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    Partition function/probability

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    Consider the lowest 3 energy levels of a hydrogen atom:

    Ground state energy : -13.6 eV degeneracy = 0
    First excited state energy : -3.4 eV degeneracy = 4
    Second excited state energy: -1.5 eV degeneracy = 9

    Ignore higher states.

    a) Estimate the partition function Z for H-atom at 5800 K. Do not forget to take degeneracy into account.
    b) Calculate the probability of finding an H-atom in the first excited state.
    c) How does the result in part (b) compare with the same at 300 K?

    © BrainMass Inc. brainmass.com June 3, 2020, 7:41 pm ad1c9bdddf

    Solution Preview

    Let's first evaluate 1 eV/(kT) at T = 5800 K. I find that:

    1 eV/(k* 5800 K) = 2.

    So, the partition function is:

    Z = Exp[13.6 eV/(kT)] + 4*Exp[3.4 eV/(kT)] + 9*Exp[1.5 eV/(kT)] =
    Exp[2*13.6] + 4*Exp[2*3.4] + 9*Exp[2*1.5] = 6.5*10^11

    The factors in front of ...

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