In a homonuclear molecule, which of the following set of orbitals is degenerated?

To determine which set of orbitals is degenerate in a homonuclear molecule, we need to understand the concept of degeneracy in molecular orbital theory.

Degenerate Orbitals

1. Definition: Degeneracy refers to two or more orbitals that have the same energy level. In homonuclear diatomic molecules, particularly, degenerate orbitals are usually associated with the symmetry of the molecule.

2. Homonuclear Molecules: These are molecules composed of two identical atoms (e.g., $\text{H}_2$, $\text{N}_2$, $\text{O}_2$). In a molecular orbital diagram for homonuclear diatomic molecules, the hydrogen-like atomic orbitals (such as $\text{s}$, $\text{p}$, $\text{d}$) combine to form molecular orbitals either bonding or anti-bonding.

Example of Degenerate Orbitals

1. In diatomic molecules like $\text{N}_2$, the $\text{p}$ orbitals (specifically the $\text{p}_x$ and $\text{p}_y$ orbitals) are degenerate due to their symmetry and the equal energy contribution from both atoms.

2. Therefore, the set of degenerate orbitals usually encountered in homonuclear molecules includes the $\text{p}$ orbitals or higher-energy d orbitals, depending on the molecule's symmetry and the number of atoms involved.

Conclusion

In summary, the set of orbitals that is typically degenerated in a homonuclear molecule includes either the degenerate $\text{p}$ orbitals or higher energy orbitals. To identify the specific sets of degenerate orbitals in a given homonuclear molecule, one must refer to its molecular orbital diagram. If you can provide me with specific options or molecules to compare, I can provide a more precise identification.