GATE PH 2016 • Q15
MCQ • 1 Mark
Section 3: Electromagnetic Theory
Waveguides and radiation
Subtopic: Electric & Magnetic Dipole Radiation
Question Statement:
Which of the following transitions is NOT allowed in the case of an atom, according to the electric dipole radiation selection rule?
Options:
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(A) $2s \rightarrow 1s$
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(B) $2p \rightarrow 1s$
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(C) $2p \rightarrow 2s$
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(D) $3d \rightarrow 2p$
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2016 Q.15 / PH Q.5)**
**1. Electric Dipole Selection Rules**:
- In atomic physics, the electric dipole selection rules for orbital angular momentum state:
$\Delta l = \pm 1, \quad \Delta m_l = 0, \pm 1$
- Transitions with $\Delta l = 0$ (such as $s \to s$, $p \to p$) are strictly forbidden for single-photon electric dipole emission because the photon carries spin $s = 1$.
**2. Evaluating the Transitions**:
- (A) $2s \to 1s$: Here $l_i = 0$ and $l_f = 0$, giving $\Delta l = 0$. This transition is forbidden.
- (B) $2p \to 1s$: $l_i = 1, l_f = 0 \implies \Delta l = -1$ (Allowed).
- (C) $2p \to 2s$: $l_i = 1, l_f = 0 \implies \Delta l = -1$ (Allowed).
- (D) $3d \to 2p$: $l_i = 2, l_f = 1 \implies \Delta l = -1$ (Allowed).
**3. Conclusion**:
- The transition $2s \to 1s$ is NOT allowed under the electric dipole selection rule.
- **Official Master Answer**: **A**
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