Distribution of electrons below the Fermi energy

[taishar]

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 $$\Delta$$N/Ntot=.566%

Any ideas ?

Thanks!

 

[2Tesla]

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 $$\Delta$$N and Ntot, what were the energy boundaries of your integrals?