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Question
Draw figure to show the splitting of d orbitals in an octahedral crystal field.
Solution
Let the six ligands be symmetrically located along the Cartesian axes and the metal atom is at the origin.
On approaching the ligand, the energy of the d-orbitals increases as expected compared to the free ions. As is the case in a spherical crystal field.
The orbitals along the axes (`d_(Z^2)` and `d_(x^2 - y^2)`) repel more strongly than the dxy, dyz and dzx orbitals and have lobes directed between the axes. In the spherical crystal field, the `d_(Z^2)` and `d_(x^2 - y^2)` orbitals increase in energy and the dxy, dyz, dzx orbitals decrease in energy compared to the average energy.
Therefore, the degenerate set of d-orbitals splits into two groups – the low energy orbital group t2g and the high energy orbital group eg separated by energy Δ0.
d orbital splitting in an octahedral crystal field
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