Fermi Energy, Temp & Wave Vector Calc for Protons & ^3He

[Winzer]

Homework Statement

Calculate fermi energy, fermi temp and fermi wave vector.
a)Protons with n= 1.0E43 m^{-3}
b) ^{3}He in liquid He (atomic volume= 46E^-3 m^3

Homework Equations

E_f=\frac{h^2}{8 m} (\frac{3 n}{\pi V})^\frac{2}{3}
T_f= \frac{E_f}{k_B}

The Attempt at a Solution

I get the energy and temp.
Is the wave vector equation:
k=\sqrt{\frac{8 \pi^2 m E_F}{h^2}}?
for the last one \frac{n}{v}=\frac{3}{ 46E^{-3}}?

 

[nickjer]

You remember E=\frac{\hbar^2 k^2}{2m}. So just replace the energy and wavevector with the Fermi variables, so you are left with:

E_F=\frac{\hbar^2 k_F^2}{2m}

For part (b) check the units on the atomic volume. Is it per mole?

 

[Winzer]

Not sure. It says ^{3}He atoms in liquid ^{3}He. So it should be n=3(3fermions) and V=46E-30 m^3. I think that sounds right.