Electric Dipole Selection Rules

Electric Dipole Selection Rules for Atomic Transitions

Electric dipole transitions are the most common type of spectroscopic transition, accounting for most of the intensity in atomic spectra. These transitions are only allowed if they satisfy the following quantum mechanical selection rules. The rules are applied to the total angular momentum quantum numbers, based on the Term Symbol: ^2S+1L_J.

The Key Selection Rules

Quantum Number	Rule	Description
Spin (S)	$$\Delta S = 0$$	The spin multiplicity (2S+1) must be conserved. A singlet (S=0) cannot transition to a triplet (S=1). Transitions violating this are called spin-forbidden.
Orbital (L)	$$\Delta L = \pm 1$$	The orbital angular momentum must change by exactly one unit. For Term Symbols: S (L=0) ↔ P (L=1); P (L=1) ↔ D (L=2).
Total (J)	$$\Delta J = 0, \pm 1$$	The total angular momentum must change by 0 or 1 unit. Exception: $$J=0 \rightarrow J=0$$ transitions are strictly forbidden.
Parity	Parity must change.	The parity of the initial and final states must be different (even ↔ odd). For orbitals, this means $s \rightarrow p$ or $p \rightarrow s$, but $s \rightarrow d$ is forbidden.

Examples of Allowed and Forbidden Transitions

We analyze the transitions based on the change in the quantum numbers:

Transition	$\Delta S$	$\Delta L$	$\Delta J$	Status	Reasoning
2S1/2 → 2P1/2	0	+1 ($0 \to 1$)	0	ALLOWED	Satisfies all three main rules ($\Delta S=0, \Delta L=1, \Delta J=0$).
1S0 → 3P1	1	+1 ($0 \to 1$)	+1	FORBIDDEN	Violates the Spin Rule: $$\Delta S = 1$$. (This transition is called a **spin-forbidden** intercombination transition).
2P1/2 → 2D3/2	0	+1 ($1 \to 2$)	+1	ALLOWED	Satisfies all three main rules ($\Delta S=0, \Delta L=1, \Delta J=1$).
2S1/2 → 2D3/2	0	+2 ($0 \to 2$)	+1	FORBIDDEN	Violates the Orbital Rule: $$\Delta L = 2$$.

JKSET: Which of the following transitions is not allowed by the electric dipole selection rules ?
(A) ²S_1/2 → ²P_3/2
(B) ²S_1/2 → ²P_1/2
(C) ²S_1/2 → ²D_3/2
(D) ¹P₁ → ¹D₂

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Answer:

Option	Transition	ΔS	ΔL	ΔJ	Allowed by Rules?
(A)	$$^2S_{1/2} \rightarrow {}^2P_{3/2}$$	$2 \rightarrow 2$ ($\Delta S=0$)	$0 \rightarrow 1$ ($\Delta L=1$)	$1/2 \rightarrow 3/2$ ($\Delta J=1$)	Allowed
(B)	$$^2S_{1/2} \rightarrow {}^2P_{1/2}$$	$2 \rightarrow 2$ ($\Delta S=0$)	$0 \rightarrow 1$ ($\Delta L=1$)	$1/2 \rightarrow 1/2$ ($\Delta J=0$)	Allowed
(C)	$$\mathbf{{}^2S_{1/2} \rightarrow {}^2D_{3/2}}$$	$2 \rightarrow 2$ ($\Delta S=0$)	$0 \rightarrow 2$ ($\Delta L=2$)	$1/2 \rightarrow 3/2$ ($\Delta J=1$)	Forbidden
(D)	$$^1P_1 \rightarrow {}^1D_2$$	$1 \rightarrow 1$ ($\Delta S=0$)	$1 \rightarrow 2$ ($\Delta L=1$)	$1 \rightarrow 2$ ($\Delta J=1$)	Allowed