Calculating The Fermi Energy - Condensed Matter Physics

[12x4]

Homework Statement

Calculate the Fermi energy, E_F at 0K for potassium (atomic weight = 39, density = 860 kgm3).

Homework Equations

K_F³ = 3π²n
Fermi Momentum ρ = h(bar)K_F

The Attempt at a Solution

:[/B]
For the first part:

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

E_F = h(bar)² K_F² / 2m

K_F² = √(3π²n) = π√(3n)

Putting all the together I got:

E_F = h(bar)² π √(3n) / 2m

which is the same as: E_F = 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.

 

[TSny]

K_F³ = 3π²n

K_F² = √(3π²n) = π√(3n)

You haven't solved for K_F² correctly. What do you get if you first solve for K_F?

... 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.

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, m_atom.

 

[12x4]

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