Which of the following orbitals has a degeneracy of 1?

The orbital with a degeneracy of 1 is the z2 orbital. To understand why, we need to consider the concept of degeneracy in quantum mechanics, which refers to the number of different quantum states of a system that have the same energy level.

The d orbitals, such as dx2-y2 and dxy, are part of a set of five degenerate d orbitals that exist at the same energy level in a free atom. These orbitals have the same energy but differ in their orientation and shape. Similarly, the p orbitals, including px, are also degenerate in groups of three, meaning that px, py, and pz all have the same energy in a hydrogen-like atom.

On the other hand, the z2 orbital is distinct in shape and has a different energy level compared to the other d orbitals. In many contexts, particularly within transition metal complexes, the z2 orbital is considered to be non-degenerate and exists as a single energy level due to its specific characteristics, which makes its degeneracy equal to 1.

Thus, the z2 orbital uniquely stands out as having a degeneracy of 1, whereas the other orbitals listed have a greater degree of degeneracy by being part of