[Mr-E]

Hello, so lost.

I've attached a picture, so is it correct in saying that 2s2 electrons can be found in 1s2?
So the orange sphere of 2s2 is actually engulfing the 1s2 orbital also?

Like in the second picture, the grey orbital of 3s2 electrons have a high probability of being located ANYWHERE in the grey?

https://www.google.com.au/search?q=orbitals&source=lnms&tbm=isch&sa=X&ved=0ahUKEwjA9JvysdjXAhVIm5QKHScYBsMQ_AUICigB&biw=1280&bih=600#imgrc=XRiUNH3iv2EKrM:

attached a link

[Enthalpy]

Yes.

Orbitals overlap very much. This is even a condition for them to be "orthogonal", that is, the integral over space of their product is zero. For instance a 1s has the same sign everywhere, so a 2s must overlap it both where the 2s is positive and where the 2s is negative.

The math expressions tell it too. All s orbitals for instance have their strongest probability density per volume unit at the nucleus.

This has consequences on the electrons' energy. For instance the 2s electron of a lithium atom has a different energy from a hydrogen electron excited to 2s.

You mentioned "be located anywhere"... That's correct, with subtleties. Since electrons repel an other, if you find by some (highly disturbing) means that one electron is located in some subvolume of the atom, then an other electron is less probably there too. However, all this is static in an atom at rest, hence I write "if" and not "when". This is formalized by writing one single wavefunction for several particles, like ψ(r₁, r₂, t) that differs from ψ(r₁, t)*ψ(r₂, t).

A nice website for orbitals:
http://winter.group.shef.ac.uk/orbitron/

[Flatbutterfly]

"Those who are not shocked when they first come across quantum theory cannot possibly have understood it." Niels Bohr.

Wave functions are solutions to the Schrödinger Wave Equation.  And the 1s wave function Ψ(1s) is indeed greatest at the nucleus, as is the Ψ^2(1s) which represents the probability of finding the 1s electron.  However the volume available to the 1s e⁻ near the nucleus is small; further away from the nucleus the volume increases but Ψ^2(1s) decreases. To take these opposing factors into account (cf. Volume×Density = Mass) chemists use the radial distribution function (RDF) 4πr^2 Ψ^2.  The best website I know for RDF functions is the orbitron site of Winter (previously mentioned by Enthalpy and given below). The RDF of the H 1s AO shows the most probable place to find the 1s e⁻ is at the Bohr radius, 59 pm.

Turning to the question at hand: the RDF of the H 2s AO shows that it too has a finite probability of being close to the nucleus and consequently spends some time closer to the nucleus than the 1s e⁻.  This is a feature of all s AOs in that they have a finite probability of being close to the nucleus.  This makes NMR possible and is used to explain relativity effects in heavy elements.  On the other hand, for p, d and f wave functions the nucleus is a node (region of zero electron density).  It is the different extent of the penetration of the core electrons that gives rise to s<p<d<f order of energy in multielectron atoms as opposed to being degenerate in the H atom.  (I blame Schrödinger!)

And remember: “I think it is safe to say that no one understands quantum mechanics…. Do not keep saying to yourself if you can possibly avoid it, “But how can it be like that?” because you will get “down the drain” into a blind alley from which nobody has yet escaped.  Nobody knows how it can be like that.” Richard Feynman

http://winter.group.shef.ac.uk/orbitron/AOs/1s/wave-fn.html

[Enthalpy]

[...] the 2s too has a finite probability of being close to the nucleus and consequently spends some time closer to the nucleus [...]

[My emphasis] just to raise a detail: orbitals are by definition independent of time, so I try to avoid all terms that suggest time. It is difficult, because our vocabulary doesn't fit QM. Wording that fits QM is heavier, like "the electron has a density there" or "has a probability of being found there".

[Flatbutterfly]

The Dirac treatment of wave functions includes time and hence I believe it is valid to say, for example, that the 6s electrons of Hg spend some of the time close to the nucleus.
 https://en.wikipedia.org/wiki/Dirac_equation

I did not check the Winter site for the RDF of the 2s AO.
I now find it did not want to plot the function.  I probably need you another update for downloads.  See if you have any more luck:
http://winter.group.shef.ac.uk/orbitron/AOs/2s/radial-dist.html

[Enthalpy]

Orbitals are time-independent, that is, ψ has the form F(x, y, z)*exp(iEt/ħ), so |ψ| does not depend on t. It's because they are defined that way. As opposed, linear combination of orbitals with different energies are still solutions of Schrödinger's equation, they are valid wave functions, but with them |ψ| depend on t, and these let say that the electron moves.

Use the Dirac equation if you prefer. It doesn't change the result, that orbitals are static because it's their definition (and that this definition is useful because it corresponds to the ground state of the atoms).

All the information about the electron is in ψ. Supposing additional information, like a more accurate location of the electron at some time, would be a hidden variable.

And even more: the electron acts simultaneously from all its possible positions. Experience goes against a more localized electrons changing its position.

The electron hopping over time among its possible positions was a very early interpretation of the wave function. It is long abandoned for being disproved - this is not just a matter of wording or interpretation.

[Flatbutterfly]

The RDFs for 1s, 2s, and 3s H AOs are shown here: 
https://ch301.cm.utexas.edu/section2.php?target=atomic/H-atom/radial-distribution.html
Note the RDFs shown are of just one quadrant and they extend in three dimensions. (The s wave functions as you are probably aware are spherically symmetric.)
The 2s and 2p H wave functions are given here:
https://chemistry.stackexchange.com/questions/152/why-is-the-2s-orbital-lower-in-energy-than-the-2p-orbital-when-the-electrons-in
This is relevant to another question posted on forum.
"I do not like it [quantum mechanics], and I am sorry I ever had anything to do with it."
Erwin Schrödinger


The Dirac time-dependent wave equation is more accurate than the Schrödinger wave equation that is required to rationalize spin, nodes and relativity effects of wave functions.  I think it also predicts antimatter but I am not an expert.  The Dirac wave functions are however more difficult to grasp than the Schrödinger functions and why we use the latter functions most of the time.  I can’t find the reference, but as I recall one prominent theoretician said, “Dirac knows what he’s talking about.”
https://en.wikiquote.org/wiki/Paul_Dirac

“Things on a very small scale [like electrons] behave like nothing that you have any direct experience about. They do not behave like waves, they do not behave like particles, they do not behave like clouds, or billiard balls, or weights on springs, or like anything that you have ever seen.” Richard Feynman

[Mr-E]

Thank you so much for your replies. Not sure I understood half of what was written as I'm not currently up to that level but very keen to progress further now.