How do orbitals exist in an atom?

There is a good answer here already, but there still seems to be some confusion, so I will give my input as well.

The regions in your diagrams correspond to the "most likely place to find the electron" if if was just in that state. Furthermore, the regions are defined by some threshold probability of finding the electron at that location. So technically, all orbitals "overlap", because the probability amplitude is defined for all of space. We just make these diagrams by only showing the most probable regions.

The issue you seem to be having is that the "location" of the electron determines which orbital it is in. The opposite is actually the case. The orbital that the electron is in determines it probability amplitude in the position basis.

Therefore, there are multiple reasons (probably more than I have just said) to be fine with "overlapping" orbitals

1. The regions in the diagram correspond to single orbitals if the electron was only in that orbital (no superpositions)
2. The regions in the diagram just show part of the probability density. Technically the probability density is defined in all space, so all orbitals "overlap" at all points in space
3. The "location" of the electron does not determine which orbital it is in. If the electron is in some given orbital, we can then use the diagram to determine the most likely region the electron could be observed to be in.

Okay, now I get you. I'll try to explain your question in the comment in simple terms.

If we agree to the fact that 1S and 2P orbitals have different energies then the volume of space common to those two orbitals cannot exist as they have quite different energies,but from the picture and 'my opinion about the observation' it seems like they do.That's the anomaly.I'm just asking how do you explain the probability of finding an electron in the volume of space common to two orbitals.

Note, however, that it is extremely difficult (and "dangerous") to try to explain it to someone who doesn't know much more than high school QM, but I'll try.

I'll go one by one.

If we agree to the fact that 1S and 2P orbitals have different energies

Yes. Well, we don't just "agree", that is just true, and it can be shown. That's right.

then the volume of space common to those two orbitals cannot exist as they have quite different energies

What? How comes a volume cannot exist? The volume is a real 3D volume. It might be empty, but it exists.

What's more, there's nothing wrong with 2 electrons together, having different energies. Pauli's exclusion principle forbids that two electrons share all their quantum numbers, but if the electrons have different energies, then it's okay to be in the same place.

I'm just asking how do you explain the probability of finding an electron in the volume of space common to two orbitals.

This is more complex, and it requires further knowledge of QM.

I'll try to make an intuitive analogy.

In QM, let's say that we just don't know things until we measure them. We don't know where an electron is until we measure its position. This is different than classic mechanics, where you can estimate positions just gazing roughly, without perturbating the system. Not here; in QM, you don't know anything until you measure it.

So, how do we measure things? Regardless of how scientists manage themselves to develop the appropriate instruments, measuring is "revealing" some unknown information. For example: where's the electron? Take a picture and find out. "Oh, it was here".

Unlike classical mechanics (CM), Quantum mechanics (QM) are random. That means position won't be always the same, even in the same system. There's essential randomness.

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So let's get to the point. Imagine you want to measure the "state". That means measuring the quantum numbers of the electron, so that you can say "oh, this is a $1s$ orbital" (let's neglect the spin for now).

So you have an atom, you use the whatever-meter and you find out that the electron was in $1s$.

You can measure another electron being in $2p$, with $m=0$, for example.

In QM, it is possible to have a "linear combination" of $1s$ and $2p$. In that case, you'll sometimes measure $1s$ and sometimes $2p$. It is random, but there is a well-defined probability of measuring each one. The probability depends on the concrete entanglement you have.

So that's a more elaborate answer to the first thing: the same electron can be found in $1s$ or $2p$, depending on your luck. This is weird to newbies, but it is basic QM.

This is just to set up some ideas. However, this was not your question. If I understood well, your question was how can an electron be in a "shared volume", right?

Well, that's because the orbital is not exclusive of one level, as you can see in the picture.

The orbital you see there is "the volume in which it is likely to measure $2p$".

You must associate the quantum numbers to the electron, not to the volume. The volume is free land, and the state (Quantum numbers) belong to the electron. So an electron can move around a $1s$ orbital. That only means that "the electron is in a volume in which $1s$ electrons are likely to be there".

So it is like a tourist visiting another country, or a land shared by two countries. The thing is that, when we make a measurement, we're asking the electron for its passport, and then we see if it was a $1s$ or a $2p$.

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To sum up:

• The orbitals you're seeing there are not like Bohr levels. In Bohr levels, an electron being in a level automatically implied having the energy of that level.
• Nevertheless, this is not a level representation. This is a picture of the "volumes that each nationality uses to visit".
• Some sub-volumes can be visited by several "nationalities", but that doesn't mean that visitors change their nationality.
• However, QM allows being "a combination of nationalities". This is, showing you different passports, randomly. This happens in entangled states.

(To be precise, after showing you one, it will remain being that one forever. After a measurement, the "system" picks only one and stays with it. The surprising thing is that identical systems, strictly identical, can show any of those passports, randomly.)

So this is all. Hope I helped.

An electron can occupy only one orbital at any given instant i.e for example,it can either be in 1s or 2p but definitely not in both the orbitals.This is because the two orbitals have quite different energies.

That is quite correct for orbitals defined by the principle quantum number n, identified with the energy eigenvalue in the simple quantum mechanical solutions for the hydrogen atom, and mathematically extrapolated to electrons in atoms and molecules.

Note that $n$ is connected with a wavefunction, it is the complex conjugate square of the wavefunction that defines the orbitals, i.e. orbitals are a probability distribution, giving a value on how probable it is to find the electron at a particular (r,theta,phi).

Note that all s states, i.e zero angular momentum, have a probability of existing around r=0. This does not mean that they have the same energy, because the quantum mechanical solution for a potential just give probabilities.

In the classical planetary model, the energy of an orbit depends on the distance from the center of force/potential. In a quantum mechanical model, the energy is an eigenvalue of the solution of the quantum mechanical equation with the potential, but the solutions are not connected to space coordinates, except through probabilities.

In proton rich nuclei, electron capture can happen, because in such nuclei there is a large enough probability for s state electrons to overlap with the probability distribution of a proton, and the proton changes into a neutron and a different nucleus . It is a complicated process which exists through the probabilistic nature of quantum mechanics.