The density and molar mass of sodium are and , respectively. We have to find (a) the fraction of the volume of the metallic sodium available to its conduction electrons. (b) We have to carry out the same calculation for copper. Its density, molar mass, and ionic radius are, respectively, , , and 96 pm. (c) We have to answer in which of these two metals conduction electrons behave more like a free electron gas.

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(a)

From the density and molar mass of sodium we calculate the number density of sodium atoms per unit volume. It is given by the equation

As each atom of sodium contributes one conduction electron, is also the number density of conduction electrons per cubic meter in the sodium metal.

It is given that the radius of a ion is 98 pm. The total volume occupied by ions in a meter cube of metallic sodium will therefore be

Therefore, in 1 cubic mete of metallic sodium the volume available for conduction electrons will be , which is 0.9 times the total volume.

(b)

We do a similar calculation for copper.

As each atom of copper contributes one conduction electron, is also the number density of conduction electrons per cubic meter in the copper metal.

It is given that the radius of a ion is 96 pm. The total volume occupied by ions in a meter cube of metallic copper will therefore be

Therefore, the fraction of the volume of metallic copper available to its conduction electrons is .

(c)

From these results we conclude that in metallic sodium conduction electrons will behave more like a free electron gas than the conduction electrons of metallic copper.