ATM-09

Term degeneracy

A term ²ˢ⁺¹L_J has multiplicity 2S+1 and (2J+1) magnetic sublevels.

Reading speed

SpectraTerm symbols

Governing equation

g=2J+1,\quad M=2S+1

where

S: Spin S (—)
J: J (—)
2S+1: Multiplicity (—)
2J+1: Degeneracy (—)

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-09 — Term degeneracy) is the form associated with Term symbols. Working symbols: $S$ , $J$ $\rightarrow$ $2S+1$ , $2J+1$ . L = 0,1,2,… → S,P,D. J runs from |L−S| to L+S. Hund fills the ground term.

Purpose

Purpose: compute

2S+1

2J+1

from

S

J

in Atomic physics via

g=2J+1,\quad M=2S+1

A term ²ˢ⁺¹L_J has multiplicity 2S+1 and (2J+1) magnetic sublevels. 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

S = 0.500\,\mathrm{—}

J = 1.500\,\mathrm{—}

, the governing relation

g=2J+1,\quad M=2S+1

yields

2S+1 = 2\,\mathrm{—}

2J+1 = 4\,\mathrm{—}

. A term label, a degeneracy bar. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Spin S S0.5 —J J1.5 —

Outputs

Multiplicity 2S+12 —
Degeneracy 2J+14 —

Reading speed

Watch on YouTube

Free library

Full library

Free PDF / open book

YouTube channels

00:0 / 00:08

Narration of this film

A term label, a degeneracy bar.

L = 0,1,2,… → S,P,D. J runs from |L−S| to L+S. Hund fills the ground term.

Reading speed

Watch on YouTube