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Why do electrons have more kinetic energy when closer to the nucleus?

  1. Jun 6, 2009 #1
    Also similarly, why do electrons have less potential energy when closer to the nucleus?

    Please can someone help me and explain in laymen's terms? I don't understand it. I know when electrons are seperated by large distances, they are less likely to interact with the positive charge of the protons of the nucleus. Is that why there is less "potential" energy?

    So, there is more kinetic energy (energy due to motion) when electrons are closer to the nucleus, because the electrostatic attraction is greater?
  2. jcsd
  3. Jun 7, 2009 #2
    Treating an electron classically, it is in a Coulomb potential well, proportional to 1/distance (similar to the one I plotted in the picture attached). The potential energy is clearly lower at small values of x, i.e. closer to the nucleus. Since total energy must be conserved the decrease in potential energy causes an increase in kinetic energy of the electron.


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    Last edited by a moderator: Aug 6, 2009
  4. Jun 7, 2009 #3
    ya thats da correct answer above this note!
  5. Jun 7, 2009 #4


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    A good classical analogy is to think of the atom in the planetary model sense. It may or may not seem like common sense to you that planets close to the sun have more kinetic energy and less potential, and those farther away have less kinetic and more potential. The reasoning is exactly the same as given in the above post, but perhaps the analogy is useful.
  6. Jun 7, 2009 #5


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    Suppose you have a positive and a negative charge, held at a certain distance from each other. In order to increase the distance between them, you have to pull them apart (against their mutual attraction) by exerting a force on one or both of them, and thereby do (positive) work on them. If the charges start at rest, and end at rest when you have finished pulling them apart (or at least have the same speed and therefore the same kinetic energy before and after), then by definition the change in potential energy equals the work that you have done. You do positive work when you move the charges further apart, therefore the potential energy increases as the distance increases, and decreases as the distance decreases.
  7. Jun 7, 2009 #6
    So moving them closer is doing negative work?
  8. Jun 7, 2009 #7


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    Yes. One thing to remember is that in quantum mechanics, the electrons are confined to constant energy levels. So in the ground state, the total energy of the electron stays constant. If the electron moves closer to the nucleus, the potential energy due to the Coulombic potential decreases and thus we must have a matching increase in the kinetic energy.
  9. Jun 8, 2009 #8


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    Yes... negative work done on the charges, which is the same as positive work done on you (or on whatever is holding the charges back and keeping them from "free-falling").