Consider the following pairs of electrons: (A) (a) n=3, l=1, ml=1, ms=+12; (b) n=3, l=2, ml=1, ms=+12 (B) (a) n=3, l=2,…

🧠 The Energy Match "Degenerate" orbitals are those that belong to the same subshell (same $n$ and $l$) but have different orientations (different $m_l$). In a typical atom, all five 3d orbitals are degenerate, and all three 3p orbitals are degenerate.

🗺️ The Pair Audit

• Pair (A): Compare $(n=3, l=1)$ vs $(n=3, l=2)$. This is a 3p orbital vs a 3d orbital. They have different energies ($n+l$ is $4$ vs $5$). NOT DEGENERATE.
• Pair (B): Compare $(n=3, l=2, m_l=-2)$ vs $(n=3, l=2, m_l=-1)$. Both are 3d orbitals. They have the same $n$ and $l$. They are merely different orientations in the same subshell. DEGENERATE.
• Pair (C): Compare $(n=4, l=2)$ vs $(n=3, l=2)$. This is 4d vs 3d. Different shells mean different energies. NOT DEGENERATE.

⚡ The "Same n, l" Rule An electron pair is in degenerate orbitals ONLY if their $n$ and $l$ values are identical. The $m_l$ and $m_s$ values can (and must) vary to represent different states within that degenerate set.

⚠️ Common Traps Magnetic quantum number ($m_l$) doesn't change the energy. Don't be fooled by the $-2$ vs $-1$; as long as $l=2$ for both, they are at the same energy level.

$\boxed{\text{Answer: (b)}}$