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

## 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.

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Oops, Looks like I messed up the problem statement. The states are:

$^1s_0, ^2D_{5/2},^5F_1, ^3F_4$

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