The number of orbitals of g-type — Atomic Structure Chemistry Question

💡 Solution & Explanation

### Step 1 - Relate Subshell Types to the Azimuthal Quantum Number The azimuthal quantum number $l$ designates subshell type: * $s$-subshell: $l = 0$ * $p$-subshell: $l = 1$ * $d$-subshell: $l = 2$ * $f$-subshell: $l = 3$ * $g$-subshell: $l = 4$ For $g$-type orbitals: $l = 4$ ### Step 2 - Formula for Number of Orbitals The number of spatial orbitals in any subshell: $$N_{\text{orbitals}} = 2l + 1$$ Corresponding to $m_l$ values from $-l$ to $+l$. ### Step 3 - Calculate for g-subshell $$N_{\text{orbitals}} = 2l + 1 = 2(4) + 1 = 8 + 1 = \boxed{9}$$ The 9 orbitals correspond to $m_l \in \{-4, -3, -2, -1, 0, +1, +2, +3, +4\}$. ### Step 4 - Evaluation of Options * **Option (A) 5:** Incorrect — this is the number of d-orbitals ($l=2$, $2\times2+1=5$). * **Option (B) 7:** Incorrect — this is the number of f-orbitals ($l=3$, $2\times3+1=7$). * **Option (C) 9:** Correct — g-orbitals: $l=4$, $2\times4+1=9$. * **Option (D) 11:** Incorrect — this would be h-orbitals ($l=5$, $2\times5+1=11$).