ATM-07

Dipole selection Δℓ = ±1

Allowed electric-dipole: Δℓ = ±1, Δm = 0, ±1. This sheet flags |Δℓ| = 1.

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SpectraSelection rules

Governing equation

\Delta\ell=\pm 1

where

\ell_1: Lower ℓ (—)
\ell_2: Upper ℓ (—)
\Delta\ell: Δℓ (—)
\mathrm{allowed}: Allowed (1/0) (—)

Lecture brief

Historical brief

Balmer, Rydberg, Bohr (1913), fine structure, Zeeman and Stern–Gerlach built the spectrum of one atom. The lab computes levels, selection and magnetic splitting. This sheet (ATM-07 — Dipole selection Δℓ = ±1) is the form associated with Selection rules. Working symbols: $\ell_1$ , $\ell_2$ $\rightarrow$ $\Delta\ell$ , $\mathrm{allowed}$ . Parity and angular momentum of the photon. ΔS = 0 in LS coupling; intercombinations are weaker.

Purpose

Purpose: compute

\Delta\ell

\mathrm{allowed}

from

\ell_1

\ell_2

in Atomic physics via

\Delta\ell=\pm 1

Allowed electric-dipole: Δℓ = ±1, Δm = 0, ±1. This sheet flags |Δℓ| = 1. Use it when a real atomic physics question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

\ell_1 = 0.000\,\mathrm{—}

\ell_2 = 1.000\,\mathrm{—}

, the governing relation

\Delta\ell=\pm 1

yields

\Delta\ell = 1\,\mathrm{—}

\mathrm{allowed} = 1\,\mathrm{—}

. Two ℓ values, a green or red gate. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Lower ℓ \ell_10 —Upper ℓ \ell_21 —

Outputs

Δℓ \Delta\ell1 —
Allowed (1/0) \mathrm{allowed}1 —

Reading speed

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Narration of this film

Two ℓ values, a green or red gate.

Parity and angular momentum of the photon. ΔS = 0 in LS coupling; intercombinations are weaker.

Reading speed

Watch on YouTube