ATM-35

Paschen–Back ratio

≫1 uncouples L and S.

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AtomicPaschen–Back

Governing equation

\eta=\mu_B B/\Delta E_{so}

$B \in \left[0.01, 50\right]$

where

B: B (T)
\Delta E_{so}: Fine split (meV)
\eta: η (—)

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

\eta=\mu_B B/\Delta E_{so}

$B \in \left[0.01, 50\right]$

$B = 0.01$ $\eta = 5.79\times 10^{-4}$

Along the curve

②

Domain of the variable — blue

B_{\min} = 0.01,\quad B_{\max} = 50

$B \in \left[0.01, 50\right]$

$B = 0.01$ $B = 0.01$

Along the curve

③

Response curve — green

\eta=\mu_B B/\Delta E_{so}

$B \in \left[0.01, 50\right]$

$B = 0.01$ $\eta = 5.79\times 10^{-4}$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}\eta}{\mathrm{d}B}

$B \in \left[0.01, 50\right]$

$B = 0.324$ $\eta^{\prime} = 0.058$

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-35 — Paschen–Back ratio) is the form associated with Paschen–Back. Working symbols: $B$ , $\Delta E_{so}$ $\rightarrow$ $\eta$ . ≫1 uncouples L and S.

Purpose

Purpose: compute

\eta

from

B

\Delta E_{so}

in Atomic physics via

\eta=\mu_B B/\Delta E_{so}

≫1 uncouples L and S. 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

B = 2.000\,\mathrm{T}

\Delta E_{so} = 1.000\,\mathrm{meV}

, the governing relation

\eta=\mu_B B/\Delta E_{so}

yields

\eta = 0.116\,\mathrm{—}

. ≫1 uncouples L and S. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

B B2 TFine split \Delta E_{so}1 meV

Outputs

η \eta0.116 —

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Narration of this film

≫1 uncouples L and S.

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