[AdiDex]

I was wondering that according to Bohr's model an electron can exist in certain orbits ( As angular momentum is quantised ) , so how the  transition of an electron happens when it go from one shell to another , as it can't exist between the shell .by which path it goes from one shell to another.
Is there any quantum theory about this ..??

And what is the modern theory about transition..??

[Corribus]

The shells are not actually shells. In modern theory, as opposed to the flawed Bohr model, electron position is described by wavefunction probability densities. These are continuous functions and they overlap with each other. In principle if the wavefunction overlap is equal to zero exactly, then there is no allowed transition for the reason you mention. In most cases, overlap is nonzero (although it can be quite small), so transitions are allowed.

Note also that electrons and other quantum particles can tunnel through barriers, which is like saying that the particle can exist where it's not classically supposed to.

[Irlanur]

The shells are not actually shells. In modern theory, as opposed to the flawed Bohr model, electron position is described by wavefunction probability densities. These are continuous functions and they overlap with each other. In principle if the wavefunction overlap is equal to zero exactly, then there is no allowed transition for the reason you mention. In most cases, overlap is nonzero (although it can be quite small), so transitions are allowed.

I am not sure if I get you right, but I think what you say is not correct.
1) Eigenfunctions to different Eigenvalues of the Hamiltonian (=Energy levels) are always orthogonal to each other (no overlap). (not considering degeneracies for now).
2) a transition is (in first approximation) allowed, if the transition dipole moment is non-zero, which doesn't have much to do with overlap.


to the original question:
1) quantum theory does not describe trajectories of individual electrons. It uses wavefunctions, which have some relation to probability densities. But then again, you can't distinguish electrons, which means you can't say that electron1 has done a transition, only the whole system can do a transition. (you could argue with the hydrogen atom, though)
2) Here it comes hard for me, since I am not an expert at all: As far as I know, the modern theory uses the formalism of "second  quantization", which uses annihilation and creation operators. Regarding the formalism, a transition is described as an electron being annihilated from one state and  created in another. But I can't argue how much this actually describes the picture physicists have to day or it's just pure formalism.

[Corribus]

I am not sure if I get you right, but I think what you say is not correct.
1) Eigenfunctions to different Eigenvalues of the Hamiltonian (=Energy levels) are always orthogonal to each other (no overlap). (not considering degeneracies for now).

Sorry for being unclear; what I mean is simpler than this. But you are right I misspoke (miswrote?) - What I meant was that the probability distributions (not the wavefunctions) overlap in real space because they are continuous functions. Which means, the electron doesn't have to be in a new place to go to a new energy level. (Insofar as the precise location of an electron can be defined at any point in time, of course.) The OP, I believe, was asking why transitions can happen between "shells" when, in the Bohr model, different shells are different distances away from the nucleus... which would mean that for an instantaneous transition an electron would have to suddenly be somewhere else. But this shell model is not accurate. The probability densities do overlap in space.

2) a transition is (in first approximation) allowed, if the transition dipole moment is non-zero, which doesn't have much to do with overlap.

Well, it depends on the transition. Wavefunction overlap is critical toward evaluating the transition moment of a vibronic transition. This is the basis of the Franck-Condon factor. Of course, vibrational wavefunctions on different electronic surfaces are not orthogonal, so there you go, but this is still often casually referred to as wavefunction overlap.

[AdiDex]

the electron doesn't have to be in a new place to go to a new energy level

Suppose an atom -

Li - 1s² 2s¹

I gave some energy to it , new state is -

Li - 1s¹, 2s²

So is this means the probability density of electron would not increase in the region of 2s orbital .??

And thank you very much for answering...

[Corribus]

It would, but you're thinking too linearly. The probability density functions are not immutable in multielectron atoms. As soon as you start changing the electron configuration, all the orbital wavefunctions change, because the inter-electronic interactions are different. In other words, the 2s orbital wavefunction in the 1s² 2s¹ configuration will be different than the 2s orbital wavefunction in the 1s¹ 2s² configuration.

[Irlanur]

to get back to the original question: it's a very fundamental quantum mechanical question. You can't discuss this with orbitals, because they are inherently an approximation and "they just don't care" about the transitions. I don't know what the current understanding of physicists is exactly, but as far as I know, we don't really know whats going on during a transition. if something is going on...

[Corribus]

Part of the problem is that it's difficult to measure electron transitions, which occur on timescales < 1 fs. Even in femtosecond pump-probe experiments, by the earliest measurable time delays, the excitation event has already long since happened.

Attosecond spectroscopy has been in large part pioneered by Ferenc Krausz and coworkers at Max Planck during the early to mid 2000s, and they're able to observe electron transition events. It's pretty cool stuff but I don't really keep up with it, because as far as practical spectroscopy of chemical systems goes, it's not very useful. So, I'm not sure what in the way of fundamental knowledge about electronic transitions it has yielded. As chemists we are primarily concerned with what happens to molecular ensembles after the initial excitation event has occured, and we can describe this collective behavior pretty well, even if, again, we have a limited understanding of the physics involved behind any singular event.

Some example references of attosecond spectroscopy by the Krausz group:

Hentschel et al. Nature, 2001, 414, 509-513
Drescher et al. Nature, 2002, 419, 803-7
Korkum and Krausz, Nature Physics, 2007, 3, 3817 (nice review)
Cavalieri et al, Nature, 2007, 449, 1029-32
Goulielmakis et al, Nature, 2010, 466, 739-43

(As you can see, they haven't done too badly in the publication department. The last one is particularly relevant to the discussion at hand.)