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Help Please! Exam later today

  1. Dec 15, 2007 #1
    Harmonic Oscillator

    9. An ideal harmonic oscillator has energy levels separated by a constant 0.05 eV. That
    is, the difference between the ground state and the first excited state of this oscillator is
    an energy of 0.05 eV. This single oscillator is brought into contact with a large solid
    composed of an enormous number of oscillators, and characterized by a temperature of
    T=150 K. What is the probability that the single oscillator will be found in its first excited
    1. 0.021
    2. 0.055
    3. 0.098
    4. 0.144
    5. 0.234
    6. 1.000

    What relationship should I even start with? Thanks for the help!
    Last edited: Dec 15, 2007
  2. jcsd
  3. Dec 15, 2007 #2
    This is a simple Boltzmann factor problem.

    Recall that the probability of an individual energy level is:



    e is the separation between energy levels
    k is the Stefan-Boltzmann constant (make sure you get its units right!)
    T is the absolute temperature

    in this case, we can neglect all terms n > 1 as they decay rapidly to zero. Also, recal that the energy level for the ground state is 0.

    That should help you complete the problem.
    Last edited: Dec 15, 2007
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