Halliday, Resnick & Walker — Coulomb's Law: Problem 27

27 In crystals of the salt cesium chloride, cesium ions \( \text{Cs}^+ \) form the eight corners of a cube and a chlorine ion \( \text{Cl}^- \) is at the cube's center (Fig. 21-20). The edge length of the cube is \( 0.40 \text{ nm} \). The \( \text{Cs}^+ \) ions are each deficient by one electron (and thus each has a charge of \( +e \)), and the \( \text{Cl}^- \) ion has one excess electron (and thus has a charge of \( -e \)). (a) What is the magnitude of the net electrostatic force exerted on the \( \text{Cl}^- \) ion by the eight \( \text{Cs}^+ \) ions at the corners of the cube? (b) If one of the \( \text{Cs}^+ \) ions is missing, the crystal is said to have a defect; what is the magnitude of the net electrostatic force exerted on the \( \text{Cl}^- \) ion by the seven remaining \( \text{Cs}^+ \) ions?