CHM 501

7. Find all of the Russell–Saunders terms for the s1d1 electron configuration. Predict the energetic ordering of the different states.

Answer

L = 0 + 2 = 2, so ML = 2, 1, 0, –1, –2

S = ½ + ½ = 1 so MS = 1, 0, –1

Number of microstates = [2!/1!1!]×[10!/1!9!] = 20

ML\MS
(s, d)

1

0

–1

2

(0+,2+)

(0+,2) (0,2+)

(0,2)

1

(0+,1+)

(0+,1) (0,1+)

(0,1)

0

(0+,0+)

(0+,0) (0,0+)

(0,0)

–1

(0+,–1+)

(0+,–1) (0,–1+)

(0,–1)

–2

(0+,–2+)

(0+,–2) (0,–2+)

(0,–2)

ML = 2, MS = 1 gives 3D (15 microstates)

ML = 2, MS = 0 gives 1D (5 microstates)

Energy ordering: 3D < 1D