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Homework Help: Derive the relation between the P & R branches

  1. Dec 4, 2017 #1
    • Moved from a technical forum, so homework template missing
    Hi,

    I have an assignment to derive the two following expressions:

    R(J)-P(J)=2B'(2J+1)
    R(J-1)-P(J+1)=2B''(2J+1)
    where Bis the rotational constant and prime ' stands for upper level and bis '' for lower level.
    Bv=Be-α(v+1/2)

    using the selection rules (I guess in this case ΔJ=±1) and ΔT=G(v')-G(v'')+F(J')-F(J'') where ΔT is the transition/energy difference
    between two energy levels expressed in wavenumbers and F(J)=BJ(J+1)
    G(v)=ωe(v+1/2)-ωexe(v+1/2)2.

    I don't understand how I'm going to put all of this together and I don't understand what they mean with R(J) and P(J) etc.
    Thankful for any help!
     
    Last edited by a moderator: Dec 5, 2017
  2. jcsd
  3. Dec 5, 2017 #2

    DrClaude

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    Staff: Mentor

    You'll have to give more background. Can you provide with the exact problem statement?
     
  4. Dec 5, 2017 #3

    TeethWhitener

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    Science Advisor
    Gold Member

    It's difficult to determine if there is a precise question in OP's post.

    R(J) refers to the energy of an R-branch transition originating from the J'th rotational state. Ditto for P(J) (for a P-branch transition). You might spend some time poring over this diagram:
    https://en.wikipedia.org/wiki/Rotat...scopy#/media/File:Vibrationrotationenergy.svg

    Also, presumably this is comparing P and R branches of the same vibrational transition, so you don't have to worry about most of the expressions you've listed involving vibrational quantum numbers. Maybe, as @DrClaude suggested, you could give us a more focused question?
     
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