- #1

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## 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.