Silver has conduction electron density , Fermi velocity

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

Silver has conduction electron density n=5.87×1028 m−3n=5.87\times10^{28}\,\mathrm{m^{-3}}, Fermi velocity vF=1.39×106 m s−1v_F=1.39\times10^6\,\mathrm{m\,s^{-1}}, and at 295 K295\,\mathrm{K} a resistivity ρe=1.59×10−8 Ω m\rho_e=1.59\times10^{-8}\,\Omega\,\mathrm{m}, giving τ=3.80×10−14 s\tau=3.80\times10^{-14}\,\mathrm{s}. A student estimates silver's electronic mean free path using the classical thermal speed, vth=3kBT/m=1.16×105 m s−1v_{\rm th}=\sqrt{3k_BT/m}=1.16\times10^5\,\mathrm{m\,s^{-1}} at 295 K295\,\mathrm{K}, getting ℓ=vthτ=4.40 nm\ell=v_{\rm th}\tau=4.40\,\mathrm{nm}, about 15 nearest-neighbour spacings of 2.889 A˚2.889\,\mathrm{\mathring{A}}, and concludes that this is "a reasonable picture of an electron bouncing off about every fifteenth ion." Find the error, correct the calculation, and say whether the corrected picture still supports the "bouncing off ions" description.

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