Question

Why can two `s` orbitals NOT be degenerate?

Answer 1

Two or more orbitals are degenerate if they have the same energy.

Answer 2

Degenerate means that they have the same energy. `ns` orbitals cannot be degenerate with respect to themselves because there is only one `ns` orbital for a given `n`.

Degeneracy is defined for a selection of orbitals that are equal in energy, irrespective of quantum number, but they must be essentially equal in energy to be degenerate, and there must be at least two of them in total.

For instance, the one `5s` and five `4d` orbitals in yttrium (`"Y"`) may as well be considered degenerate with respect to each other, as their orbital potential energies are about `-"6.70 eV"` and `-"6.49 eV"`, respectively (Appendix B.9), a difference of `"0.39 eV"`, or `"8.99 kcal/mol e"^(-)` (`3.82%` the `1s->2s` transition energy of the hydrogen atom).