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[PoM] Average rotational energy

  1. Feb 20, 2017 #1

    BRN

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    1. The problem statement, all variables and given/known data
    Determines the average energy of rotation (per molecule) of a rarefied gas of HF at T = 50 K, knowing that the wave number of rotational absorption for the transition L = 2 → 3 worth 121.5 cm-1. [Hint: it performs the calculation by limiting the number of levels taken into account, making sure to get the numerical result by 5%.]

    Solution:##E_{rot}=5.493*10^{-22} [J]##

    3. The attempt at a solution
    In the classical limit, the average rotational energy per molecule is:

    ##\frac{E_{rot}}{N}=\frac{1}{2}I\omega^2##

    For transition L = 2 → 3, I have:

    ##\nu=\frac{E_{rot}}{h}=\frac{\hbar^2l(l+1)}{2hI} \Rightarrow I=\frac{\hbar^2l(l+1)}{\nu 2h}##

    then,

    ##\omega^2=(2\pi \nu)^2=\frac{2k_BT}{I}=3.3318*10^{17} [rad/s]##

    so:

    ##E_{rot}=\frac{1}{2}I\omega^2=k_BT=6.903*10^{-22} [J]###

    But, in what way I have to limit the number of levels taken into account?
     
    Last edited: Feb 20, 2017
  2. jcsd
  3. Feb 21, 2017 #2

    BRN

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    Nobody?:sorry:
     
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