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## Homework Statement

Calculate the Fermi energy, E

_{F}at 0K for potassium (atomic weight = 39, density = 860 kgm3).

## Homework Equations

K

_{F}

^{3}= 3π

^{2}n

Fermi Momentum ρ = h(bar)K

_{F}

## The Attempt at a Solution

:[/B]For the first part:

Using: E = ρ

^{2}/ 2m

Can substitute Fermi momentum into that to get:

E

_{F}= h(bar)

^{2}K

_{F}

^{2}/ 2m

K

_{F}

^{2}= √(3π

^{2}n) = π√(3n)

Putting all the together I got:

E

_{F}= h(bar)

^{2}π √(3n) / 2m

which is the same as: E

_{F}= h

^{2}√(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.