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Why relativistic inner core?

  1. May 8, 2006 #1
    Can anyone please explain why the inner core electrons for heavier elements would have relativistic momenta? I have not seen this clearly explained before.

    My thinking is: given the stronger coloumbic interaction with the nucleus (and e-e repulsion with the higher energy shells) that the spatial regions that these electrons can occupy for a given energy is limited, in order for the electrons to exist in these regions they must have a certain minima (quanitized) energy - the remainder of which is kinetic.

    is this right?
  2. jcsd
  3. May 9, 2006 #2


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    Last edited: May 9, 2006
  4. May 10, 2006 #3


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    The Bohr calculation (although not good for accuracy, but still good enough for an OoM estimate perhaps) throws some light: [itex]v_n ~~\alpha~~ z/n [/itex].

    Alternatively, you could think of this in terms of the higher (in magnitude) potential energy and the virial theorem.
  5. May 10, 2006 #4
    thanks guys, the Bohr velocity makes sense to me, the virial theorem as well

    could the HUP also be used to show this somehow - that since the core electrons are restricted (probabilistically) to certain spatial regions, that the uncertainty in the momentum will go up?
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