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Homework Help: Rotational Energy

  1. Dec 7, 2008 #1
    1. The problem statement, all variables and given/known data
    Calculate the internuclear distance R0 for the HCL molecule from the fact that some of the lines of its pure rotation spectrum occur at wavelengths: 120.3 um, 96.0 um, 80.4 um, 68.9um, 60.4um.
    Assume 1H1 and 17Cl35
    2. Relevant equations

    [tex]E_{ROT} = \frac{ hbar^2 } {2I} l(l+1)[/tex]
    3. The attempt at a solution

    I found the energy of each of the wavelengths:
    E1 = 1.65 J
    E2 = 2.07 J
    E3 = 2.47 J
    E4 = 2.89 J
    E5 = 3.29 J
    (that's really x 10^-21 for each)

    Turns out that they are all .4 or .42 x 10^-21 Joules apart.
    Why can they be .42/.4 joules apart? I was under the impression that a pure rotational spectrum would be like this: 0, 2Er0, 6Er0, 12Er0.

    If I could figure this part out, I could easily calculate the moment of inertia and subsequently R0.
  2. jcsd
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