ATM-30

Dipole Δℓ allowed

Electric dipole rule.

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Atomicselection

Governing equation

\Delta\ell=\pm 1

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

where

\ell_1: ℓ1 (—)
\ell_2: ℓ2 (—)
\mathrm{ok}: Allowed (—)

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

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

$\ell_2 = 0$ $\mathrm{ok} = 0$

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

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

$\ell_2 = 0$ $\mathrm{ok} = 0$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}\mathrm{ok}}{\mathrm{d}\ell_2}

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

$\ell_2 = 0.038$ $\mathrm{ok}^{\prime} = 0$

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-30 — Dipole Δℓ allowed) is the form associated with selection. Working symbols: $\ell_1$ , $\ell_2$ $\rightarrow$ $\mathrm{ok}$ . Electric dipole rule.

Purpose

Purpose: compute

\mathrm{ok}

from

\ell_1

\ell_2

in Atomic physics via

\Delta\ell=\pm 1

Electric dipole rule. 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

\mathrm{ok} = 1\,\mathrm{—}

. Electric dipole rule. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

ℓ1 \ell_10 —ℓ2 \ell_21 —

Outputs

Allowed \mathrm{ok}1 —

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Narration of this film

Electric dipole rule.

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