JEE Main · 2022 · 24 Jun 2022 · Shift 1 · Atomic Structure

Orbitals are called degenerate only when they have exactly the same energy, and in a multi-electron atom that requires them to belong to the very same subshell, that is, to share both the principal quantum number $n$ and the azimuthal quantum number $l$, differing only in the orientation $m_l$. In the first pair one electron has $n=3,l=1$ while the other has $n=3,l=2$; these are a $3p$ and a $3d$ orbital, different subshells of different energy, so they are not degenerate. In the second pair both electrons carry $n=3,l=2$ and differ only in $m_l$ ($-2$ against $-1$); they occupy two of the five $3d$ orbitals, which are genuinely degenerate. In the third pair one electron is in $4d$ ($n=4,l=2$) and the other in $3d$ ($n=3,l=2$); the azimuthal number matches but the principal number does not, so their energies differ and they are not degenerate. Only the second pair lies in degenerate orbitals.