The orbitals of an atom can be thought of as being formed from the probability of finding electrons in those orbitals. If the orbital is 1s (n = 1, l = 0), then it has a certain "volume" for which the electron can be at any position, and in some radial distances from the nucleus, it will be at those distances with more probability than in other distances. Imagine then a 2s orbital (n = 2, l = 0), it will have a bigger volume than the 1s orbital, which represents the probabilities of finding the electron at certain points in that volume.
Now, since the volume of 2s is greater than 1s, that means that if there are electrons in the 2s orbital, they will have a certain probability of being at a place where the 1s orbital is. Now, if this is a hydrogen or helium neutral atom with its electron in an excited state, then there would be no problem with this, I guess. However, if we talk about Lithium, which has 3 electrons, the aufbau's principle and Pauli's exclusion principle would imply that 2 electrons are at the 1s orbital, and 1 electron at the 2s orbital. Now, as I said in the first paragraph, that 1 electron at 2s will have a probability of being at 1s! Then, Pauli Exclusion Principle would be violated because only 2 electrons can occupy the 1s orbital, so this could not happen, if Pauli Exclusion Principle does hold. However, then, how can one explain this?
Why is there a probability of finding an electron of a 2s orbital at a same radius as one that holds for a 1s orbital? The only reasonable explanation that I can come up with is: If the electron in the 2s orbital shifts to the 1s orbital (since it would be possible since it has probability to be there), then one electron in the 1s orbital immediately shifts to the 2s orbital, and Pauli Exclusion Principle would hold. Is this reasoning correct? If not, why is there a probability of being at 1s orbital for an electron at the 2s orbital?
As an aside: I am struggling to think intuitively of why is energy quantized. If an electron is at 1s orbital, it will have a certain energy. But why is this energy fixed for that orbital? If the electron can be at points closer to the nucleus, then the potential energy of the system would be lower... Are the energy levels an average? I think the correct question would be: "Why is energy quantized and not continuous?"
If I said something that is wrong, do not hesitate to correct me please. As I understand that these topics deal with Quantum Mechanics, I can be completely wrong at some stuff because my knowledge of this area is little and it is just from what is usually learned in Chemistry. Thanks a lot in advance!