A low-temperature resistivity measurement on three copper samples of different purity…

PHYSICS · Subjective · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Free electrons, energy bands and electronic structure · Electronic transport in solids

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

Problem

A low-temperature resistivity measurement on three copper samples of different purity gives residual resistivities (the temperature-independent part that survives at

4\,\mathrm{K}

) of

\rho_0=1.0\times10^{-10}

3.0\times10^{-10}

and

1.5\times10^{-9}\,\Omega\,\mathrm{m}

for samples A, B and C. Using copper's

n=8.47\times10^{28}\,\mathrm{m^{-3}}

and

v_F=1.57\times10^6\,\mathrm{m\,s^{-1}}

, find the electronic mean free path of each sample at

4\,\mathrm{K}

, in micrometres. Which sample is purest, and how do you know?

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