Radius per conduction electron

Band Structure for the Free-Electron Case. If the electron is free, then the Bloch functions are simple plane waves, because the wavef unctions nk(r) used for the expansion Eq. (8.4.2) are themselves plane waves. For an electron gas with no lattice and no imposed symmetry, Fermi-Dirac statistics apply At 0 K all electrons pair up (spin-up and spin-down), with an occupancy of 2 for every k value from k 0 to the Fermi wavevector kF =1.92/rs = 3.63 a0/rs, and from zero energy up to the Fermi energy eF = h2kF2 /rn 50.1 eV rs/a0) 2, where rs is the radius per conduction electron and a0 is the Bohr radius, and the energy levels are spherically symmetric in k-space. The Fermi surface is a sphere of radius kF. Note that the ratio (rs/a0) varies from 0.2 to 1.0 nm for metals (Table 8.3). 

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