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

  • #1
103
4

Homework Statement


What are S, L and J for the following states: ##^1S_0, ^2D_{5/2} ^5F_1, ^3F_4##

Homework 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.

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.
 

Answers and Replies

  • #2
103
4
Oops, Looks like I messed up the problem statement. The states are:

##^1s_0, ^2D_{5/2},^5F_1, ^3F_4##
 
  • #3
blue_leaf77
Science Advisor
Homework Helper
2,629
784
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:

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