Fred wrote: ... >> > The potential V of a `particle with charge - q at a distance r >> > from a particle with charge + q equals V = k*q/r independent >> > of the mass of either particle. k = 1/4(pi)eo ... >> > The velocity v = [2 V*q/r * (1/m)]^1/2 = [2 V*q/r (1/2m)]^1/2 at that >> > point is also the same (c * alpha or c/137 at a distance >> > r = 5.29E-11 meters, the bohr radius). >> >> Where does this come from? >> > The velocity in the classical Bohr ground state orbit. ...
OK one step at a time so Bohr proposed in 1913 (cf this article http://en.wikipedia.org/wiki/Bohr_model ) an ad hoc not-too-bad semi-classical model of the H atom where the electron's angular momentum can only take some discrete values: L=n*(h/2pi) Where n = 1,2,3,. is called the principal quantum number, and h is Planck's constant. Angular momentum L is r*m*v isn't it, so for ground state n=1 we have: r*m*v=1*(h/2pi) => v=1/r * 1/m * h/2pi How does one get from this to your v formula above? Wait a minute, your v formula simply results from equating centripetal coulombic force k*q^2/r^2 = V*q/r to centrifugal force m*v^2/r doesn't it? But then there is a mistake, the "2" factor in front of V*q/r shouldn't be there, which is confirmed by your second expression for v where the "2" factor cancels out. Or maybe your second expression was for your electronium (same charge as electron, twice the mass, right?) in which case it's wrong too! Please let me know if you agree with the above and we'll proceed from there. Michel
