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Coulomb force vs. Pauli principle in atoms

  1. Sep 16, 2010 #1
    1. The problem statement, all variables and given/known data

    In the absence of the Pauli principle, the Coulomb force would not be saturated, and the energy of a system containing N atoms would vary as N^(5/3).

    Show that a system of 2N atoms would have an energy lower than that of two N - atom systems.

    2. Relevant equations

    E = c * N^(5/3)

    3. The attempt at a solution

    E(2N) = c * (2N)^(5/3) = c * 2^(5/3) * N^(5/3)
    2 * E(N) = 2 * c N^(5/3)

    Since, 2^(5/3) > 2, then obviously E(2N) > 2 E(N), contrary to the what had to be shown. Where's the error in my reasoning?
     
  2. jcsd
  3. Sep 16, 2010 #2

    gabbagabbahey

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    Is [itex]c[/itex] positive or negative, and why?
     
  4. Sep 16, 2010 #3
    I can't see how could c be anything but positive due to Coulomb repulsion of like charges.
     
  5. Sep 16, 2010 #4
    True, but this is an atom: it has a large positive nuclei
     
  6. Sep 16, 2010 #5
    But then then energy wouldn't depend on N as N^(5/3) but also as N^2
     
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