# Relation between no. of electrons in a small enery interval at vacuum and fermi level

1. Oct 17, 2012

### magnusse

I posted this in the math forum by mistake, so posting it here now instead

1. The problem statement, all variables and given/known data
The cutoff frequency for the photoelectric effect for silver is 1.089*10^15 Hz and its Fermienergy at T = 0 degrees Celsius is 5.5 eV.

Calculate the relation between the number of electrons in a very small energyinterval at vakuumlevel (that is, the energylevel at which electrons are "freed" from the metal) and a small interval att the Fermilevel.
Assume T = 0 degrees Celsius.

2. Relevant equations
I THINK theses are the relevant equations.

Fermi-dirac distribution
f(E) = 1 / (e(E-EF)/(kT)+1)

(density of states, free-electron model)
g(E) =((2m)3/2 * V) / (2*Pi2*(h/2*pi)3) * E1/2

V = L^3 (L = length of cubic "box")
￼￼￼￼￼￼￼￼￼￼￼￼￼￼￼

3. The attempt at a solution

I know that because the intervals are small, there should be some way to use the derivate to find what I'm seeking. And I think I need to combine the two equations i wrote earlier.

But I'm stuck and now time is running out. I would really appreciate some help.

Sorry for my english, it's not my native language.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution