INO-06

Madelung energy

U = − NA α k e² / r. Point-charge lattice sum.

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LatticeMadelung

Governing equation

U=-N_A\alpha\dfrac{ke^2}{r}

where

\alpha: Madelung constant (—)
r: Nearest-neighbour r (Å)
U: Madelung energy (kJ/mol)

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-06 — Madelung energy) is the form associated with Madelung. Working symbols: $\alpha$ , $r$ $\rightarrow$ $U$ . α encodes the structure (NaCl 1.748, CsCl 1.763, ZnS 1.638).

Purpose

Purpose: compute

U

from

\alpha

r

in Inorganic chemistry via

U=-N_A\alpha\dfrac{ke^2}{r}

U = − NA α k e² / r. Point-charge lattice sum. 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

\alpha = 1.748\,\mathrm{—}

r = 2.820\,\mathrm{Å}

, the governing relation

U=-N_A\alpha\dfrac{ke^2}{r}

yields

U = -861.2\,\mathrm{kJ/mol}

. Singly charged pair, r in Å, output kJ/mol. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Madelung constant \alpha1.748 —Nearest-neighbour r r2.82 Å

Outputs

Madelung energy U-861.2 kJ/mol

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Narration of this film

Singly charged pair, r in Å, output kJ/mol.

α encodes the structure (NaCl 1.748, CsCl 1.763, ZnS 1.638).

Reading speed

Watch on YouTube