Fermi energy/temperature

AriAstronomer
Posts: 76
Joined: Thu May 12, 2011 4:53 pm

Fermi energy/temperature

Postby AriAstronomer » Fri Oct 07, 2011 5:32 pm

Hey everyone,
So unfortunately I haven't taken Stat Mech yet, but through casual reading and forums I've gathered what the concept of fermi temperature and energy is...or thought I did. From what I understand, below the fermi energy (the fermi energy within an atom corresponding to some highest orbital) all orbitals below it are completely filled, and all orbitals above it are completely empty. I assumed however, that this happens at the fermi temperature, which I thought was going to be close to T=0K, but apparently for most elements is like 10,000K? What gives? Also, what's this about below the fermi temperature things get degenerate (as in, more than one electron configuration corresponding to the same energy), but above there is no degeneracy? I was under the impression that at fermi temperature (which I thought was close to 0Kelvin), all electrons fill the lowest possible orbitals without violating the Pauli Exclusion Principle, and then as you raise temperature as things get more energy they gain more freedom and thus degeneracy starts....

The GRE is in a week, any chance someone can resolve this for me?!! I'd really appreciate it!

Ari

The_Duck
Posts: 41
Joined: Tue Nov 16, 2010 12:04 pm

Re: Fermi energy/temperature

Postby The_Duck » Sat Oct 08, 2011 1:00 pm

At absolute zero, all energy levels below the Fermi energy are filled, and all levels below it are empty. At nonzero temperature, some electrons will be excited to energy levels above the Fermi energy, and there will correspondingly be some empty levels below the Fermi energy. The Fermi temperature is the temperature at which the typical electron has a thermal energy equal to the Fermi energy, meaning that the typical electron is reasonably likely to be excited above the Fermi level. Far above the Fermi temperature, the effects of the exclusion principle are not important because the electrons are not all packed into the low energy states. Far below the Fermi temperature, the electrons are mostly in the low energy states and the exclusion principle dominates; here the "Fermi gas" is said to be "degenerate." This is a different meaning from the use of degeneracy to refer to multiple energy eigenstates having the same energy. The fact that the Fermi temperature for a typical metal is far above room temperature indicates that most of the electrons are sitting in the low energy states, and only a relatively small fraction of the electrons are in excited states.

AriAstronomer
Posts: 76
Joined: Thu May 12, 2011 4:53 pm

Re: Fermi energy/temperature

Postby AriAstronomer » Sat Oct 08, 2011 6:18 pm

Thanks for the speedy reply. So my last question is then, this new meaning of 'degenerate' by definition means 'when the exclusion principle becomes "sufficiently" important'?? Is there a rigid definition for this new meaning of degenerate?


Ari




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