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)}

where

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

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