# Homework Help: Distribution of electrons below the Fermi energy

1. Dec 7, 2007

### 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.

1. The problem statement, all variables and given/known data
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

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

3. 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!

2. Dec 7, 2007

### 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?