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During a thought experiment, I observed that I was not able to figure the Bohr model in 3d.
In every picture I saw up to today, the electrons orbit the nucleus on a fixed circle-like path.
But while modelling this behaviour in 3d some questions arose:

  1. Do electrons "change their direction" on their orbit? (Or do they fly on a circle embedded in 3d?)
  2. If 1. is correct (which is what I assume), how could you describe this process mathematically? It could be something like a random walk, but on a sphere surface and with parameters which I do not know.
  3. Electrons are able to change their orbital by "jumping" a quantized energy level.
    Is the location within the after-jump-orbit stochastically (in)dependent of the location on the previous orbital? That is, does the position on the previous orbital in some degree determine the position within the after-jump-orbital? I'm not interested in the distance between the orbitals, but wether the electron jump lies on a line with three points: the nucleus, the previous location and the after-jump-location.
    Or could it be that the electron jumps one orbital higher, but is after the jump on the other side of the nucleus than its previous location?
    enter image description here

Please remain relaxed: I know of the quantum model, but the Bohr model is often sufficient in simple chemistry.
Please excuse my bad description, I lack knowledge as well as the english technical vocabulary. Feel free to improve.

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The Bohr model is already in 3 dimensional space. In this model the electron orbit would be a circle around the atom embedded in 3D space, and the orbit would not change because of conservation of angular momentum. And yes, the initial orbit determines the final orbit for a given amount of energy given to the electron, but the model does not talk about position of electrons within an orbit, because it is not equipped to treat such a problem, if that’s what you are asking

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  1. With a radial potential, as assumed in the Bohr model (Coulomb potential is radial), the equation of motion for the azimuthal angle $\theta$ is $$\dot{\theta}=0$$ Which means that once the angle is fixed, it won't change. And so, if there isn't any external forces, it won't change the circular orbit in another one on the same sphere.

  2. Is not correct from 1.

  3. The change in the orbit is made possible by adding or subtracting energy. If you send a photon with the right frequency to the electron, it will absorb it, change the orbit (jump in one orbit with a bigger radius) and he will eventually come back to its ground state by re-emitting a photon. The orbits in which the electron will go, can be calculated by the formula: $$E=R_e\left(\frac{1}{n_f^2}-\frac{1}{n_i^2}\right)$$ Where $R_e$ is the Rydberg's constant and $n_f, n_i$ are the final and initial orbital quantum number respectively.

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