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

$\ell_2 \in \left[0, 6\right]$

where

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

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

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①

Governing law — red

\Delta\ell=\pm 1

$\ell_2 \in \left[0, 6\right]$

$\ell_2 = 0$ $\Delta\ell = 0$

Along the curve

②

Domain of the variable — blue

\ell_2_{\min} = 0,\quad \ell_2_{\max} = 6

$\ell_2 \in \left[0, 6\right]$

$\ell_2 = 0$ $\ell_2 = 0$

Along the curve

③

Response curve — green

\Delta\ell=\pm 1

$\ell_2 \in \left[0, 6\right]$

$\ell_2 = 0$ $\Delta\ell = 0$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}\Delta\ell}{\mathrm{d}\ell_2}

$\ell_2 \in \left[0, 6\right]$

$\ell_2 = 0.038$ $\Delta\ell^{\prime} = 0$

Along the curve

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 —

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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