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Homework Help: Estimate vibrational frequency of N2 molecule

  1. Apr 26, 2016 #1
    1. The problem statement, all variables and given/known data
    Experimental data for the heat capacity of N2 as a function of temperature are provided.

    Estimate the frequency of vibration of the N2 molecule.

    2. Relevant equations
    Energy of harmonic oscillator = (n+1/2)ħω


    Average molecular energy = C*T

    But this is an expression for the total energy of a molecule.
    Presumably the amount of energy within the two vibrational modes is:




    3. The attempt at a solution
    All I can think to do is equate the two expressions for the energy of the oscillator:


    But I have no idea where to go now. In order to find frequency I would want to solve for ω, from which frequency can be trivially determined. However, how am I to know which integer value to use for n?

    I am also very unsure as to my construction of the problem.

    Any help/guidance greatly appreciated.
  2. jcsd
  3. Apr 27, 2016 #2


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    Staff: Mentor

    What does this curve look like?
  4. Apr 27, 2016 #3
    T (Kelvin) 170 500 770 1170 1600 2000 2440
    C/NkB 2.5 2.57 2.76 3.01 3.22 3.31 3.4

    Apologies, not sure how to post a table of data.
  5. Apr 27, 2016 #4


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    Staff: Mentor

    Clearly, the heat capacity is not constant, whereas you expect it to be of the form C = f kB T / 2, where f is the number of quadratic degrees of freedom. What could be happening here?
  6. Feb 4, 2018 #5
    You access rotational energy as well? So you have more degrees of freedom? But this doesn't answer the question "However, how am I to know which integer value to use for n?'..........
  7. Feb 5, 2018 #6


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    Staff: Mentor

    n is not necessarily an integer. There can be situations where you get an effective number of dofs that is not a whole number.
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