[lboyer]

As my first post I would like to introduce myself as someone who is just getting into chemistry and is trying to learn on my own in my spare time.

My question is in particular about orbitals.

Carbon for example, to my knowledge has 3 orbitals, 1s, 2s, 2p.
Do each of these "bubbles" overlap each other?
Does the orbitals in an outer shell overlap with the inner?
Can I visualize this by placing each orbital shape on top of each other?

[AdiDex]

Do you know about principle of Superposition ??

[AdiDex]

Carbon for example, to my knowledge has 3 orbitals, 1s, 2s, 2p.

Correction - Carbon has 4 orbitals occupied in its ground state ,i.e. 1s , 2s and two 2p orbitals . Yep you can say it has 3 Subshells .

[Borek]

Do each of these "bubbles" overlap each other?
Does the orbitals in an outer shell overlap with the inner?

Yes, they all occupy the same space around the nucleus

[mikasaur]

Electrons and their orbitals/shells/subshells are a little tricky because an electron isn't really a "particle" like you'd imagine a golf ball or something similar to be. Each electron doesn't really exist in one place at one time.

Each subshell is really just a mathematical concept for where an electron could be at any moment in time. If you have a relatively strong math background this site might help you. Each mathematical expression in that table corresponds to the wave function of a subshell (the wave function is related to the probability of finding an electron at some place relative to the nucleus. If you're really interested in that relationship you can start here).

Focus on the expressions where [itex]\ell=0[/itex] -- these are your s-orbitals. Note that they are all expressions of r - the distance from the nucleus. Look at the 1s, 2s, and 3s expressions and you'll see that they are non-zero pretty much for all values of r (except for the nodes!). This means that these orbitals occupy the same space around the nucleus, as Borek says. But it is more likely that you'd find a 2s electron farther from the nucleus than a 1s electron.

[AdiDex]

If you have no internet data limitation .

Try this -:
http://demonstrations.wolfram.com/UnsoeldsTheorem/

Download CDF player and Download this Demostration as CDF .

[aga]

As a beginner i really would not get too hung up on quantum mechanics too much - do some actual chemical reactions or procedures first and have some fun.

Having said that, electron behaviour is at the very heart of Chemistry.

Orbitals are basically the shape of the space where you can expect to find an electron some of the time.
The shape of the orbitals can be very strange, such as above or below the nucleus (but Not in the middle).

E.g. in the Benzene molecule the electrons whizz about in a donut below and a donut below the carbon ring, transitioning from one to the other without ever passing through the ring ...

I found this helpful in visualising atomic orbitals :-
https://www.youtube.com/watch?v=K-jNgq16jEY

[Enthalpy]

Yes, orbitals do overlap, a lot. The "outer" orbitals extend farther, that's all  - keeping their fuzzy limit in mind.

For instance, all s orbitals have their maximum density (per volume unit, not per radius unit) right at the nucleus.

They are orthogonal in the sense that the sum of their product over space is zero, which implies that they change their sign at different places.

So for carbon:

• 1s is + everywhere;
• 2s is + at the center and - farther away;
• one 2p has a + lobe in one direction and a - lobe in the opposite direction, hence is orthogonal (integral of product) to all spherical orbitals;
• an other 2p has + and - lobes too but in a direction perpendicular to the previous orbital, so the integral of the product is zero with the previous too.

Note that any linear combination of the three 2p orbitals is an orbital too (because these have exactly the same energy) and that other choices are just as good to make bases for the 2p orbitals. The two-lobed set is convenient for chemistry and bonds but is just one possible choice: the one with a zero orbital momentum around the lobes axis. If you add with 90° phase the two previous 2p aligned on x and y, you get the orbital with the definite angular momentum of 1 around z, which looks like a doughnut instead of a peacock. Three doughnuts make a basis too, and for instance their limear combinations make the peacocks again. Other linear combinations would make elliptic orbitals, which are stable and have just no definite angular momentum around any axis. A 2p electron has no reason to follow a peacock nor doughnut shape.

If you come from an optics or radiocomms background, the 2p base is the same story as the linear and circular polarization of the EM field. Better: the shape and direction of a 2p corresponds to the polarization of a photon emitted during a transition to 1s.

Higher orbitals make more complicated combinations as there are more of them in a basis.

One should remember too that the known orbitals are only for one lone hydrogen atom. We use them at other atoms because they're understandable, not because they're accurate. Repulsion among electrons deform all orbitals because they overlap so much, and this changes the energy a lot. It also explains why individual electrons use to occupy all the accessible orbitals (2px and 2py for atomic carbon) instead of pairing on a single one. The same happens with O₂, and in a more complicated form, in transitions metals.

Nice representations of orbitals there:
http://winter.group.shef.ac.uk/orbitron/

[Enthalpy]

Orbitals are basically the shape of the space where you can expect to find an electron some of the time.
The shape of the orbitals can be very strange, such as above or below the nucleus (but Not in the middle).

"Some of the time" and "whizz" are already a misconception, because orbitals are immobile. QM vocabulary calls them "stationary" solutions.

At s orbitals (and only these), the electron density is maximum at the nucleus.

[aga]

At s orbitals (and only these), the electron density is maximum at the nucleus.

With all orbitals the spatial plots are of probability densities, not actual probabilities.

Orbital theory is really very fuzzy indeed, however it is the best tool we've had so far, and works better than any tool we've ever had.

[Enthalpy]

Beware with "probability" too.

In conditions that localize an electron more precisely than its initial wavefunction did, and only then, the initial wavefunction defines a probability density that the electron interacts, hence is localized in the interaction region when the interaction takes place, and the electron evolves further starting from that region. This happens when the other interacting particle is more localized than said electron.

In other interactions, where the other particle spreads over a volume as big or bigger, the electron does not reduce the volume it occupies, nor does the interaction take place at a point. The electron interacts simultaneously from all the volume it occupies. This is how interactions are computed.

In other words: interactions happen over the common volume of the particles. Only if some reason makes this volume small, we know after an interaction where it happened.

That's why I write shortly "the electron's volume" rather than something like "the extension of its wavefunction" or "its probability density". Schrieffer for instance did it too. Limits to this wording are that
- The electron doesn't repel itself.
- Its intrinsic angular momentum shows a null extension.

Some situations, especially the double slit experiment, lead easily to misinterpretations, akin "the wavefunction only tells the probability to find the point electron in a volume element". This is not the general case. For instance the operation of an atomic force microscope does not localize the observed electron more than necessary, and especially it leaves the electron (pair) as its orbital untouched when the probe is taken away. That is, the electron force microscope (not the tunnel effect microscope) observes the shape of a molecular orbital by feeling the same electron (pair) at successive locations over time.
Google the images:
pentacene "atomic force microscope"

Orbitals are fuzzy but the theory is clear - in fact, it's not a theory, but the strict application of QM to atoms and molecules. I haven't heard of any limitation or inaccuracy, and they answer everything. Their only drawback is the absence of analytical solutions.