Question

In crystals of the salt cesium chloride, cesium ions Cs⁺ form the eight corners of a cube and a chlorine ion Cl^- is at the cube's center (see the figure). The edge length of the cube is L = 0.42 nm. The Cs⁺ ions are each deficient by one electron (and thus each has a charge of +e), and the 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 Cl^- ion by the eight Cs⁺ ions at the corners of the cube? (b) If one of the Cs⁺ ions is missing, the crystal is said to have a defect; what is the magnitude of the net electrostatic force exerted on the Cl^- ion by the seven remaining Cs⁺ ions?

Answer 1

a)

Edge length of cube is .

Distance from the center(Cl^-) to any corner of cube ( Cs⁺) is (Where   )

Charge on is and is .

Force on (at center) due to all (at corner) are equal in magnitude and are directed towards the each ion., along 8 directions.

Force on due to each pair of located diametrically opposite corners cancel each other.Since the two forces are equal in magnitude and opposite in directions.

There will be 4 pairs of forces which are equal in magnitude and opposite in directions.when all the 8 forces added up the resultant force has zero magnitude.

Hence net force acting on ion due to eight ions is zero.

b)

Now, only 7 ions are present.

There will be 3 pairs of forces which are equal in magnitude and opposite in directions. Force between the 7th ion and ion is

Direction of force is away from the missing ion.