Exclusion Principle application to very large systems

[Xcellerator]

Hi,
I've had something that's been bothering me for a while and I've been researching it, but I just want to clear something up.
I understand that the exclusion principle dictates that fermionic particles with half-integer spin have an anti-symmetrical wavefunction under exchange, and therefore implies that no two fermions can have have the exact same quantum numbers.
I understand how this can apply to a single atom, in that each electron must be in a different quantum state (of n,l,m & s), but I do not understand how it can still apply to anything larger than a single atom.
If I had two hydrogen atoms, then the two innermost electron shells of one of them would have the same set of quantum numbers as the other one. Does the exclusion principle not apply to larger systems?
Also, if a wavefunction was computed of two hydrogen atoms then how can the two innermost electrons of each atoms NOT have the same quantum number.

I get the feeling I've either missed something tiny or something massive, so any response is greatly appreciated...

 

[Wolfgang2b]

The exclusion principle is not applicable just to a single atom. Let us say, you have 2 Hydrogen atoms with electrons in each of them in the 1s orbital. When you bring them together to form a bond, the 2 1s orbitals mix/hybridize into two energy levels named as bonding (sigma) and anti-bonding levels (sigma*). The bonding level has a lower energy state than 1s (thus favorable to bond) and anti-bonding has an higher energy than 1s. As per Pauli's exclusion principle, the bonding level can contain only 2 electrons with opposite spins.

So for H2 molecule, the bonding level is occupied with 2 electrons and the energy is less than the energy of 2 separate Hydrogen atoms. Hence bonding is favorable.

But now consider the scenario for Helium molecule. Having two electrons from each atom, and because of the exclusion principle, both the bonding and anti-bonding levels are occupied with electrons. The net result is that there is no energy gain by forming a molecule. Hence Helium doesn't form a molecule like Hydrogen.

Apart from this exclusion principle can be used to explain many things - band structure of materials, stability of neutron star etc...

You may refer this for more consequences
http://en.wikipedia.org/wiki/Pauli_exclusion_principle#Consequences