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In valence bond theory, I suppose that electrons in say, 2px and 2py have the same energy because of the same structure of orbitals. But what about 3dxy and 3dz^2? Do they also have the same energy? I would say, no for the difference in their shape. But I am not quite sure since they are in the same subshell. could anyone plz clarify?

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  • $\begingroup$ Yes they also have the same energy because of the same structure of orbitals. Their apparently different shape is not a fact of any consequence. $\endgroup$ Mar 3 at 6:37
  • $\begingroup$ But then how would one describe the colour of transition metals? Since I have learnt that they are colourful because of the energy emitted while electrons jump in between 3dxy and 3dz^2 $\endgroup$
    – Habib
    Mar 3 at 6:44
  • $\begingroup$ That's a different story altogether. They have the same energy in a lone atom, but not necessarily so in various compounds. $\endgroup$ Mar 3 at 6:46
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In the isolated atom, yes, they will have the same energy. Dealing with d orbitals, you are in the field of transition metal chemistry. As correctly said by Buck Thorn, the degeneracy can be removed by external electromagnetic field. In the case of transition metals, it can be extensively seen in the crystal field theory. The ligands act as a source of electric field, then the spherical symmetry of the metal center is removed. Therefore an electronic configuration like d$^2$ will split into terms, which are a collection of microstates. You have to see in advanced inorganic chemistry textbooks.

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Degeneracy (=equal energy) may be broken by external electric or magnetic fields.

For instance, in NMR the application of an external magnetic field can break the degeneracy of possible nuclear spin states (in $\ce{^1H}$, antiparallel $\alpha$ and $\beta$). This is known as the Zeeman effect and its influence on atomic (electronic) spectra lead to the postulation of angular momentum quantum numbers by Arnold Sommerfeld (for which he should have received a Nobel Prize) and to the discovery of quantum spin.

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