When you have a free metal ion, how do the energies of these orbitals relate to one another (are they the same, different, etc.)?

The energy of the orbitals are the same

Explanation:

For a free metal ion, all the d-orbitals are of the same energy. The five d-orbitals are said to be five fold degenerate in the free metal ion. Hence all the d-orbitals will possess the same energy irrespective of which one is first filled.

In an octahedral or tetrahedral crystal field, the d-orbitals will loose their degeneracy and become different in energy based on their orientation towards the ligands.

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b) nuclear ive learned that in a pedtrodic table