Question

Copper crystal has a face centred cubic structure. Atomic radius of copper atom is 128 pm. What is the density of copper metal? Atomic mass of copper is 63.5.

Answer 1

In face centred cubic arrangement, face diagonal is four times the radius of atoms face
diagonal = $4\times 128=512pm$
Face diagonal = $\sqrt{2}\times$ edge length
Edge length =$\frac{512}{\sqrt{2}}=362\times {10}^{-10}cm$
Volume of the unit cell =$(362\times {10}^{-10}{)}^{3}c{m}^3=47.4\times {10}^{-24}c{m}^3$
In a face centred cubic unit cell, there are four atoms per unit cell
Mass of unit cell =$4\times \frac{63.5}{6.023\times {10}^{23}}g=4.22\times {10}^{-22}g$
Density =$\frac{massofunitcell}{volumeofunitcell}=\frac{4.22\times {10}^{-22}}{47.4\times {10}^{-24}}=8.9gc{m}^{-3}$