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The force, which attracts e to nucleus

  1. Nov 8, 2008 #1
    Everybody knows that the nucleus attracts the electron by the Coulomb discovered electric attraction force: F = k / r2, which means the further is the electron from the nucleus r, the weaker is the attraction force.

    On the other hand, those familiar with the classic radio wave theory know that the electrons interact with their nucleus as if they would be connected by a spring. The spring attracts the bob stronger the greater is the displacement x: F = -kx. This kind of force allows the radio waves to force harmonic oscillations of electrons.

    If the radio wave model is right, the electron can cross the atom along its diameter likewise an object via the Earth over a tunnel -- it will experience to gravity in the center of the Earth. This contradicts to the first view, which tells that the attraction must be infinite in the center. Am I missing something?
  2. jcsd
  3. Nov 8, 2008 #2
    1) is correct 2) is an approximation and so ultimately false. The k s differ btw. The electron will form the bob for quantum mechanical reasons around the center of the 1/r potential. This pretty much takes care of the infinity. If you displace the bob a little, you can do the F=-kx approximation. If you would displace the bob by a lot you would feel the 1/r potential.

    3) The contradiction is resolved in quantum mechanics.
  4. Nov 8, 2008 #3


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    I will have to guess that "classic radio wave theory" is something like what happens with an antenna. If that is the case, you are misapplying the concept to the wrong thing. The interaction of EM wave with electrons in an antenna is not an interaction of electrons with a nucleus. Those electrons in an antenna are electrons in a metal and thus, are governed by the properties of conduction electrons in a metal. This has nothing to do with electrons tied to nucleus and is a completely different scenario.

    Here's a hint next time you are faced with this kind of a puzzle - figure out which scenario provides the best match to the experimental observation. In this case, the coulombic interaction have given so many valid matches with experiments, whereas the harmonic potential hasn't, at least, not for the case of atoms.

  5. Nov 8, 2008 #4
    I is an extremely close approximation...which can be corrected when there is relative motion between the particles....
  6. Nov 8, 2008 #5


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    Good question, it sure seems to suggest the electron can cross the atom along its diameter right through the center. This certainly does suggest the force should become infinite.

    In an atomic orbital model I think people are suggesting you can drop an electron into an orbital (up to 2 in the first hydrogen orbital). Once inside the orbital, the electron is nolonger influenced by the atom, but is still subject to outside forces and in fact may be pulled right out of that orbital by some great attraction, or get knocked out of the orbital by another moving electron or a passing photon.

    In your radio wave example, perhaps one could visualize the electron going from side to side of whatever orbital its stuck in at the time.
  7. Nov 8, 2008 #6
    The electron does pass through the nucleus, and in the electron capture decay it even gets caught there.

    No that is incorrect. The field is too slow and the electron too fast. It really is a movement of the orbital.
    Last edited: Nov 8, 2008
  8. Nov 8, 2008 #7


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    The nucleus is not really a mathematical point.
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