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HUP inside the atom

  1. Mar 23, 2007 #1
    I am kinda confused on the whole electrons falling into the nucleus thing (I know you guys have probably seen this question a million times but when I searched the forum, I could hardly find a satisfying answer :frown: )

    So I have heard that the reason electrons don't fall into the nuclues is because of the HUP - if they did fell into the nucleus then their uncertainty in the position would very small which would imply that their momentum would be very large and hence making them fly off elsewhere.

    But then what about energy levels? Can't you say that an electron can't fall into the nucleus because it can't go below the lowest energy level? (Bohr's explanation I believe).

    Also, what do we do about the Coulomb force of attraction? It should technically be cancelled out by some other force right?

    Also, what keeps the protons inside the nuclueus? Is it also because of HUP? What about the strong nuclear force? Isn't it responsible for the stability of the nucleus? Are these two explanations self-consistent?
  2. jcsd
  3. Mar 26, 2007 #2
    Anyone? Please? About 40 people have looked at my question but nobody has given me a reply.
  4. Mar 26, 2007 #3
    I think the fact is, it's a QM thing. You can try to justify it with different simple arguments, but at the end of the day it wouldn't be such a triumph for QM if it had ever truly made sense classically.
  5. Mar 26, 2007 #4


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    In fact, there is a rather easy and a difficult answer to this question. The difficult answer is in fact so difficult, that no rigorous answer has been found yet (although I vaguely remember a recent paper that treated this, but I should look for it).

    So let's go for the easy answer. The easy answer only considers Coulomb interaction (the electrostatic attraction of the nucleus and the electron(s)). Now, if it were so that we should only take into account the Coulomb interaction, then classically, atoms would be stable too! (hence, the difficult answer...).

    If you consider an electron (let's keep it simple) in the electrostatic potential of a proton (we're doing hydrogen atoms here), then you can solve this classically, and find exactly the Kepler problem: all kinds of elliptic orbits are possible, as close to the nucleus as desired, as eccentric as desired... exactly as a planetary system.
    But if you treat this system quantum-mechanically, then it turns out that there are only certain solutions possible, and they are linear combinations of what are called "stationary states", that is, eigenstates of the energy operator (also called, the Hamiltonian). To each of these eigenstates corresponds a specific energy, and it turns out that there is a lowest one: the "ground state". It has, for hydrogen, -13.6 eV. With it goes a wavefunction that has a certain spread in space around the nucleus (although the maximum density is ON TOP of the nucleus). All other states have higher energies, and are more spread out in space, so any superposition will also be at least as spread out as the ground state.

    Now, what's then the difficult problem ? We know that one of the objections to the classical atom model was that classically, an orbiting electron should radiate. So it should loose energy, and it should hence spiral into the nucleus. However, in order for this to be so, we have to "switch on" full electrodynamics, because statical Coulomb forces do not make the electron spiral into the nucleus.

    Now, if we consider this radiation as a small perturbation, then, given that classically, all orbits exist, of no matter how low energy, from small emission to small emission, classically the electron could radiate away an infinite amount of energy and be arbitrary close to the nucleus. If we do this quantum-mechanically, and consider the EM emission as a small perturbation, then there IS no lower state below the ground state in which to fall. So the electron cannot "go below" the ground state. But the question is: what if we cannot consider this as a small perturbation ? What if we have to treat the full EM interaction from scratch in the hydrogen atom ? Is there then still a ground state ? And this is a question that has remained unanswered for long.
  6. Mar 27, 2007 #5
    Here is the answer from our FAQ thread !

  7. Mar 28, 2007 #6
    could the same principle not be used to prove that an electron cant occupy a specific energy level? If the electron is known to occupy a specific energy level (ie position) then the uncertainty in momentum is huge. Anyway, surely the estimation of the bohr radius using the HUP only gives an uncertainty in electron position, rather than a distance from the nucleus? I did this in my course but now that i think about it i really dont understand it
  8. Mar 29, 2007 #7
    This is incorrect because when an electron "sits on some energy level" it does not mean that "it has a certain position, connected to this energy level". I mean, you are making a semantics error here. You cannot connect energy levels to spatial positions !

  9. Mar 29, 2007 #8
    Ok. But what if we considered the electron not as point-like but instead smeared out in the orbit? In this case there shouldn't be any resultant radiation.
    Jackson-Classical Electrodynamics-exercise 14.12 asks to prove that the resultant radiation emitted by N charges moving in a circular path at constant distances goes to zero when N goes to infinity.
    So, if we could think of the electron in the H atom as a continuous distribution of charge, it shouldn't radiate.
    Last edited: Mar 29, 2007
  10. Mar 29, 2007 #9


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    The plain fact is that the classical and quantum worlds are very different, and, for all practical purposes, undergo very different dynamics. Small wonder that all the geniuses of late 19th century physics could never find a satisfactory explanation of atomic spectra. It took Bohr's brilliant intuition to realize that what we now call quantum electrodynamics, can explain atomic spectra with the assumptions that electrons "move" in stable orbits without radiation, and radiate only when making a transition from one state to another. In effect, Bohr assumed the answer and worked backwards. The quantum mechanics we know today come straight from Bohr -- and Einstein --and has become, in its early adulthood, an extraordinary success. And, the stability of atoms and nucleii is directly connected with the idea of bound states. Basically simple, if you accept QM.

    Imgood -- you should study the history of QM and atomic physics -- all the answers you wish have been around for70-80 years.Learn about bound states, and Dirac's QED.

    QM is just different. That it is seems to bother some people, but Nature has thrown a few non-19th century curveballs our way.Tough, but interesting.

    lightarrow -- So how does your system produce discrete spectra?

    Reilly Atkinson
  11. Mar 29, 2007 #10
    Are you asking why they don't spiral in or why they can't exist within the nucleus? I'm going through this right now in my modern physics class and from what I've pieced together, using Bohr's model, is about the latter. The energy of the electron is the kinetic minus the potential (difference of charges). The Bohr radius can be shown to be the minimum energy level. If you use HUP to solve for the velocity and substitute it into the energy expression, it can be seen that as the radius of the electron shortens, the kinetic energy rises inversely proportional to the square of the radius. In the same way, the potential energy increases negatively and is inversely proportional to the radius. Therefore, the kinetic energy begins to increase faster than the potential energy the smaller the radius. To get to the size of the nucleus would take a large amount of energy. This can be graphed with the energy expression which results in an energy well where the lowest possible energy is at the Bohr radius.

    Another way to see this is through De Broglie matter waves. For a matter wave to be confined to the size of the nucleus, on the order of 10^-14 meters, it would result in a very large momentum.

    Neither way truthfully makes complete sense to myself. I've been wondering if it would work to have an electron shoot "straight" into the nucleus rather than move around it and what would happen in the collision if possible.
  12. Mar 30, 2007 #11
    Never said or thought it. Just that one important piece of "classical impossibility", that is, the classical instability because of radiation, doesn't seem really so, to me.
  13. Mar 30, 2007 #12


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    But that's nothing else but the s-orbitals ! There is no orbital angular momentum for s-orbitals, so they "shoot straight" at the nucleus (in as much as this is meaningful in QM).
  14. Mar 30, 2007 #13


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    Sure, that's true. S-states wouldn't even be moving (no angular momentum, and hence no angular momentum induced magnetic moment, and hence no current: just some static form of charged jelly). So this would solve that individual part of the atomic structure. This was, if I understand correctly, the initial view by Schroedinger himself, when he found the Schroedinger equation.
  15. Mar 30, 2007 #14
    Thank you Vanesh.
  16. Mar 31, 2007 #15
    What about this question:
  17. Apr 1, 2007 #16
    Because of the strong force which has to be so strong to counterbalance the high momentum of the very space confined protons.
  18. Apr 4, 2007 #17
    Quantised of magnetic field

    Hi, madness. First, do you believe that charge is quantized? If Yes, then I explained in this way. According to faraday and maxwell. change of electric produces magnetic field and change of magnetic field produces electricl field. If charge can be quantized, then, magnetic field shall be able to be quantized too. At the level of macroscopic, the magnetic field is recessive. but at microscopic level, magnetic field is dominant. The electron must not tied to something, but able to jump from one level to another level which is caused by the magnetic gauss line as described in the website below:-
    Due to this reason, electron is able to jump from one level to another level specifically. If base on uncertainty, there should be no quantization because uncertainty means no quantization.
  19. Apr 4, 2007 #18


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    Er.. this is wrong.

    The "quantization" of magnetic field has nothing to do with charge being quantized. We know current is made up of quantized charges, but we still do not see such quantization of magnetic field based on Maxwell equation alone.

    The quantization of the magnetic field comes in through the discrete flux that we measure using superconducting devices, for example. This, in fact, has nothing to do with quantized charges, but rather due to the uniqueness of the wavefunction's boundary condition.

  20. Apr 4, 2007 #19
    Clashing of electrons

    Will the electrons clash with each other?
  21. Apr 4, 2007 #20
    quantized magnetic field

    Hi, Zapper. How about if I put it this way? in the sense of changing the electric field, we remove or add one electron by one electron, the change of electron is quantized. according to the law of induction. The magnetic field generated is purely depends on the change of electric field. If the change of electric field is quantized, the change of magnetic field shall also be quantized. Am I right? Can we conclude that if charge can be quantized, magnetic field shall also be quantized?
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