# A measure of the density of the free-electron gas in a metal is the distance rs, which is defined as the radius of the sphere whose volume equals the volume per conduction electron. (a) Show that rs = (3/4n)1/3, where

A measure of the density of the free-electron gas in a metal is the distance rs, which is defined as the radius of the sphere whose volume equals the volume per conduction electron.

(a) Show that rs = (3/4πn)1/3, where n is the free-electron number density.

(b) Calculate rs for copper in nanometers.

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