Bohr Model of Atom: Stability Condition Explained

[connor415]

Eisberg and Resnick says that the condition for stability of the atom is:

k Ze²/r²=mv²/r

What I fail to understand is why the Z isn't square too. I mean surely you have Z electrons interacting with Z protons which which would surely give q1q2=(Ze)(-Ze)=-Z²e²?

What am I missing?

 

[Philip Wood]

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$\hbar$.