Frequently Asked Question

The ground state free ion term symbol for V³⁺ can be determined using Hund's rules. V³⁺ has the electronic configuration [Ar] 3d², which gives us two unpaired electrons in the d orbitals.
Following Hund's rules:
1. Maximum Multiplicity: The maximum spin multiplicity (2S+1) is achieved by maximizing the total spin angular momentum (S). With two unpaired electrons, S = 1, giving a multiplicity of 2(1)+1 = 3, denoted as ³.
2. Maximum L: The total orbital angular momentum (L) is maximized by aligning the individual orbital angular momenta (l) of the electrons in the same direction. For d orbitals, l = 2. The two electrons in the 3d orbitals are aligned, giving L = 2+2 = 4, which corresponds to the symbol 'F'.
3. Lowest J: For less than half-filled d orbitals, the ground state term has the lowest possible J value. J = L + S = 4 + 1 = 5. So, the ground state free ion term symbol is ³F₅.
In octahedral and tetrahedral fields:
The ground state energy terms in octahedral and tetrahedral fields differ due to the splitting of the d orbitals. In an octahedral field, the d orbitals split into two levels: t₂g (dxy, dyz, dxz) and eg (dx²-y² and dz²). The t₂g level is lower in energy than the eg level.
For V³⁺ in an octahedral field, the two electrons will occupy the t₂g orbitals. Since the t₂g orbitals are lower in energy, the ground state term symbol remains the same: ³F₅. However, the ground state energy term is now ³T₂g, reflecting the occupancy of the t₂g orbitals.
In a tetrahedral field, the splitting is reversed. The eg orbitals are lower in energy than the t₂g orbitals. Therefore, the ground state term symbol for V³⁺ in a tetrahedral field is also ³F₅, but the ground state energy term is ³T₁, indicating occupancy of the eg orbitals.
Note: There are no multiple ground state term symbols for V³⁺ in both octahedral and tetrahedral fields. This is because the splitting of the d orbitals affects the energy levels but does not change the overall electron configuration, which determines the term symbol.