Helium-3 is fermion with spin 1/2 (unlike the more common isotope helium-4 which is a boson). At low temperatures (T << T_F) , helium-3 can be treated as a Fermi gas (Section 5.3.1). Given a density of 82 kg/m³, calculate T_F (Problem 5.21(c)) for helium-3.

Problem 5.21(c)

(c) At what temperature would the characteristic thermal energy (k_B T , where k_B is the Boltzmann constant and T is the Kelvin temperature) equal the Fermi energy, for copper? This is called the Fermi temperature, T_F . As long as the actual temperature is substantially below the Fermi temperature, the material can be regarded as “cold,” with most of the electrons in the lowest accessible state. Since the melting point of copper is 1356 K, solid copper is always cold.