Question

Which of the following orbitals are degenerate?

• A. $3d_{xy},\\ 3d_{z^2},\\ 3d_{yz}$
• B. $4d_{xy},\\ 3d_{z^2},\\ 3d_{yz}$
• C. $3d_{z^2},\\ 3d_{yz},\\ 5d_{z^2}$
• D. None

Answer 1

Answer: (A)

$3d_{xy},\\ 3d_{z^2},\\ 3d_{yz}$

Answer 2

Degenerate orbitals have the same principal quantum number $n$ and same angular quantum number $l$.
All the orbitals in option 1 are 3d orbitals ($n=3,\ l=2$), hence they are degenerate.
Options 2 and 3 mix different $n$ values (3 and 4 or 3 and 5), so they are not degenerate.