Spectroscopic Selection Rules: Allowed Transitions Guide

Atoms and molecules have many energy levels, but not every jump between levels produces a bright spectral line. Spectroscopic selection rules are the allowed-or-forbidden conditions that decide which transitions actually appear in a spectrum. They arise from conservation of angular momentum: the photon carries one unit, so the electron's angular momentum must change to match.

These rules matter because they explain the pattern of lines we observe, from the yellow sodium street lamps to the fingerprints of elements in starlight. For JEE and NEET, selection rules turn spectra into logical puzzles: given two levels, predict whether the transition appears.

Key Concepts

For electric-dipole transitions, the orbital rule is Δl = ±1 (Laporte rule): s ↔ p and p ↔ d are allowed, but s ↔ s and p ↔ p are forbidden. The spin rule is ΔS = 0: singlet-to-singlet is allowed, singlet-to-triplet is forbidden. The total angular momentum rule is ΔJ = 0, ±1, except that J = 0 to J = 0 is forbidden. The magnetic rule is Δml = 0, ±1. There is no restriction on the principal quantum number: Δn can be anything. For vibrational spectra of a harmonic oscillator, the rule is Δv = ±1.

How It Works

To test a transition: Step 1: compute Δl; it must be +1 or -1. Step 2: check spin multiplicities match (ΔS = 0). Step 3: check ΔJ is 0 or ±1, but not 0 to 0. Step 4: if all pass, the transition is allowed. Example: sodium's 3p → 3s line has Δl = -1, allowed and intense; the 4s → 3s jump has Δl = 0, forbidden.

Worked Example

The sodium D-line at λ = 589 nm corresponds to the 3p → 3s transition. First verify the selection rule: l changes from 1 to 0, so Δl = -1, allowed. Now compute the photon energy. E = hc/λ = (6.626 × 10-34 J s × 3.0 × 108 m s-1) / (589 × 10-9 m). The numerator is 1.9878 × 10-25 J m; dividing by 5.89 × 10-7 m gives 3.375 × 10-19 J, which is 3.375 × 10-19 / 1.602 × 10-19 = 2.11 eV. Each yellow photon carries 2.11 eV from an allowed Δl = -1 transition.

Common Misconceptions

• Forbidden means the transition never happens. Forbidden transitions are not impossible, just extremely weak and slow. Phosphorescence is a spin-forbidden emission that still occurs, over seconds instead of nanoseconds.
• The principal quantum number can only change by one. Wrong: Δn has no restriction. The 3p → 1s jump (Δn = -2) is perfectly allowed since Δl = -1.
• All spectroscopies share the same rules. They differ: rotational spectra require ΔJ = ±1, vibrational spectra Δv = ±1, and Raman scattering follows its own polarisability-based rules.

Real-World Applications

Astronomers identify elements in distant stars by matching observed lines to allowed transitions. Lasers work by arranging allowed stimulated emissions between chosen levels. Fluorescence microscopes tag cells with dyes chosen for bright allowed transitions. Mercury vapour lamps and neon signs glow in characteristic colours dictated by their allowed lines.

Selection rules are angular-momentum conservation in disguise. Apply Δl = ±1, ΔS = 0, ΔJ = 0, ±1 to any level pair to predict the spectrum.