When you take some quantum mechanics courses in college, you will begin to understand. There simply is no “where” to the electron like there is for classical objects. It’s a difficult concept to grasp because you’ve spent you entire life observing objects move in the classical world. Even chemistry grad students don’t allways get it.
I think that “when” should be more of an “if.” I doubt I’ll ever take a quantum mechanics course. I plan on going into computer engineering, personally. Though there is a lot of potential in quantum computers…
But yes, that is a difficult concept to grab. Though it amuses me how, by sticking the word “quantum” before anything, you can excuse any lack of practical sense that applies to the reality we are familiar with.
Then again orbitals are just constructions for “visualization” as well. In many-electron atoms it is “incorrect” to talk about separate electrons occupying single orbitals anyway. While the ground state of He can be written as 1s^2 (for example) this is indeed another approximation.
It doesn’t excuse any sense of understanding. The word “quantum” has a definite meaning and can’t be arbitrarily stuck anywhere. The math behind it is very well known and understood. It’s just that the real world at that scale is very different. Trying to make a classical analogy to a quantum reality will almost always lead you to the wrong answer.
Chingon is right. Distinguishing between one electron and the other is also not realistic, but as a chemist I think that gets a little outside my expertise. I’m not exactly certain what he/she means by He is only approximated as 1s^2. Anything beyond a single Hydrogen atom is an approximation, but that doesn’t mean that standard molecular orbitals don’t serve as a useful basis set.
Sure, the space that isn’t occupied by any particle is “vacuum”. But saying which space is occupied or unoccupied is not so simple. Remember the uncertainty principle – the particles don’t have definite positions, they’re more like smeared out probability distributions. So at a given time, you’d say “There’s some probability P that there’s an electron in this unit of volume, and probability 1 - P that this unit of volume is empty.”
Gotta love the SDMB. 
Let me rephrase your question in two different ways. I’ll use helium (or, if you prefer, H[sup]-[/sup]) and ask about the space “between” the two electrons.
(1) If I have a helium atom in the ground state, where are the electrons (and what’s in between them)?
They are everywhere. You can’t say where each electron is exactly. They are everywhere at once, although some locations more probable than others, as specified by the spatial probability distribution that is the orbital. At this point (namely, while we haven’t disturbed the atom at all), the second part of the question (what’s between the electrons) can’t really be asked. But, we can ask a different one:
(2) If I perform a measurement on the atom that tells me simultaneously where both electrons are in space, and I very quickly after that perform a measurement that asks what is exactly between them, what do I get?
The answer is vacuum, but it’s no longer a helium atom that you’re talking about. If you try to measure the location of one of the electrons to better than a tenth of a Bohr radius, say, you will not be able to know the energy of that electron to better than about 340 eV (via the Heisenberg uncertainty principle). You can’t even know that it is bound anymore, as the binding energy is much less than this. Another way to look at it: To ask your question you must perform a measurement on the electrons (to locate them) which necessarily disturbs your system. In this case, the required disturbance is enough to mean you aren’t actually measuring what you wanted, since you have free electrons and an alpha particle, not helium. This annoyance is one and the same with the answer to (1) above, namely that the electrons really are in overlapping orbitals when they are in the bound state.
A third way to look at it: To find out where the electrons are (to find out what’s between them), you have to ping them so hard that you’d no longer be asking about the helium bound state. How hard? Here’s a back of the envelope calculation.
If they are moving at speed v on average, then we can isolate them to within a tenth of a Bohr radius if we “strobe” them more quickly than:
T = (0.0529 nm * 0.1) / v
To approximate v, we invoke the virial theorem and note that the kinetic and potential energies are, on average, equal. So, roughly:
0.5 * mv[sup]2[/sup] = (e[sup]2[/sup])/(0.0529 nm)
v = 0.010c
Thus, we need to strobe the system with a frequency faster than:
f = 1/T = 5.67 x 10[sup]17[/sup] Hz
Multiplying by Planck’s constant tells us the energy of the photon that has this frequency:
E = 2.3 keV
This is in the middle of the X-ray band.
When written as 1s^2 what is assumed is that the state you are looking at is actually a product state of two 1s orbitals without taking into account electron correlations. This is a useful way to describe the ground state of He, but the ground state of He cannot be fully reconstructed using product states. In fact a complete picture of the ground state of He would require the infinite sum of orbitals that share the same overall symmetry (say for the ground state: singlet S even). However small it may be, there is a contribution from the 1s30s orbital in the ground state of helium.
Gotcha, but your getting a little complicated for highschool. Heck, your getting a little complicated for chemistry grad school. 
To quote Raymond Hall of Fermilab: “Stuff is made out of particles. Therefore, particles cannot be made of stuff.”
As others have already noted, subatomic ‘particles’–that is, those whose behavior is more accuracy described by the principles of quantum mechanics than by classical Newtonian mechanics and Maxwellian electrodynamics–simply don’t behave like anything that we experience on the scale of our experiential world. We often refer to them as particles because in their interactions they occur at a specific locus, i.e., the impact of a single photon on a receptor will occur at a specific place, but the interactions are governed by a probabilistic mechanic that is best described as a stochastically defined waveform. That is to say, where the photon will land on the receptor can be strictly predicted as falling within a statistical distribution, but you can’t ever predict the exact point at which it will occur.
This itself is not hard to understand in classical terms; if you throw a ball at a target, you know that the point of impact will vary owing to your throwing skill, external influences like wind, et cetera. However, on the level governed by quantum mechanics all interactions are interconnected. In other words, there is no “statistical ball” and a classical target; both the ball and target are themselves subject to a complex interaction which will ultimately effect where the ball contacts the target. And strictly speaking, the observer who sees and records where the ball lands also influences the interaction, as can be seen from the quantum double slit experiment; when the observer attempts to detect the photon or electron going through one of the slits before impacting the target, the interference pattern between the two paths the ‘particle’ would take disappears, and instead you get two distinct, non-interfering paths that you would expect with a classical analysis of the dynamics of the system. But take away the observer and you get wave behavior. Hence the supposed “wave/particle duality” of objects on the scale of quantum mechanics.
This doesn’t literally mean that particles turn into waves, and then back into particles; what it indicates is that our current ability to model these dynamics, based upon the concepts and math that are suitable at the everyday macro scale of the world we experience, are inadequate to comprehensively describe what occurs on the scale of quantum mechanics. Instead, we have to apply the rules piecemeal as they world best and continue to come up with some kind of underlying mechanic that gives a complete, non-patchwork description of what really occurs.
What does this tell us? Does consciousness effect reality? Are there multiple realities layered upon one another? Is there some kind of propagating wavefront that occurs from the observer to the external world? Is there a manifold of non-local hidden connections between all particles? If Wigner’s friend gets bored and goes off for a beer before checking on the cat, is it still in a state of mortal superposition? There are no definitive answers to these questions, which fall into the realm of utter speculation and noodling solipsistic coffehouse philosophy b.s., but applying the principle of parsimony, a desire to accept some kind of deterministic mechanic, and a willingness to admit that we don’t really know any more about what is actually going on than we did before Heisenberg and Bohr started on this whole business (Max Planck was always suitably regretful about ever suggesting a statistical foundation to reality), and are only capable of blindly describing it in terms of probability functions rather than a deterministic set of rules or a fundamental understanding of how or why the interactions occur.
To address the o.p.'s original question, to wit, “what is in the space between all the parts?”, there is no ‘space’ and no ‘parts’, or rather no boundaries between the ‘space’ and ‘parts’. The ‘parts’ are actually fields that have a focus at a specific point but which are smeared out everywhere (although their probability of interacting arbitrarily far away from the focus is vanishingly tiny), and the ‘space’ is completely filled with these fields; not only the fields created by the ‘parts’ we directly observed, but also the ‘virtual particles’ that we never see but which can spontaneously come into being and then, just as quickly, disappear back into the background.
If that sounds like voodoo…well, it kind of is. And anyone who seriously claims to understand quantum mechanics is either delusional or insufficiently educated in his own ignorance. However, the math of it works out in a way that very accurately describes observations and interactions at that level; in quantum electrodynamics, the behavior of charged particles and electromagnetic force carriers is described to a precision greater than any other prediction in all of the natural sciences, so if the theory is fundamentally wrong, it is at least wrong in a way that is still highly useful.
[thread=442637]Here[/thread], [thread=412580]here[/thread], and [thread=299054]here[/thread] are some old threads on this topic you may find of interest and/or entertainment.
Stranger