What is wrong with the Bohr model?

Question

What is wrong about the Bohr model? Many books say it is wrong but doesn't say why and I don't know why.

Answer 1

I quote from the Bohr model Wikipedia page,

... depicts the atom as a small, positively charged nucleus surrounded by electrons that travel in circular orbits around the nucleus - similar in structure to the solar system...

Why is the model wrong? In reality the electrons do not orbit the nucleus. Consider the simplest case of a hydrogen-like ion, with a single proton and electron, with Hamiltonian

$$H=\frac{1}{2m}p^2 -\frac{Ze^2}{4\pi \epsilon_0 r}.$$

The solution to the Schrödinger equation is a wave function $\psi_{nlm}(r,\theta,\phi)$ which one can employ to determine probabilites of the electron being found within a volume, but we cannot claim it is precisely at a location. For example,

$$\int_{0}^{r} dr \, \int_{0}^{\pi} d\phi \int_{0}^{2\pi} d\theta \, |\psi_{nlm}|^2 \, r^2 \sin \phi$$

denotes the probability for it to be found within a sphere centered at the origin of radius $r$, in the state indexed by the quantum numbers, $(n,l,m)$. In addition, the Bohr model applies classical mechanics to model the electron, e.g. using the notion of centripetal force, but the approach neglects and is completely against the true reality which is that it is quantum mechanical.

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An example of a flaw demonstrated empirically: the Bohr model predicts the incorrect value for the orbital angular momentum in the ground state of the system. In addition, the radiation one would expect due to a uniformly rotating charged particle is not present. See the Larmor derivation for an explanation of how radiation arises due to acceleration of charged matter, e.g. Walter Lewin's derivation.

Answer 2

The Bohr model does not contain any dynamics. The Classical Electrodynamics gives a different dynamics - a continuous radiation. So the model is incomplete. It is not sufficient to postulate things, it is necessary to obtain these discrete levels from dynamical equations. QM provides such a dynamical description and it is richer than just the Bohr model.

Answer 3

Bohr's model was the simple basic structure of an atom and it's electrons (How the electrons move around the nucleus). However, it did not explain the entire "story" of how the electrons orbited the nucleus. Since there are different kinds of orbitals, sub levels and principle energy levels, this gives each electron it's own way of orbiting depending on the sub level. S has one orbital, P has 3 orbitals, D has 5 orbitals, f has 7 orbitals. (Remember each orbital can only have 2 electrons which is stated in the Pauli Exclusion Rule)

Answer 4

Well, to put simple, the Bohr's model of the atom was not wrong TOTALLY - it was only acceptable for the hydrogen atom.

Why? Because, in reality, electrons do not travel in a circular orbit. They travel in an elliptical orbit.

Bohr's model had one significant drawback - they were only a 2-D diagram of the truth. In reality the actual model of the atom is the Sommerfield atom, where we see electrons travelling in an elliptical path around the nucleus, but in the xyz plane. In plain words, Bohr's model was a 2-D shape while Sommerfield's was a 3-D shape of an atom.