INO-10

Spin-only magnetic moment

μso = √(n(n+2)) BM. Unpaired-electron moment.

Reading speed

MagnetismSpin-only

Governing equation

\mu_{so}=\sqrt{n(n+2)}

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

where

n: Unpaired electrons (—)
\mu_{so}: Spin-only moment (\mu_B)

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

\mu_{so}=\sqrt{n(n+2)}

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

$n = 0$ $\mu_{so} = 0$

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

\mu_{so}=\sqrt{n(n+2)}

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

$n = 0$ $\mu_{so} = 0$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}\mu_{so}}{\mathrm{d}n}

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

$n = 0.044$ $\mu_{so}^{\prime} = 4.87$

Along the curve

Lecture brief

Historical brief

Pauling and Allred–Rochow electronegativity, Kapustinskii lattice energy, CFSE and Goldschmidt radii organise the periodic solid. The sheets predict bond character and crystal packing. This sheet (INO-10 — Spin-only magnetic moment) is the form associated with Spin-only. Working symbols: $n$ $\rightarrow$ $\mu_{so}$ . Orbital angular momentum is quenched in many Oh complexes. n unpaired electrons.

Purpose

Purpose: compute

\mu_{so}

from

n

in Inorganic chemistry via

\mu_{so}=\sqrt{n(n+2)}

μso = √(n(n+2)) BM. Unpaired-electron moment. Use it when a real inorganic chemistry question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

n = 5.000\,\mathrm{—}

, the governing relation

\mu_{so}=\sqrt{n(n+2)}

yields

\mu_{so} = 5.916\,\mathrm{mu_B}

. Enter the number of unpaired electrons. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Unpaired electrons n5 —

Outputs

Spin-only moment \mu_{so}5.916 \mu_B

Reading speed

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Narration of this film

Enter the number of unpaired electrons.

Orbital angular momentum is quenched in many Oh complexes. n unpaired electrons.

Reading speed

Watch on YouTube