Question

Determine the term symbols for :

A) 3P² , B) s¹p¹d¹ electron configuration.

C) Determine the energy free ion spectroscopic state (ground state) of a d³ species.

Answer 1

The molecular term symbol is written as ^2S+1L_J.

A) for a p orbital having two electrons occupy orbitals with m_l values +1 and 0 and so the L value is +1+0=1 which gives term P. The electrons are unpaired. So S= 2*(1/2) = 1. So 2S+1 is 3. J varies from L+S to L-S. So in this case, J is 0 and 1, 2.. So the term symbols are ³P₀, ³P₁, ³P₂.

Now looking at the question I think the electronic configuration for a ³P₂ term symbol may be asked. In that case the answer can be readily worked out backwards as p2 configuration.

B) In a similar way the L value will be L= 2+1+0=3 which gives term F. The 3 unpaired electrons shall give S=3* (1/2)= 3/2.2S+1= 4. J will be from L+S i.e. 3+3/2 to L-S i.e. 3-3/2. So J values are 9/2, 7/2, 5/2 and 3/2. So the term symbol are ⁴F_3/2, ,⁴F_{5/2 ,}⁴F_{7/2 ,}⁴F_9/2.

C) For a d3 species the electrons will ocuppy orbitals with m_l values +2, +1 and 0. So L= 2+1+0=3 i.e. F. All the electrons are unpaired. So S= 3x1/2 =3/2. So 2S+1 =4. So J will be 9/2, 7/2, 5/2 and 3/2. However only the ground state term symbol has been asked. This configuration is less than half-filled d-orbital configuration. So J will be minium in ground state. So the ground state term symbol is ⁴F_3/2