2. Find all of the Russell-Saunders and J terms for the f1 electron configuration. Predict the energetic ordering of the different states.

L = 3

S = ½

14 microstates
 
ML\MS
+½
–½
3
(3+)
(3–)
2
(2+)
(2–)
1
(1+)
(1–)
0
(0+)
(0–)
–1
(–1+)
(–1–)
–2
(–2+)
(–2–)
–3
(–3+)
(–3–)

 

Terms:

ML = 3, MS = ½ gives 2F accounting for all 14 microstates.

J = 3 + ½ = 7/2 and J = 3 – ½ = 5/2

The configuration is less than half-filled so the smaller J value is lower energy:

2F5/2 < 2F7/2