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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

    I have an assignment to derive the two following expressions:

    where Bis the rotational constant and prime ' stands for upper level and bis '' for lower level.

    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)

    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


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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


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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:

    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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