Question

We know that Bohr model (i.e., the “old” quantum mechanics) for the hydrogen atom is a semiclassical model and is not (always) consistent with quantum mechanics. Specifically, it is not (always) consistent with the uncertainty principle. Show why.

Answer 1

According to Bohr theory the electron revolve around the nucleus in circular orbits whose momentum and position is precisely defined at ant time. But according to Heisenberg's uncertainty principle the position and momentum can't to be precisely defined simultaneously. Hence Bohr's theory contradict Heisenberg's uncertainty principle.

Heidelberg's uncertainty principle is

But according to Bohr

Because ∆x = 0 and ∆p= 0.