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I was recently asked the question "Why are noble gases stable? with the expectation of providing an answer beyond the general explanation of "they have full valence layers" and I couldn't think of one.

I would love to hear a full description of the this stability, I have a solid background in quantum mechanics, so feel free to speak of wave functions or the like if necessary.

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Actually it is not necessary to dig deep into quantum mechanics. There are several reasons why noble gasses are stable (as gasses at room temperature).

First of all, there is the obvious full valence shell. Trend in the periodic table make clear that the charge of the nucleus grows from left to right in every period. The attractive force towards the electrons therefore increases. (This holds also from top to bottom.) Electrons in lower orbitals ($n<\text{period}$) now shield the charge of the nucleus. This will be somewhat the same throughout the period. (The orbitals also shrink due to higher charge of the nucleus.) In noble gasses the valence shell is completely filled, providing quite a good shield for the next shell. Also the increase in the main quantum number means a significant increase in the energy level of the next orbital. This makes it unlikely, that a noble gas will accept another electron.

Due to the high charge of the nucleus it is also not easy to remove an electron from an orbital. However, this is possible from (at least) Argon on downwards. For example: $\ce{HArF}$ is stable in a matrix at room temperature. It has a strong covalent $\sigma$ bond ($\ce{H\bond{-}Ar+}$) and a not quite as strong ionic bond ($\ce{[HAr]+\cdots F-}$). Krypton already does some fancy chemistry, that is stable at room temperature. As Uncle Al has pointed out Xenon is well known for its reactivity.

But why the sudden change? It is fairly intuitive, that the maximum electron density for each orbital with increasing main quantum number is also further away from the nucleus. That makes the valence shell very well polarizeable. Also the electrons are better shielded by the previous shells. However, the natural occurrence of these elements are as (homonuclear) gasses.

However, if you bring these elements in close contact with each other it was found out, that they have a very small dissociation energy ($D_e<1~\text{meV}$). This is due to dispersion, and van-der-Waals Forces, which is the main interaction between these elements. However, in $\ce{He2}$ no binding mode was observed (instant dissociation).

But that still does not answer, why those elements are stable as gasses, as pointed out that there are in fact attractive forces. The reason is as simple as obvious: Entropy. If two noble gasses would form a molecule/adduct, the bond/association energy of this molecule would have to compensate for the loss of entropy (Two volume elements would become one, hence the gas would have to expand to cover the room previously occupied, which requires work energy).

The explanation by tschoppi also covers, why from a MO point of view there could not be a bond in $\ce{He2}$. Go ahead and ask yourself the question if this would be true for $\ce{He3}$. We also know that orbital overlap is only one component to the truth. There are many other more. If it was not for such a nice thing like dispersion and other weak chemical interactions we would not exist.

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They are stable because the energy is lower. (Ah, the universal answer to every chemistry problem!)

Let me elaborate: If noble gases would occur as diatomic elements, the energy should be lower in comparison to their monoatomic form. But when you combine the atomic orbitals of the bonding partners to the molecular orbitals (MO-LCAO), you then fill in the electrons into all MOs, the bonding as well as the antibonding MOs.

Because antibonding orbitals are more antibonding than bonding orbitals bonding, the overall energy of the compound is raised. So this is a state which the system prefers to avoid, giving you monoatomic elements.

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http://chemistry.about.com/od/noblegasfacts/a/Noble-Gas-Compounds.htm
Noble gases are reactive. Following are some examples,
enter image description here

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  • $\begingroup$ I quote the website you link to: "Helium, neon, argon, krypton, xenon, radon have completed valence electron shells, so they are highly stable." They're not as reactive as, say, oxygen. You need high pressures to get these compounds. $\endgroup$ – tschoppi Mar 7 '14 at 16:47
  • $\begingroup$ Xenon difluoride forms from the elements at low pressure with UV light, J. Am. Chem. Soc., 184(23) 4612 (1962). Xe reacts with PtF6 like shot, on a vacuum line or at 77 kelvin in liquid SF6, doi:10.1016/S0010-8545(99)00190-3 $\endgroup$ – Uncle Al Mar 7 '14 at 20:16
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    $\begingroup$ It's certainly true that noble gas compounds aren't entirely inert, but it's also certainly true that they are very inert to most conditions. While informative, without context this answer is a bit misleading. $\endgroup$ – Nicolau Saker Neto Mar 7 '14 at 20:34
  • $\begingroup$ Wrap pipe thread with Teflon tape before screwing together. It seals better, prevents galling, and facilitates dismounting. If it is aluminum pipe, the taped joint often explodes. Look up the /_\H_f of anhydrous AlF3. All the fun is in the footnotes. $\endgroup$ – Uncle Al Mar 8 '14 at 16:42

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