Question

What do you mean by degenerate orbitals? Give examples.

Answer 1

In atomic theory and quantum mechanics, an atomic orbital is a mathematical function describing the location and wave like behavior of an electron in an atom. This function can be used to calculate the probability of finding any electron of an atom in any specific region around the atom’s nucleus. s orbitals are spherical in shape, p orbitals are dumb-bell shaped, four d orbitals are cloverleaf shaped whereas one d orbital is shaped like an elongated dumbbell with a doughnut around its middle.

Complete step by step answer:
Degenerate orbitals are the orbitals which have the same energy (These orbitals may have different orientations in space around the nucleus but they are associated with the same energy). When an electric or magnetic field is applied on the system having degenerate orbitals then the degeneracy of the orbitals breaks and degenerate orbitals are split into high and low energy orbitals.
For explaining the concept of degenerate orbitals let us take an example of p orbitals which contain three degenerate orbitals that all have the same energy. a 2p sublevel has $2{p_x}, 2{p_y}\;and\;2{p_z}$ orbitals which are equal in energy and hence are called degenerate orbitals.
Similarly, d orbitals are five-fold degenerate and for $n = 3$, $3{d_{xy}},3{d_{yz}},3{d_{zx}},3{d_{{z^2}}}\;and\;3{d_{{x^2} - {y^2}}}$ are degenerate orbitals.

Note: The degeneracy in a quantum mechanical system can be removed by external perturbation which causes splitting of degenerate levels.
The degeneracy of p, d and f orbitals is 3, 5 and 7 respectively.
Degeneracy of energy levels of the hydrogen atom is given as ${n^2}$ where n is the principal quantum number.
In coordination chemistry when the ligands approach the central metal ion, degeneracy gets broken.