Download The states of Cr 3+

The states of Cr3+ involved in laser action in a Ruby Laser.
Cr3+ configuration 3d3 results in many atomic states. Hunt’s rule is that the lowest energy
state has maximum spin unpairing and then maximum orbital angular momentum.
Therefore in terms of the (ml , ms) quantum numbers of the three electrons, one
component of the lowest energy state would be:
(0, ½) (1, ½)) (2, ½)
-2
-1
0
+1
+2
which means ML = 3 and MS = 3/2.
As these are the maximum values then L = 3 (an F state) and S = 3/2 therefore term
symbol, (2S+1)L is 4F.
(In fact d3 gives rise to 2P, 4P, 2D, 2D, 2F, 4F, 2G, 2H
Check the degeneracies:
Number of possible arrangements of d3 = 10C3 =120
Degeneracies: 2P(6) 4P(12) 2D(10) 2D(10) 2F(14) 4F(28) 2G(18) 2H(22) = 120)
In an octahedral crystal field, F  A2, T1, T2 (ignoring the centre of symmetry) therefore
4
F  4A2, 4T1, 4T2
Cr3 (aq) : 4A2 ground state, 2E at 15 000 cm-1, 4T2 at 17 400 cm-1, 4T1 at 24 700 cm-1
The 2E state comes from the crystal field splitting of an atomic doublet (probably the
lowest energy doublet state which is 2G).
Other states
2
G
3d3
4
F
4
T1 , 4T2
2
E
4
A2