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Homework Help: Turning Off Pauli Exclusion Principle

  1. Apr 19, 2012 #1
    1. The problem statement, all variables and given/known data
    How would the world change if there were no Pauli exclusion principle? Specifically, how would the band theory of metals change?

    a) Assume you had a small copper coin of mass 3.12 grams. How much energy would be released from the coin if the Pauli exclusion principle were suddenly turned off?

    Copper has a Fermi energy of 7 eV, an atomic number of 29, a molar mass of 63.54 gram/Mol, a density of 8.96 gram/cm3 and a specific heat of 0.385 J/g oC.

    Ereleased = J
    11791034.3623 NO

    HELP: This may require some thought. First off, what happens to all the different energy levels when the Pauli Exclusion Principle is turned off?
    HELP: What is the total energy stored in all the energy bands based on the information given? (This will require an integral, but not difficult one. Almost everything will drop out.)

    b) How long would this energy keep a 40 W light bulb light?
    Tbulb = s

    Closing thought: The Pauli Exclusion Principle seems to be an extremely important concept in the world around us. How would all of electrical engineering and the world of solid state electronics change if it weren't there? Why isn't it discussed more? Is there a way to turn it off? (We don't think so, but....) How did it come about?

    2. Relevant equations
    Eo (ground state energy) = 13.6 eV * (z^2), z=29

    3. The attempt at a solution
    3.12 g / (63.54 g/mol) = .0491 mol * 6.022e23 atoms/mol = 2.957e22 atoms
    The electrons in copper are: 1s2 2s2 2p6 3s2 3p6 3d10 4s1. Because there is 1 electron in the outer shell, I can use the Bohr model (which was how I calculated Eo for copper in the Relevant Equations section).

    The total energy of copper is 212Eo. If Pauli were to be shut off all those electrons would drop to the n=1 (ground state) and release photons. There are 29 electrons, and if they acted like bosons (when Pauli gets shut off) the energy of those electrons would be 29Eo. So I'm releasing 212Eo - 29Eo = 183Eo in photon energy.

    Eo = 13.6eV * 29^2 = 11437.6 eV

    Energy released by 1 copper atom = 11437.6 eV * 183Eo = 2 093 080.8 eV
    Energy released by all copper = 2 093 080.8 eV * 2.957e22 atoms = 6.1892e28 eV

    6.1892e28 eV -> J = 9.9162599e9 J

    But it doesn't like my answer.
    Last edited: Apr 19, 2012
  2. jcsd
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