Editing Bohr model (section)

== Shortcomings ==
The Bohr model gives an incorrect value {{math|''L''{{=}}''ħ''}} for the ground state orbital angular momentum: The angular momentum in the true ground state is known to be zero from experiment. Although mental pictures fail somewhat at these levels of scale, an electron in the lowest modern "orbital" with no orbital momentum, may be thought of as not to revolve "around" the nucleus at all, but merely to go tightly around it in an ellipse with zero area (this may be pictured as "back and forth", without striking or interacting with the nucleus). This is only reproduced in a more sophisticated semiclassical treatment like Sommerfeld's. Still, even the most sophisticated semiclassical model fails to explain the fact that the lowest energy state is spherically symmetric – it doesn't point in any particular direction.

In modern quantum mechanics, the electron in hydrogen is a [[Electron cloud|spherical cloud of probability]] that grows denser near the nucleus. The rate-constant of probability-decay in hydrogen is equal to the inverse of the Bohr radius, but since Bohr worked with circular orbits, not zero area ellipses, the fact that these two numbers exactly agree is considered a "coincidence". (However, many such coincidental agreements are found between the semiclassical vs. full quantum mechanical treatment of the atom; these include identical energy levels in the hydrogen atom and the derivation of a fine-structure constant, which arises from the relativistic Bohr–Sommerfeld model (see below) and which happens to be equal to an entirely different concept, in full modern quantum mechanics).

The Bohr model also failed to explain:

* Much of the spectra of larger atoms. At best, it can make predictions about the K-alpha and some L-alpha X-ray emission spectra for larger atoms, if ''two'' additional ad hoc assumptions are made. Emission spectra for atoms with a single outer-shell electron (atoms in the [[lithium]] group) can also be approximately predicted. Also, if the empiric electron–nuclear screening factors for many atoms are known, many other spectral lines can be deduced from the information, in similar atoms of differing elements, via the Ritz–Rydberg combination principles (see [[Rydberg formula]]). All these techniques essentially make use of Bohr's Newtonian energy-potential picture of the atom.
* The relative intensities of spectral lines; although in some simple cases, Bohr's formula or modifications of it, was able to provide reasonable estimates (for example, calculations by Kramers for the [[Stark effect]]).
* The existence of [[fine structure]] and [[hyperfine structure]] in spectral lines, which are known to be due to a variety of relativistic and subtle effects, as well as complications from electron spin.
* The [[Zeeman effect]] – changes in spectral lines due to external [[magnetic field]]s; these are also due to more complicated quantum principles interacting with electron spin and orbital magnetic fields.
* Doublets and triplets appear in the spectra of some atoms as very close pairs of lines. Bohr's model cannot say why some energy levels should be very close together.
* Multi-electron atoms do not have energy levels predicted by the model. It does not work for (neutral) helium.