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I know that angular momentum and energy of the electron is quantized in the model. When we wrote down the equations and get the velocity equation, if I am not mistaken, we find the velocity to be quantized.

There are some teachers I know, who are saying that the velocity is not quantized because the direction changes all the time. This does not make any sense in my opinion. So, is it quantized or not? Or is it just a silly question to ask, because even Bohr himself was not bothered with that?

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The first paragraph of your question is indeed correct. Under Bohr's model of the atom angular momentum is quantized (meaning discretized) and therefore there is a discrete number of allowed radii that lead to stable "orbits" for the electron. Then if you want to be very pedantic, you can say the speed (the modulus of the velocity) is discrete too. (see the wikipedia page for the details https://en.wikipedia.org/wiki/Bohr_model)

However we know this picture is just incomplete and one should not think about particles as following pointlike classical trajectories. Instead, one should understand the physics is governed by wave functions which describe probability densities, from which we can compute observables. I can only recommend you to read some of the fundamentals of quantum mechanics, so you can "update" your picture :).

I particulary find both volumes of "Quantum Mechanics" from Claude Cohen-tannoudji & Bernard Diu & Frank Laloe very complete.

Sakurai is also a very popular option for basic and advanced levels.

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The Bohr model is simply not good enough and that's why more sophisticated models based on e.g. the Schrödinger equation, were developed. I'd encourage you to look at those.

There are some teachers I know, who are saying that the velocity is not quantized because the direction changes all the time.

Velocity is a vector quantity. It has both direction and a magnitude.

Ignoring the problems with the Bohr model, consider a circular orbit. Clearly the magnitude of the velocity is constant, but the direction changes all the time.

So your teachers are correct in this sense.

Note that the energy level doesn't change, but that depends on the square of the magnitude of velocity, not on the direction.

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  • $\begingroup$ Cant we also change the direction of angular momentum by just interacting with the atom? Then by the same logic, I would say the angular momentum is not quantized because it can have continuous direction of its angular momentum. $\endgroup$ – physicsguy19 Apr 30 '18 at 12:07
  • $\begingroup$ You are spotting all the problems with the Bohr model (and in fairness Bohr never claimed it solved these issues, just to reproduce the spectrum). :-) Unfortunately to solve these problems requires learning Quantum Theory and accepting some unintuitive ideas that don't seem fit with the human everyday-world. $\endgroup$ – StephenG Apr 30 '18 at 12:26
  • $\begingroup$ I know a little bit about things like electron clouds etc.. but when they ask a question like this in the exams, it becomes a problem.. because it is strictly about Bohr model. $\endgroup$ – physicsguy19 Apr 30 '18 at 12:29

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