Distribution of electrons below the Fermi energy

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SUMMARY

The discussion centers on calculating the percentage of electrons below the Fermi energy (Ef) at a temperature of 300K, with Ef set at 5eV. The user initially estimated that approximately 30% of electrons lie within KbT (0.0259 eV) below Ef, but the correct answer is 0.566%, as indicated in the textbook. The discrepancy arises from the integration boundaries used in the Fermi function, which must be correctly defined to yield accurate results.

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taishar
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I feel dumb that I can't figure this out. I'm sure its something simple that I'm just not seeing, but its really frustrating.

Homework Statement


How many electrons (in percent of the total number of electrons per mole) lie KbT (ev) below the Fermi energy? Take Ef=5eV and T=300K

Homework Equations


Not quite sure, since the Fermi function did not work.


The Attempt at a Solution


I tried using the Fermi function and end up with values around 30%. The answer (from the back of the book) is [tex]\Delta[/tex]N/Ntot=.566%

Any ideas ?

Thanks!
 
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Since Ef is much larger than kT, you wouldn't expect 30% of the electrons to lie between Ef-kT and Ef, right? You'd expect a much smaller fraction, like the answer from the book.

When you integrated the Fermi function to get [tex]\Delta[/tex]N and Ntot, what were the energy boundaries of your integrals?
 

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