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Homework Help: What are S, L and J for the following states...?

  1. Apr 18, 2016 #1
    1. The problem statement, all variables and given/known data
    What are S, L and J for the following states: ##^1S_0, ^2D_{5/2} ^5F_1, ^3F_4##

    2. Relevant Equations
    The superscript is defined as: 2S + 1
    The subscript is defined as: J = L + S
    The letter denotes the angular momentum number (s, p, d, f...) starting at s = 0.

    3. The attempt at a solution
    ##^1S_0##: 2S + 1 = 1, S = 0 and S + L = 0, 0 + L = 0, L = 0. This makes me feel warm and fuzzy because the angular momentum quantum number does equal S, also the because we're in the S orbital with two electrons, electron spin must sum to zero because of the Pauli exclusion principle, which it does.

    ...The second problem also works out nicely... Here is the 3rd...
    ##^5F_1##: 2s+1 = 5, s = 2 and 2 + L = 1, L = -1. I don't think I'm violating the exclusion principle here with all the possible orbits in F, but why doesn't my calculated value for L correspond to the given value of F = 3? Also, I am aware that L most range anywhere from 0 to (n-1) and cannot be negative.
  2. jcsd
  3. Apr 18, 2016 #2
    Oops, Looks like I messed up the problem statement. The states are:

    ##^1s_0, ^2D_{5/2},^5F_1, ^3F_4##
  4. Apr 20, 2016 #3


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    Homework Helper

    There are generally more than one possible values for J for a given L and S. Don't rely on the potentially misleading equation J = L+S to determine L or S. Just rely on the indices inscribed in the state notation.
    Last edited: Apr 20, 2016
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