Eisberg and Resnick says that the condition for stability of the atom is: k Ze^{2}/r^{2}=mv^{2}/r What I fail to understand is why the Z isnt square too. I mean surely you have Z electrons interacting with Z protons which which would surely give q1q2=(Ze)(-Ze)=-Z^{2}e^{2}? What am I missing?
No. They are dealing with a one electron atom. You might say: then it's hydrogen, so why not put Z = 1? They leave Z open so the same treatment will do for, an He^{+} ion and so on. Incidentally the equation you give isn't really the condition for stability. It is the classical F = ma equation for circular orbits. The stability condition is Bohr's condition: mvr = n[itex]\hbar[/itex].