Question

Copper crystallizes with a face-centered cubic lattice and has a density of 8.93 g/cm3.

a.) Calculate the mass of one unit cell of copper (in grams) b.) Calculate the volume of the copper unit cell (in cm3). c.) Calculate the edge length of the unit cell (in cm). d.) Calculate the radius of a copper atom (in pm).

Answer 1

Part a

Atomic mass of unit cell = Z x M / NA

Z = Number of atoms in fcc lattice = 4 atoms

M = molecular weight = 63.5 g/mol

NA = Avogadro number = 6.023 x 10^23 atoms/mol

= (4 atoms x 63.5 g/mol) / (6.023 x 10^23 atoms/mol)

= 4.22 x 10^-22 g

Part b

Density =Mass of unit cell/Volume of unit cell

8.93 g/cm3 = (4.22 x 10^-22 g) / V

V = 4.725 x 10^-23 cm3

Part c

Density = Mass of unit cell/Volume of unit cell

8.93 g/cm3 = (4 atoms x 63.5 g/mol)/(a^3 x 6.02 x 10^23 atoms/mol)

a^3 = 4.722 x 10^-23 cm3

a = 3.614 x 10^-8 cm x 10^10pm/cm

Edge length = 361 pm

Part d

For FCC lattice

a =   x R

R = 361 pm /

Radius R = 127.63 pm