Fermi Energy of Liquid He3

atomicpedals

1. The problem statement, all variables and given/known data

The atom [itex]He^3[/itex] has spin 1/2 and is a fermion. The density of liquid [itex]He^3[/itex] is [itex]0.081g/cm^3[/itex] near absolute zero. Calculate the Fermi energy [itex]\epsilon_F[/itex] and the Fermi temperature [itex]T_F[/itex]

2. Relevant equations

[itex]\epsilon_F = \frac{\hbar^2}{2m}(\frac{3 \pi^2 N}{V})^{2/3}[/itex]

[itex]T_F = \frac{\epsilon_F}{k}[/itex]

3. The attempt at a solution

In the problem I'm given the density is [itex]0.081g/cm^3[/itex], which is my N/V. Assuming that m is the mass of [itex]He^3[/itex], then [itex]m = 5.008*10^{-24}g[/itex]. I should then be able to do a straight forward plug-n-chug; however my units don't work out as I get:

[itex]\epsilon_F = \frac{\hbar^2}{1.0016*10^{-23}g}(3 \pi^2 0.081g cm^{-3})^{2/3}=1.99*10^{-50} kg^{5/3} m^2 s^{-2}[/itex]

Clearly, this is not a unit of energy. What am I doing wrong?

atomicpedals

I need to use number density, rather than straight density. Which should take care of my problem.