ATM-23

Landé g-factor

g_J = 1 + [J(J+1)+S(S+1)−L(L+1)] / [2 J(J+1)]. Anomalous Zeeman g.

Reading speed

StructureLandé

Governing equation

g_J=1+\dfrac{J(J+1)+S(S+1)-L(L+1)}{2J(J+1)}

$J \in \left[0.5, 6\right]$

where

L: L (—)
S: S (—)
J: J (—)
g_J: Landé g (—)

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.

00:0 / 00:08

①

Governing law — red

g_J=1+\dfrac{J(J+1)+S(S+1)-L(L+1)}{2J(J+1)}

$J \in \left[0.5, 6\right]$

$J = 0.5$ $g_J = 0.667$

Along the curve

②

Domain of the variable — blue

J_{\min} = 0.5,\quad J_{\max} = 6

$J \in \left[0.5, 6\right]$

$J = 0.5$ $J = 0.5$

Along the curve

③

Response curve — green

g_J=1+\dfrac{J(J+1)+S(S+1)-L(L+1)}{2J(J+1)}

$J \in \left[0.5, 6\right]$

$J = 0.5$ $g_J = 0.667$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}g_J}{\mathrm{d}J}

$J \in \left[0.5, 6\right]$

$J = 0.535$ $g_J^{\prime} = 1.931$

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-23 — Landé g-factor) is the form associated with Landé. Working symbols: $L$ , $S$ , $J$ $\rightarrow$ $g_J$ . g = 2 for a pure spin, g = 1 for a pure orbit. Alkali D2 has g = 4/3 for ²P_{3/2}.

Purpose

Purpose: compute

g_J

from

L

S

J

in Atomic physics via

g_J=1+\dfrac{J(J+1)+S(S+1)-L(L+1)}{2J(J+1)}

g_J = 1 + [J(J+1)+S(S+1)−L(L+1)] / [2 J(J+1)]. Anomalous Zeeman g. 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

L = 1.000\,\mathrm{—}

S = 0.500\,\mathrm{—}

J = 1.500\,\mathrm{—}

, the governing relation

g_J=1+\dfrac{J(J+1)+S(S+1)-L(L+1)}{2J(J+1)}

yields

g_J = 1.3333\,\mathrm{—}

. Three quantum numbers, a g bar. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

L L1 —S S0.5 —J J1.5 —

Outputs

Landé g g_J1.3333 —

Reading speed

Watch on YouTube

Free library

Full library

Free PDF / open book

YouTube channels

00:0 / 00:08

Narration of this film

Three quantum numbers, a g bar.

g = 2 for a pure spin, g = 1 for a pure orbit. Alkali D2 has g = 4/3 for ²P_{3/2}.

Reading speed

Watch on YouTube