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I understand (to a degree) Pauli's exclusion principle in terms of electrons in an atom but I'm a little confused about the scales involved with free electrons, say electron gasses in metals......

My text book gives an example:

"consider a 1cm cube of copper at room temperature. The number of free electronsNcan be found from Table 1.3 to beN=nV= 8.45 × 10^{28}m^{−3}× 10^{−6}m = 8.45 × 10^{22}. The total number of quantum states up to energykT, (found by using the density of statesDe(E)in a definite integral) has the value 2 × 10^{19}. You can see that this number of states can accommodate only about 0.02% of the free electrons. The rest have to pile up into states of higher energy, a long way abovekT. If we ask how far up the energy scale we have to go to accommodate all the free electrons, we obtain the amazing answer of about 7 eV. This is about 300kTat room temperature."

1cm is quite large compared to the de Broglie wavelength of an electron soLdoesn't appear to make much difference here. To take it to an extreme, if I regard the hull of a battleship as a block of iron, the surfaces of which contain an electron gas, does the quantum state of an electron in the bow forbid an electron in the stern from having that state? Also, it would seem that with a big enough sample, some electrons would have to occupy unimaginably high states.

I suspect that separationisrelevant to exclusion but I can't seem to find a rule, or I have fundamentally misunderstood the whole thing.......

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# Exclusion principle in quantum gasses

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