In presence of external magnetic field, p-orbital is — Atomic Structure Chemistry Question

💡 Solution & Explanation

**Step 1 - Degeneracy of p-orbitals Without Magnetic Field** For a p-subshell, $l = 1$, giving $2l+1 = 3$ spatial orbitals with $m_l \in \{-1, 0, +1\}$ (the $p_x$, $p_y$, $p_z$ orbitals). In the absence of external fields, all three have identical energy — they are **3-fold degenerate**. --- **Step 2 - Effect of External Magnetic Field (Zeeman Effect)** Each orbital has an orbital magnetic dipole moment that interacts with an external magnetic field $\vec{B}$. The interaction energy is: $$E_{\text{mag}} = m_l \cdot \mu_B \cdot B$$ Where $\mu_B = \frac{e\hbar}{2m_e}$ is the Bohr magneton. For the three p-orbitals: * $m_l = +1$: energy increases by $+\mu_B B$ * $m_l = 0$: energy unchanged * $m_l = -1$: energy decreases by $-\mu_B B$ The three formerly equal energies now split into three **distinct** levels — this is the **Zeeman effect**. --- **Step 3 - Degeneracy State in Magnetic Field** Since all three p-orbitals now have different energies, the 3-fold degeneracy is completely lifted. The p-orbitals become **non-degenerate**. --- **Step 4 - Evaluation of Options** * **Option (A) 3-fold degenerate:** Correct for field-free environment, not in magnetic field. Incorrect. * **Option (B) 5-fold degenerate:** Describes d-orbitals ($l=2$, $2l+1=5$) in field-free environment. Incorrect. * **Option (C) 7-fold degenerate:** Describes f-orbitals ($l=3$, $2l+1=7$) in field-free environment. Incorrect. * **Option (D) non-degenerate:** Zeeman effect splits 3 p-orbitals into 3 distinct energy levels. Correct. $$\text{Correct Option: } \boxed{\text{D}}$$