Question

Which of the following orbitals are degenerate?
(A) \[4{d_{xy}},3{d_{yz}},4{d_{yz}},4{d_{{z^2}}}\]
(B) \[3{d_{yz}},4{d_{yz}}\]
(C) \[3{d_{xy}},3{d_{yz}}\]
(D) \[4{d_{xy}},4{d_{yz}},4{d_{{z^2}}}\]

Answer 1

Hint: In order to find which of the given orbitals are degenerate, we must first know what a degenerate orbital is. Degenerate orbitals are the energy orbitals which are having the same energy levels.

Complete step by step answer:
Let us first understand the degenerate orbitals. Degenerate orbitals are the energy orbitals which are having the same energy levels. The filling of the electrons in the orbitals will take place based on these rules they are:
- Aufbau’s rule
This means that the electron will be filled first in the lower energy orbitals. The filling of the electrons will take place in increasing order.
- Hund’s rule:
Based on this rule, the greatest number of parallel spins will take place in the ground state electronic configuration in any electron shell. This rule can be used to determine the ground state of an atom or molecule.
- Pauli’s exclusion principle:
 No two electrons in an orbital will have all the four quantum numbers identical.
The total number of different states of the same energy is called degeneracy. In other words, it can also be called the degree of degeneracy.
Therefore, in the given question the orbitals having same energy are \[4{d_{xy}},4{d_{yz}},4{d_{{z^2}}},3{d_{xy}}~and~3{d_{yz}}\]. So, the correct answer is “Option C and D”.

Note: We have to remember the degree of degeneracy of various orbitals. They are:
- the degree of degeneracy of the s-orbital is 1.
- the degree of degeneracy of the p-orbital is 3.
- the degree of degeneracy of the d-orbital is 5.
- the degree of degeneracy of the f-orbital is 7.