Assume that the total volume of a metal sample is the sum of the volume occupied by the metal ions making up the lattice and the (separate) volume occupied by the conduction electrons. The density and molar mass of sodium (a metal) are 97l kg/m³ and 23.0 g/mol, respectively; assume the radius of the Na⁺ ion is 98.0 pm. 

(a) What percent of the volume of a sample of metallic sodium is occupied by its conduction electrons? 

(b) Carry out the same calculation for copper, which has density, molar mass, and ionic radius of 8960 kg/m³, 63.5 g/mol, and 135 pm, respectively. 

(c) For which of these metals do you think the conduction electrons behave more like a free-electron gas?