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.