ATM-20

Hund ground-term spin

S = n_unpaired / 2. First Hund rule: maximise spin in an open subshell.

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StructureHund

Governing equation

S=n_{\mathrm{unpaired}}/2

where

n: Unpaired electrons (—)
S: Spin (—)
2S+1: Multiplicity (—)

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-20 — Hund ground-term spin) is the form associated with Hund. Working symbols: $n$ $\rightarrow$ $S$ , $2S+1$ . Then maximise L, then J = |L−S| if the shell is less than half full.

Purpose

Purpose: compute

S

2S+1

from

n

in Atomic physics via

S=n_{\mathrm{unpaired}}/2

S = n_unpaired / 2. First Hund rule: maximise spin in an open subshell. 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

n = 3.000\,\mathrm{—}

, the governing relation

S=n_{\mathrm{unpaired}}/2

yields

S = 1.5\,\mathrm{—}

2S+1 = 4\,\mathrm{—}

. A subshell, arrows of spin, an S. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Unpaired electrons n3 —

Outputs

Spin S1.5 —
Multiplicity 2S+14 —

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Narration of this film

A subshell, arrows of spin, an S.

Then maximise L, then J = |L−S| if the shell is less than half full.

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Watch on YouTube