# Calculating The Fermi Energy - Condensed Matter Physics

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1. Feb 3, 2015

### 12x4

1. The problem statement, all variables and given/known data
Calculate the Fermi energy, EF at 0K for potassium (atomic weight = 39, density = 860 kgm3).

2. Relevant equations
KF3 = 3π2n
Fermi Momentum ρ = h(bar)KF

3. The attempt at a solution:
For the first part:

Using: E = ρ2/ 2m
Can substitute Fermi momentum into that to get:

EF = h(bar)2 KF2 / 2m

KF2 = √(3π2n) = π√(3n)

Putting all the together I got:

EF = h(bar)2 π √(3n) / 2m

which is the same as: EF = h2 √(3n) / 4m

I'm not too sure what to do after this point as i'm not sure how the atomic weight or density can give me a value for n and m. I do have written in my notes that n = N/v but again I wasn't sure how this would help me. I feel like I must be going down the wrong path to come out with an equation that needs completely different things to what the question is providing me with. But honestly I have just started this condensed matter course and haven't really got my feet yet.

Thanks in advance to anyone that replies.

2. Feb 3, 2015

### TSny

You haven't solved for KF2 correctly. What do you get if you first solve for KF?
n is the number of atoms per unit volume, whereas mass density ρ is the mass per unit volume. Try to think of a way to relate n to ρ using the atomic mass, matom.

3. Feb 5, 2015

### 12x4

Ooops yes not sure what i was thinking there. Thank you for your help i think i've cracked it now.