INO-26

Spin-only μ

First-row ions.

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Inorganicspin-only

Governing equation

\\mu=\\sqrt{n(n+2)}

$n \in \left[0, 5\right]$

where

n: Unpaired (—)
\mu: μ (\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=\\sqrt{n(n+2)}

$n \in \left[0, 5\right]$

$n = 0$ $\mu = 0$

Along the curve

②

Domain of the variable — blue

n_{\min} = 0,\quad n_{\max} = 5

$n \in \left[0, 5\right]$

$n = 0$ $n = 0$

Along the curve

③

Response curve — green

\\mu=\\sqrt{n(n+2)}

$n \in \left[0, 5\right]$

$n = 0$ $\mu = 0$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}\mu}{\mathrm{d}n}

$n \in \left[0, 5\right]$

$n = 0.031$ $\mu^{\prime} = 5.727$

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-26 — Spin-only μ) is the form associated with spin-only. Working symbols: $n$ $\rightarrow$ $\mu$ . First-row ions.

Purpose

Purpose: compute

\mu

from

n

in Inorganic chemistry via

\\mu=\\sqrt{n(n+2)}

First-row ions. 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 = 3.000\,\mathrm{—}

, the governing relation

\\mu=\\sqrt{n(n+2)}

yields

\mu = 3.87\,\mathrm{mu_B}

. First-row ions. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Unpaired n3 —

Outputs

μ \mu3.87 \mu_B

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Narration of this film

First-row ions.

Reading speed

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