The electrons that support a white dwarf star against gravity behave

PHYSICS · Subjective · Fermi University Physics · Thermal, Statistical & Complex Systems · Condensed Matter, Materials & Soft Matter · Free electrons, energy bands and electronic structure

Condensed Matter Physics, Ch The free-electron gas: what Drude gets right and what only Fermi fixes

Problem

The electrons that support a white dwarf star against gravity behave, to a first approximation, like the free-electron gas of this chapter, but at an electron density around n=1.0×1036 m−3n=1.0\times10^{36}\,\mathrm{m^{-3}}, some 10710^7 times copper's. Using the formulas of Section 8.5, estimate these electrons' Fermi wavevector, Fermi energy (in MeV) and Fermi velocity. Then check whether the assumption behind E=ℏ2k2/2mE=\hbar^2k^2/2m, that the electrons move much slower than light, still holds, and say what that means for trusting the numbers you have just computed.

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