A quantitative theory of bonding in ionic crystals was developed by Born and Meyer along the following lines: the total force of the system is taken to be: ae² F(r) = N-NAT where N is number of positive - negative ion pairs, A and n are constant determined from experiment and at the Madelung constant which depends on the crystal structure of the solid. 1) Derive an expression of the total potential energy and identify the repulsion and the attraction terms. 2) Derive an expression of the equilibrium interatomic distance, re 3) Derive an expression of the bonding energy. 4) if the charge of the ions is double, by what factor both the equilibrium interatomic spacing ro and the bonding energy U(ro) change. Indicate which parameter increase or decrease. Comment on the magnitude of the change of both parameters.

A quantitative theory of bonding in ionic crystals was developed by Born and Meyer along the following lines: the total force of the system is taken to be: ae² F(r) = N-NAT where N is number of positive - negative ion pairs, A and n are constant determined from experiment and at the Madelung constant which depends on the crystal structure of the solid. 1) Derive an expression of the total potential energy and identify the repulsion and the attraction terms. 2) Derive an expression of the equilibrium interatomic distance, re 3) Derive an expression of the bonding energy. 4) if the charge of the ions is double, by what factor both the equilibrium interatomic spacing ro and the bonding energy U(ro) change. Indicate which parameter increase or decrease. Comment on the magnitude of the change of both parameters.

Principles of Modern Chemistry

8th Edition

ISBN:9781305079113

Author:David W. Oxtoby, H. Pat Gillis, Laurie J. Butler

Publisher:David W. Oxtoby, H. Pat Gillis, Laurie J. Butler

Chapter13: Spontaneous Processes And Thermodynamic Equilibrium

Section: Chapter Questions

Problem 55AP

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