4

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

Qmechanic
  • 201,751
Locke
  • 47

4 Answers4

3

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.

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.

Emilio Pisanty
  • 132,859
  • 33
  • 351
  • 666
JamalS
  • 19,254
  • 3
    It is not convincing to just assert what electrons do or do not in reality. You only showed where the Bohr model is different from the Schroedinger model, not where it is wrong. – Ján Lalinský May 25 '14 at 20:36
  • @JánLalinský: Well, we know empirically that the electron is not orbitting the nucleus in the classical sense, and in that sense the model is wrong. If the question was to be interpreted as, 'why is the model bad or not acceptable?' then it is because it's predictions are not sufficiently precise, or rather not as precise as other models. – JamalS May 25 '14 at 20:40
  • the potential term should be ~ 1/r, not 1/r^2 :) – eqb May 25 '14 at 20:52
  • @eqp: Thank you for catching that; I should have included a $Z$ for generality too. – JamalS May 25 '14 at 20:53
  • 1
    JamalS, the only "prediction" of the Bohr model commonly known are the frequencies of the emission lines. These are the same as the "predictions" based on the Schroedinger equation. (in fact in both cases they are post-dictions, or better explanations of already known values, of course). In this respect both models are equally accurate. – Ján Lalinský May 25 '14 at 21:08
  • There are more things that can be extracted from the Schroedinger equation, so I agree that the Bohr model is less capable. – Ján Lalinský May 25 '14 at 21:09
1

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.

Vladimir Kalitvianski
  • 13,885
1

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)

Sophh
  • 11
  • 1
-2

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.

Shreyas Naik
  • 1
  • where we see electrons travelling in an elliptical path around the nucleus, Isn't part of the failure of the Bohr atom that the electrons don't actually orbit the nucleus? – Kyle Kanos Nov 24 '15 at 11:30
  • 2
    In reality the actual model of the atom is the Sommerfield atom No, the orbital model is superior and QED would be more accurate even. – jinawee Nov 24 '15 at 11:45