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The Crystal Field Theory experiment shows the effects on metal d orbital energies of moving a set of negative point charges close to a metal ion. As one would expect, the energies of the d orbitals rise as the negative charges approach the metal ion, owing to the repulsions among the d orbital electrons and the surrounding charge.
If the surrounding negative charge is spherically symmetric, all five d orbitals are equally affected. In practice, the surrounding negative charge is never spherically distributed, due to the charge is associated with specific ions that occupy specific positions. The consequence is each d orbital is affected differently, and how a particular d orbital is affected depends upon the geometry of the surrounding point charges. This effect is clearly seen in the splitting of the energy levels for the five d orbitals. When point charge enters a region of high electron density, the orbital energy rises significantly owing to the repulsion among the electron and the point charge. When the point charge approaches the ion along a nodal surface, the orbital energy does not increase as greatly.
The results from the Crystal Field Theory experiment are summarized in the chart shown below. Every geometry of point charges (linear, square planar, tetrahedral, or octahedral) makes a characteristic splitting pattern for the five d orbitals (xy, xz, yz, x2-y2, and z2). If you do not understand why the d orbitals split to form these specific patterns, revisit the previous experiment and carefully examine whether the point charges enter regions of high electron density or approach along nodal surfaces for a particular geometry and d orbital.
Prove that the number of orbitals in a principal quantum level is n^2 using the fact that the number of orbitals in a subshell is (2L-1) where L is the azimuthal quantum number.
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