Which of the following orbital does not exist according to quantum theory? — Atomic Structure Chemistry Question

💡 Solution & Explanation

### Step 1 - Quantum Mechanical Boundaries for Orbitals According to quantum mechanics, the permitted values for quantum numbers are governed by the Schrödinger wave equation: 1. **Principal Quantum Number ($n$):** $n \in \{1, 2, 3, 4, \dots\}$ 2. **Azimuthal Quantum Number ($l$):** $0 \le l \le n - 1$, so $l < n$ always. Subshell letter designations: * $l = 0 \rightarrow s$, $l = 1 \rightarrow p$, $l = 2 \rightarrow d$, $l = 3 \rightarrow f$, $l = 4 \rightarrow g$, $l = 5 \rightarrow h$ ### Step 2 - Systematic Analysis * **Option (A) $5g$:** $n=5$, $l=4$ (g). Since $4 < 5$: **exists.** * **Option (B) $4f$:** $n=4$, $l=3$ (f). Since $3 < 4$: **exists.** * **Option (C) $5h$:** $n=5$, $l=5$ (h). Since $l = n$ (not $l < n$): **does NOT exist.** * **Option (D) $6h$:** $n=6$, $l=5$ (h). Since $5 < 6$: **exists.** $$\text{Correct Option: } \boxed{\text{C}}$$