How Does the Uncertainty Principle Invalidate the Bohr Model?

[84527]

Why the uncertainly relation ΔxΔp>h forces us to reject the semiclassical Bohr model for the hydrogen atom?

 

[chaoseverlasting]

This is fairly easy to prove, the diameter of the atom is of the order of $$10^{-15}$$. Therefore an electron MUST be present in the volume of the atom. So, the maximum uncertainty that can be allowed is $$10^{-15}m$$. Plug this into the equation and what do you get for the uncertainty in velocity?

HINT: Its greater than the speed of light, and that's just the UNCERTAINTY!

And the equation is $$dx\times dp>=\frac{h}{4\pi}$$.