INO-28

Born–Landé U

Ionic lattice.

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InorganicBorn–Landé

Governing equation

U=\\dfrac{N_A A z^2 e^2}{4\\pi\\varepsilon_0 r_0}(1-1/n)

where

A: Madelung (—)
z: z (—)
r_0: r0 (Å)
n: Born n (—)
U: U (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-28 — Born–Landé U) is the form associated with Born–Landé. Working symbols: $A$ , $z$ , $r_0$ , $n$ $\rightarrow$ $U$ . Ionic lattice.

Purpose

Purpose: compute

U

from

A

z

r_0

n

in Inorganic chemistry via

U=\\dfrac{N_A A z^2 e^2}{4\\pi\\varepsilon_0 r_0}(1-1/n)

Ionic lattice. 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

A = 1.750\,\mathrm{—}

z = 1.000\,\mathrm{—}

r_0 = 2.800\,\mathrm{Å}

n = 9.000\,\mathrm{—}

, the governing relation

U=\\dfrac{N_A A z^2 e^2}{4\\pi\\varepsilon_0 r_0}(1-1/n)

yields

U = 772\,\mathrm{kJ/mol}

. Ionic lattice. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Madelung A1.75 —z z1 —r0 r_02.8 ÅBorn n n9 —

Outputs

U U772 kJ/mol

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Narration of this film

Ionic lattice.

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