Question

Copper crystallizes in a face-centered cubic lattice (the Cu atoms are at the lattice points and at the face centers). If the density of the metal is 8.96 g/cm3, what is the unit cell edge length in pm? × 10 pm

Answer 1

Answer:

The unit cell edge lenght in pm is equal to 361 pm

Explanation:

Data provided:

ρ=Copper density=8.96 g/cm3

Atomic mass of copper=63.54 g/mol

Atoms/cell=4 atoms (in theory)

Avogadro's number=6.02x$10^{23}$ atoms/mol

Since copper has a cubic structure, its cell volume is equal to $a^{3}$, which can be obtained through the relationship:

cell volume=$\frac{(atoms/cell)(atomic mass)}{(density)(Avogadros number)}$

Substituting the values:

cell volume=$\frac{(4 atoms)(63.54 g/mol)}{(8.96 g/cm3)(6.02x10^{23}) }=4.71x10^{-23}cm^{3}$

clearing, we have:

a=$\sqrt[3]{4.71x10^{-23}cm^{3} }=3.61x10^{-8}cm$

We convert from centimeter to picometer, 1cm=1x$10^{10}$pm

a=$3.61x10^{-8}cmx\frac{1x10^{10}pm }{1cm} =361 pm$