Potential energy of charged particles

Actually, stability is related more directly to the energy of the compound. You will probably remember that energy is the ability to do work and that work is accomplished when a force is exerted through a distance. 

Kinetic energy, which is the ability of an object to do work by virtue of its motion, and potential energy, the ability of an object to do work by virtue of its position. 

A boulder perched on the top of a cliff has no kinetic energy because it is not moving. However, it could fall at any moment and then its motion could be harnessed to do work (for example, if attached to a rope and pulley it could lift a weight). Thus, this motionless boulder has the potential to do work that is, it has potential energy. 

Of course, our ions are not boulders, but they also have the potential to move (if they are oppositely charged they can move toward one another) and thus have potential energy. They also have a small amount of kinetic energy because they vibrate back and forth in their positions in the solid. The potential energy (V) is expressed mathematically by an expression that is very similar to that derived by Coulomb for the force  

Notice that the difference between the two expressions is that the force has in the denominator, while the potential energy has r in the denominator. The important point is that the energy of an ionic compound, which is primarily electrostatic potential energy, depends on the charge on each ion and the distance between the ions. 

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