Chapter 2: Problem 14
Ionic crystals consist of a three-dimensional array of positive and negative ions and the calculation of its potential energy due to Coulomb forces is tedious. As a simpler example, consider a one-dimensional array consisting of a straight row of \(N\) point charges, alternately \(+e\) and \(-e\) and each a distance \(a\) from its nearest neighbours. If \(N\) is very large, find the potential energy of a charge in the middle of the row and of one at the end in the form \(\alpha e^{2} /\left(4 \pi \varepsilon_{0} a\right)\). This sets upper and lower bounds to the Coulomb energy of the whole array. \(\alpha\) is known as the Madelung constant for such systems.
Short Answer
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Key Concepts
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