ATM-05

Zeeman shift

ΔE = μ_B B g m_J. Linear Zeeman energy of a magnetic sublevel.

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SpectraZeeman

Governing equation

\Delta E=\mu_B B g m_J

$B \in \left[0, 12\right]$

where

B: Field (T)
g: Landé g (—)
m_J: m_J (—)
\Delta E: Shift (µeV)
\Delta\nu: Frequency (GHz)

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 E=\mu_B B g m_J

$B \in \left[0, 12\right]$

$B = 0$ $\Delta E = 0$

Along the curve

②

Domain of the variable — blue

B_{\min} = 0,\quad B_{\max} = 12

$B \in \left[0, 12\right]$

$B = 0$ $B = 0$

Along the curve

③

Response curve — green

\Delta E=\mu_B B g m_J

$B \in \left[0, 12\right]$

$B = 0$ $\Delta E = 0$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}\Delta E}{\mathrm{d}B}

$B \in \left[0, 12\right]$

$B = 0.075$ $\Delta E^{\prime} = 115.8$

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-05 — Zeeman shift) is the form associated with Zeeman. Working symbols: $B$ , $g$ , $m_J$ $\rightarrow$ $\Delta E$ , $\Delta\nu$ . μ_B = 5.788×10⁻⁵ eV/T. Anomalous Zeeman uses the Landé g; normal Zeeman has g = 1.

Purpose

Purpose: compute

\Delta E

\Delta\nu

from

B

g

m_J

in Atomic physics via

\Delta E=\mu_B B g m_J

ΔE = μ_B B g m_J. Linear Zeeman energy of a magnetic sublevel. 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 = 1.000\,\mathrm{T}

g = 2.000\,\mathrm{—}

m_J = 1.000\,\mathrm{—}

, the governing relation

\Delta E=\mu_B B g m_J

yields

\Delta E = 115.768\,\mathrm{\mu eV}

\Delta\nu = 27.992\,\mathrm{GHz}

. A line that splits in B. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Field B1 TLandé g g2 —m_J m_J1 —

Outputs

Shift \Delta E115.768 µeV
Frequency \Delta\nu27.992 GHz

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Narration of this film

A line that splits in B.

μ_B = 5.788×10⁻⁵ eV/T. Anomalous Zeeman uses the Landé g; normal Zeeman has g = 1.

Reading speed

Watch on YouTube