Re: What are the problems with the Bohr model?

Michael,

The book to read is Gerhard Herzberg,  Atomic Spectra and Atomic 
Structure, Dover Publications.  Herzberg explains the Bohr atom picture 
and then shows how wave mechanics or the Quantum Theory more naturally and 
completely explains the finer details of hydrogen-like species and allows 
the consideration of multiple electron atoms.

Bohr’s picture modified the classical theory by allowing only certain 
discrete states of the atom;  the model quantizes the angular momentum of 
the electron about the nucleus.  This allowed an almost exact description 
of the various series in the hydrogen spectrum.  The calculations agreed 
exactly with those from spectroscopy.  This was a breakthrough and is 
still worth while as a simplified approach to atomic structure.  However, 
close examination caused modifications of the initial theory.  
Consideration of the mass of the nucleus with the mass of the electron 
gave a more exact calculation of the Rydberg constant [the ionization 
potential of the atom] which was calculated from measurements of the 
Balmer series of lines.  Secondly the possibility of elliptical orbits 
[corresponding to p, d, and f etc. electrons] necessitated the addition of 
a new quantum number [l] to quantize the radial momentum of the electron.  
The addition of space quantization [m] and electron [s] and nuclear spin 
was difficult to incorporate.  The Bohr model was  only a simplified 
Hydrogen atom.

The Bohr model did not consider the wave properties of matter.  Once 
DeBroglie showed these to exist, Wave and Quantum mechanics proved much 
more correct description of atoms and molecules, indeed the limitations 
are mostly in the calculations.  One immediate basic difference is in the 
description of the s orbitals.  The Bohr atom has the lowest unit of 
angular momentum in the lowest energy level, the 1s orbital.  The wave 
mechanics representation assigns the quantum number l  [ = n-1,2 ..]to the 
angular momentum. This gives the s orbital a zero angular momentum which 
wasn’t possible classically.  In wave mechanics the quantum numbers are a 
natural result of the boundary conditions of the wave representations of 
matter.  Of course quantum mechanics also describes the electron orbital 
as an electron probability over space rather than the precise orbit of the 
original Bohr model.

QM allows the calculation of transition probabilities between states of an 
atom and of the lifetimes of excited states, a topic not even considered 
by classical methods.  QM also allows the description of multi electron 
atoms and of molecular electronic structure, which are completely beyond 
the classical theory and the Bohr model.

Again Herzberg’s book[s] describe this elegantly and simply.  They tell 
almost everything you want to know about atoms and, if you want to know 
more, are an excellent start.

Regards,
Jim Griepenburg  jgriep@msn.com