Question

In the cesium chloride crystal shown below we have eight
cesium atoms at the edges and a chlorine atom in the center consider
the cesium atom of the upper right front corner is torn out
by some process, leaving an empty space. (a) What is the
magnitude, direction and direction of the resulting electrostatic force on the
central chlorine atom? (b) Consider now that the empty space has been
filled by another ion with + 2e charge. What is the new magnitude and direction of the resulting force exerted on the chlorine atom?

Answer 1

Suppose the cesium ion at point X is torn out, as shown in the figure.

a) If the atom is neutral, the resultant force by rest of the atom is exactly equal and opposite to the force due to missing ion. As the force due to each charge is distributed by 8 oppositely charged ions, the magnitude will be equal to

F = k/(8r^2); where k= 9*10^9 Nm^2/C^2

and r for cesium= 4.123 Angstrom

and the direction will be along XY direction in the figure.

b) Now if the charge is 2e, the extra charge is only e here, so the magnitude of the force is equal to that of the previous case but with the opposite direction i.e. along YX.