In a multielectron atom, which of the following orbitals described by three quantum numbers have same energy in absence…

🧠 Degeneracy in Complex Atoms In a simple Hydrogen atom, energy only depends on $n$. But in a multi-electron atom, subshells ($s, p, d, f$) have different energy levels due to shielding and repulsion. In such an atom, orbitals only share the same energy if they belong to the same subshell ($l$).

🗺️ The Orbital Audit

• (A) (1,0,0): $1s$ subshell.
• (B) (2,0,0): $2s$ subshell.
• (C) (2,1,1): $2p$ subshell.
• (D) (3,2,1): $3d$ subshell.
• (E) (3,2,0): $3d$ subshell. In the absence of external magic (electric or magnetic fields), all five $d$-orbitals of the $3d$ subshell are equal in energy. Since both (D) and (E) describe $3d$ orbitals ($n=3, l=2$), they have the same energy.

⚡ The "Start Tag" Rule In JEE, energy depends on $(n, l)$. If two sets of quantum numbers have the same $n$ and $l$ values, they belong to the same subshell and are "degenerate" (same energy). D and E both start with $(3, 2)$. Match found!

⚠️ Beware the Fields The phrase "absence of electric and magnetic fields" is a key reminder. If a magnetic field was present, the $m_l$ values would matter, and (D) and (E) would split into different energy levels (Zeeman Effect).

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