In crystals of the salt cesium chloride, cesium ionsCs + form the eight corners

Question

In crystals of the salt cesium chloride, cesium ionsCs+ form the eight corners of a cube and a chlorineion Cl- is at the cube's center (Fig. below). Theedge length of the cube is L = 0.49 nm. TheCs+ ions are each deficient by one electron (andthus each has a charge of +e), and theCl- ion has one excess electron (and thus has acharge of -e). (a) What is themagnitude of the net electrostatic force exerted on theCl- ion by the eight Cs+ ions atthe corners of the cube? (b) If one ofthe Cs+ ions is missing, the crystal is said tohave a defect; what is the magnitude of the netelectrostatic force exerted on the Cl- ion by theseven remaining Cs+ions?

Explanation / Answer

b)
   F= ke2/d2= ke2/(3/4)a2        =( 9 x109Nm2/C2)(1.6x10-19C)2 / (3/4)(0.4x10-9m)2           = 1.9*10-9 N
       =( 9 x109Nm2/C2)(1.6x10-19C)2 / (3/4)(0.4x10-9m)2           =( 9 x109Nm2/C2)(1.6x10-19C)2 / (3/4)(0.4x10-9m)2           = 1.9*10-9 N

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