# Fermi Energy of Liquid He3

by atomicpedals
Tags: energy, fermi, liquid
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 P: 196 1. The problem statement, all variables and given/known data The atom $He^3$ has spin 1/2 and is a fermion. The density of liquid $He^3$ is $0.081g/cm^3$ near absolute zero. Calculate the Fermi energy $\epsilon_F$ and the Fermi temperature $T_F$ 2. Relevant equations $\epsilon_F = \frac{\hbar^2}{2m}(\frac{3 \pi^2 N}{V})^{2/3}$ $T_F = \frac{\epsilon_F}{k}$ 3. The attempt at a solution In the problem I'm given the density is $0.081g/cm^3$, which is my N/V. Assuming that m is the mass of $He^3$, then $m = 5.008*10^{-24}g$. I should then be able to do a straight forward plug-n-chug; however my units don't work out as I get: $\epsilon_F = \frac{\hbar^2}{1.0016*10^{-23}g}(3 \pi^2 0.081g cm^{-3})^{2/3}=1.99*10^{-50} kg^{5/3} m^2 s^{-2}$ Clearly, this is not a unit of energy. What am I doing wrong?
 P: 196 I need to use number density, rather than straight density. Which should take care of my problem.

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