The quantum number which determines the shape of the orbital is — Atomic Structure Chemistry Question

💡 Solution & Explanation

### Step 1 - Overview of the Four Quantum Numbers The four quantum numbers describing an electron: 1. **Principal quantum number ($n$):** Determines the main energy level and **size** of the orbital. 2. **Azimuthal quantum number ($l$):** Determines the subshell and **shape** of the orbital. 3. **Magnetic quantum number ($m_l$):** Determines the **spatial orientation** of the orbital. 4. **Spin quantum number ($m_s$):** Describes the intrinsic **spin** of the electron. ### Step 2 - Role of the Azimuthal Quantum Number ($l$) The azimuthal quantum number $l$ (also called orbital angular momentum quantum number or subsidiary quantum number) determines the **geometric shape** of the atomic orbital: | $l$ | Subshell | Shape | |-----|----------|-------| | 0 | $s$ | Spherical | | 1 | $p$ | Dumbbell | | 2 | $d$ | Double-dumbbell (clover-leaf) | | 3 | $f$ | Complex, 8-lobed | ### Step 3 - Evaluation of Options * **Option (A) Magnetic quantum no. ($m_l$):** Determines the **orientation** of the orbital in space (not shape). Incorrect. * **Option (B) Azimuthal quantum no. ($l$):** Determines the **shape** of the orbital. **Correct.** * **Option (C) Principal quantum no. ($n$):** Determines the **size** of the orbital and energy level. Incorrect. * **Option (D) Spin quantum no. ($m_s$):** Describes electron spin direction only. Has no effect on orbital shape. Incorrect. $$\text{Correct Option: } \boxed{\text{B}}$$