For normal Zeeman lines observed ∥ and ⊥ to the magnetic field applied to an
atom, which of the following statements are true?
Options:
(A) Only 𝜋-lines are observed ∥ to the field
(B) 𝜎-lines ⊥ to the field are plane polarized
(C) 𝜋-lines ⊥ to the field are plane polarized
(D) Only 𝜎-lines are observed ∥ to the field
Official Answer Key:
B,C,D
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2022 Q.22)**
**1. Normal Zeeman Effect Physics**:
- Magnetic field $\vec{B} = B\hat{z}$ defines the quantization axis.
- Selection rules: $\Delta m_l = 0$ gives $\pi$-lines; $\Delta m_l = \pm 1$ gives $\sigma$-lines.
**2. Polarization and Directional Emission Breakdown**:
- **Observation Parallel to Field ($\| \vec{B}$, along $\hat{z}$)**:
- Dipole radiation along its axis is zero. The $\Delta m_l = 0$ dipole oscillates along $\hat{z}$ and emits no light along the $z$-axis.
- Hence, **no $\pi$-lines** are observed along $\| \vec{B}$; **only $\sigma$-lines are observed $\| \vec{B}$**, circularly polarized ($L$ and $R$). **Statements (A) is FALSE and (D) is TRUE**.
- **Observation Perpendicular to Field ($\perp \vec{B}$, in $xy$ plane)**:
- The $\pi$-line (dipole along $\hat{z}$) emits linearly polarized light with $\vec{E} \parallel \vec{B}$. **Statement (C) is TRUE**.
- The $\sigma$-lines (circular motion in $xy$-plane) are viewed edge-on, so they appear linearly (plane) polarized with $\vec{E} \perp \vec{B}$. **Statement (B) is TRUE**.
**3. Official Verification**:
The verified official IIT Master Answer is **Options (B, C, D)**.
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