CHM 501

9. Find all of the term symbols for the s1p1 electron configuration, including J values. Energy order these states.

Answer

In this case there are no Pauli forbidden states because each electron is required to have a different l quantum number. Thus, L = 1 and S = 1. The total number of microstates is (6!/1!5!)(2!/1!1!) = 12.

ML\MS

1

0

–1

1

(0s+, 1p+)

(0s+, 1p) (0s, 1p+)

(0s, 1p)

0

(0s+, 0p+)

(0s+, 0p) (0s, 0p+)

(0s, 0p)

–1

(0s+, –1p+)

(0s+, –1p) (0s, –1p+)

(0s, –1p)

Find the states:

ML = 1, MS = 1: 3P (9 states), J = 2, 1, 0

ML = 1, MS = 0: 1P (3 states), J = 1

Since the configuration is less than half–filled, the smallest J value is the lowest energy, so the energy order is 3P0 < 3P1 < 3P2 < 1P1.