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Question A quantitative theory of bonding in ionic crystal was developed by Born and Meyer along the following the lines: the total force of the system is taken to be: ae² V-N 7-72 4πεor² F(r) = N- where N is the number of positive - negative ion pairs, A and n are constants determined from experiment and a the Madelung constant which depends on the crystal structure of the solid. 1. Derive an expression of the total potential energy of the ionic crystal and identify the repulsion and the attraction terms. 2. Derive an expression of the equilibrium interatomic distance ro. 3. Derive an expression of the bonding energy U(ro).

Question A quantitative theory of bonding in ionic crystal was developed by Born and Meyer along the following the lines: the total force of the system is taken to be: ae² V-N 7-72 4πεor² F(r) = N- where N is the number of positive - negative ion pairs, A and n are constants determined from experiment and a the Madelung constant which depends on the crystal structure of the solid. 1. Derive an expression of the total potential energy of the ionic crystal and identify the repulsion and the attraction terms. 2. Derive an expression of the equilibrium interatomic distance ro. 3. Derive an expression of the bonding energy U(ro).

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Question A quantitative theory of bonding in ionic crystal was developed by Born and Meyer along the following the lines: the total force of the system is taken to be: αe² 4πε r2 where N is the number of positive - negative ion pairs, A and n are constants determined from experiment and a the Madelung constant which depends on the crystal structure of the solid. 1. Derive an expression of the total potential energy of the ionic crystal and identify the repulsion and the attraction terms. Derive an expression of the equilibrium interatomic distance ro. Derive an expression of the bonding energy U(ro). 4. If the charge of the ions is double (2e), by what factor both the equilibrium interatomic spacing ro and the bonding energy change. Indicate which parameters increases or decreases. Comment on the magnitude of the change of both parameters. 2. 3. NA- N 7-72 F(r) = N
Transcribed Image Text:Question A quantitative theory of bonding in ionic crystal was developed by Born and Meyer along the following the lines: the total force of the system is taken to be: αe² 4πε r2 where N is the number of positive - negative ion pairs, A and n are constants determined from experiment and a the Madelung constant which depends on the crystal structure of the solid. 1. Derive an expression of the total potential energy of the ionic crystal and identify the repulsion and the attraction terms. Derive an expression of the equilibrium interatomic distance ro. Derive an expression of the bonding energy U(ro). 4. If the charge of the ions is double (2e), by what factor both the equilibrium interatomic spacing ro and the bonding energy change. Indicate which parameters increases or decreases. Comment on the magnitude of the change of both parameters. 2. 3. NA- N 7-72 F(r) = N
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