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Energy of Atomic Electrons

  1. Sep 25, 2009 #1
    I was previously under the impression that an atomic electron in its lowest orbit has a larger wavelength than an electron in a higher atomic orbit. I read earlier today that lower orbiting electrons actually have smaller wavelengths. :confused:

    This seems backwards since electrons naturally try to settle into lower orbits, which have lower energies (I thought). And I normally equate energy with wavelength.
     
  2. jcsd
  3. Sep 25, 2009 #2

    PeterDonis

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    Energy is proportional to frequency, which means it's *inversely* proportional to wavelength.
     
  4. Sep 25, 2009 #3

    So electrons in lower orbits have...

    * Relatively less energy
    - Higher Kinetic Energy
    - Lower Potential Energy
    * Smaller Wavelength
    * Higher Frequency
     
  5. Sep 25, 2009 #4
    Wavelength isn't something that is well defined for an electron in an atom, for the same reason that momentum [tex]p = \hbar/\lambda[/tex] can't be well defined; the potential keeps the electron from settling into a momentum eigenstate.

    You can do things like compute the expectation value of kinetic energy [tex]1/2m \langle p^2 \rangle[/tex] which will be non-zero. And it will be true that electrons in lower energy levels will have more kinetic energy, but they will also have a much more negative potential energy. In fact, the Virial theorem applies, so [tex]\langle V \langle = -2\langle T \rangle[/tex], so an electron in a state with large kinetic energy will have a much larger potential energy than an electron in a state with low kinetic energy.
     
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