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

$n \in \left[0, 7\right]$

where

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

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

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

$n \in \left[0, 7\right]$

$n = 0$ $S = 0$

Along the curve

②

Domain of the variable — blue

n_{\min} = 0,\quad n_{\max} = 7

$n \in \left[0, 7\right]$

$n = 0$ $n = 0$

Along the curve

③

Response curve — green

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

$n \in \left[0, 7\right]$

$n = 0$ $S = 0$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}S}{\mathrm{d}n}

$n \in \left[0, 7\right]$

$n = 0.044$ $S^{\prime} = 0.5$

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-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.

Reading speed

Watch on YouTube