### Related Formula For single-electron systems like the hydrogen atom: E_n = -frac13.6 cdot Z^2n^2 text eV$E_n = -\frac{13.6 \cdot Z^2}{n^2} \text{ eV}$ where energy depends strictly and solely on the principal quantum number (n$n$). ### Core Logic In multi-electron atoms, orbital energy is governed by the (n+l)$(n+l)$ rule due to inter-electronic repulsions. However, in single-electron species like Hydrogen, subshells within the same main shell are degenerate (possess identical energy levels). Let's map the principal quantum numbers: * For (A) 4s ightarrow n = 4$4s ightarrow n = 4$ * For (B) 3p_x ightarrow n = 3$3p_{x} ightarrow n = 3$ * For (C) 3d_x^2-y^2 ightarrow n = 3$3d_{x^{2}-y^{2}} ightarrow n = 3$ * For (D) 3d_z^2 ightarrow n = 3$3d_{z^{2}} ightarrow n = 3$ * For (E) 4p_z ightarrow n = 4$4p_{z} ightarrow n = 4$ Orbitals with n = 3$n = 3$ have lower energy than those with n = 4$n = 4$. Since (B), (C), and (D) all share n = 3$n = 3$, they are degenerate and together represent the lowest energy states among the options provided. ### Pattern Recognition Classic Trap: Do not apply the (n+l)$(n+l)$ rule for Hydrogen or hydrogen-like single-electron ions (He^+, Li^2+$He^{+}, Li^{2+}$). For these systems, energy is determined purely by the shell index n$n$. ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 11 Chemistry: Structure of Atom