The electrostatic potential energy that Bohr used was about right, although in general there are magnetic terms due to relativistic effects too. The classical mv2
/2 for kinetic energy is pretty close for the electrons in the low-energy states of small atoms, if you use the right translation of "v2
" into a local property of the quantum mechanical state.
The big way in which Bohr differs from modern quantum mechanics is that Bohr treated the electron as having an orbit, with a precisely defined position (at least in two dimensions) and speed. Actual quantum states of electrons or anything else do not have these properties. They are always spread out in all three dimensions and also always have a spread of velocities in all three directions.
Bohr also assumed that each electron always has a definite energy. While states with definite energy exist, quantum objects do not have to be in such states. General states have a range of possible energies, just as they have a range of positions and velocities.
(published on 11/15/2010)