due to the boundary conditions.

    Secondly, I'm not sure what you mean by "But the main peculiarity of standing waves remains: it is the result of constructive interference" in the case of an infinite spherical well. The radial solutions here are the spherical Bessel functions. These look nothing like "standing waves ... the result of constructive interference" as what one sees in standing waves in strings fixed at both ends, for example.

    But I tend to guess that I'm wrongly interpreting what you wrote.

    Zz.
     
  12. Apr 22, 2004 #11

    TeV

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    Problem in the atom case might be characterisation of 3D well to be infinite in all the cases.I like your analogy of the waves bouncing in the "wall" ,being reflected ,forming interfference patterns like in classical cavity but this shouldn't be understood literarly of course.Does this analogy help in calcultions?Also,shouldn't there be limitations (you say it is always valid since it is analogous to every other manipulation of atomic wavefunction).The "wall" you mentioned corresponded to what (is it somehow correlated to the concept of a potential barrier??)
    For instance,how to treat cases when 3D spherical wells "interact" to form stable configurations, when atoms join in molecules in calculation of say water molecule plane angle between 2 hydrogens and oxigen (~105°) ,and other things related ?
    We can always join the wavefunction to any physical system.
    The wavefunction alone has no physical sense,but its square gives the probability of a particle to be found in a certain volume of 3D space.For macroscopic body the wavefunction is located in the body (result is correspondingly extra small wavelenght of motion) and the state of the system is completely described by coordinater,momentum p,and energy E. This is embeded in Newton's classical equation.Similar equation exists for the microscopic systems (Schroedinger eq) but the wavelenght joined isn't irrelevant,and QM operators such equation must contain.Once I came across thought that in higher dimension representation,could be maybe possible to give description of microscopic system that would look more like a classical description (without probabilities) than like Schroedinger.I highly doubt it would possible though.
    Anyway any classical analogy in description of QM system ,that can give more naive picture of the process,or help in calculation is certainly progress and I'm interested in such ideas.
     
  13. Apr 22, 2004 #12

    arivero

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    Ah, the idea was that the wave around central potential suffers a force field in every point of the space... so it can not be said to be "free" in any sense. On the other hand the wave on the well does not suffer any force except in the wall, where a impulsive bouncing happens. So in some sense it is really "free" in the inside.

    The classical example of standing wave is a guitar string, where the wave is free along the string but it suffers bouncing in the extremes. So it was a very similar example.

    The idea of suggesting an spherical well instead of for instance a cubic one is that here we have rotational symmetry. Thus angular momentum is preserved, and we can decompose the wave in eigenfunctions of angular moment, very much as in the central potential problem.
     
  14. Apr 22, 2004 #13

    arivero

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    Let me stress that I was not suggesting to use cavities (3D infinite spherical wells) to model atoms; I was just advancing another example where it was easier to see that the standing wave approach is really the standard view of quantum mechanics.

    ZapperZ, the point is if you are able to see the effect of constructive interference in the trivial case, the one dimensional string guitar, or its quantum mechanics equivalent, the one dimensional infinite square well. If so, just go up to 3D for instance in the inside of a cube (tridimensional infinite square well) and you should still be able to see the constructive interference component by component.

    Now deform the cube smoothly to get a circular cavity. You should visualise that the standing wavefunction deforms accordingly. But it is still a 3D standing wave. The new thing here is that spherical symmetry lets you to decompose it in a radial part and an angular part. Of course the radial and angular part, by themselves, are not a standing wave, but its composition is.

    Last step, enable slowly a central force field while moving the spherical wall away to large, large radious. Again the wavefunction deforms smoothly and then you get the eigenfunctions of the corresponding QM problem. If you use a central inverse square field, you will get the levels and funcions of hidrogen atom.
     
  15. Apr 22, 2004 #14

    ZapperZ

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    OK, so I'm almost certain we have problems of semantics here. You said that for the cubic case, we should be able to see the "constructive interference component by component". Yet, as we go to spherical symmetry, you said that the radial and angular part, by themselves, are not standing waves. Aren't the radial and angular part the "components" of the wave in spherical coordinates? The "r, theta, phi" components are as separable as the "x,y,z" components in cartesian in the two cases.

    The "standing waves" in 1D case looks different than the standing wave in 2D case, and these in turn look different than the standing wave in 3D case. An oscillating drum membrane (standing wave in 2D) has more of a 2D Bessel function look - largest amplitude in the middle antinode, and tapering off as it gets to the edge. In the 1D string case, the antinodes tend to have constant amplitude throughout the length of the string. This differences continue into the 3D case. While single-valuedness of the angular component is maintained for whole integer solution of the angular momentum, take note that when we solve for the spin angular momentum with half-integral values, this is no longer true. You need a rotation of 4pi (not 2pi) to get back the same symmetry for a spin 1/2 case. Again, that doesn't feel like the same old "standing wave".

    I think I am being nitpicky here (anal-retentiveness is a curse that I live with). I would rather tell students that these are similar to the "available modes of oscillation" for a particular geometry and boundary conditions. If they have done E&M and Solid State Physics, this would fit very well with what they have already learned. In fact, even some electrical engineering majors would know this if they have done waveguides and transmission lines, etc. However, having said that, I also think that we don't do any damage if we tell them about these things as "standing waves". I just don't think it should be the one depicted from the Bohr-Sommerfeld model. :)

    Zz.
     
  16. Apr 22, 2004 #15
    Thats why its called a "theory"
     
  17. Apr 22, 2004 #16

    ZapperZ

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    I was going to refrain from replying to this one, but against my better judgement, I will.

    You need to keep in mind that in science, and in physics in particular, a "theory" is not a designation that it is unverified or untested. It is more of a dichotomy between "experimental" and "theoretical". In other words, a "theory" doesn't graduate into being called a "law" or a "principle" after it has acquired sufficient verification. It is simply a label to distinguish something from experimental work.

    So the use of the word "theory" isn't the same as used in the pedestrian way. The reason why I feel that I have to respond to this is that this is the very same argument being used against the "theory" of evolution - that it is JUST a theory (as if Quantum Theory is JUST a theory). This is a complete misconception of the context of the word "theory" as used in science.

    I'm not implying that this is what you had in mind. I just want to make sure that people who read the comment are clear about this.

    Zz.
     
  18. Apr 22, 2004 #17

    arivero

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    I partly concede the point. The "r, theta, phi" are standing waves in some sense. Point is that in the "x,y,z" decomposition of the cubic problem, each component can in turn be mapped to a one dimensional problem in a trivial way, while for the "r, theta, phi" decomposition of the spherical problem, one must consider the fictitious forces (eg the repulsive core for l>1) and visualisation is not so easy.

    I would not say "in the two cases". In the cubic case you can separate in product of functions of x,y,z. In the spherical case you can separate in product of functions of t, theta, phi

    That was all the history. Lets keep the perspective. We are answering a question from brookstimtimtim who wonders if the current atomic model is or not a standing wave model. I sustain that the standard QM interpretation of a eigengunction of the hamiltonian is just a standing wave; it is only that it is a complex wave and the wave equation is schroedinger equation.

    Aha, I see. Perhaps our semantic problem, at the end, is our interpretation of the Bohr-Sommerfeld model!
     
  19. Oct 8, 2006 #18
    I know this is off-topic, so ill make it quick

    I can understand why you couldn't refrain from replying to the post, as I agree with you completly. People do tend to missunderstand what a theory is, and how it isn't the lack of verification that keeps it from being a law, but the lack of falsification that allows it to maintain its place as a principle.
     
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