# Exercise 8 | Liquids and Solids

Copper has a face-centered cubic lattice and a density of 8.96 g.cm-3.

What is the crystallographic radius of a copper atom?

d = $\frac{\mathrm{M}}{{\mathrm{V}}_{\mathrm{mol}}}$

d = density (g.m-3)

M = mass molar (g.mol-1)

Vmol = molar volume (m3.mol-1)

Vmol =  x NA

Vunit cell = unit cell volume (in m3)

N = number of atoms in a unit cell

NA = Avogadro’s number = 6.022 x 1023 mol-1

⇒ d = $\frac{\mathrm{M}}{{\mathrm{V}}_{\mathrm{mol}}}$

⇒ Vmol = $\frac{\mathrm{M}}{\mathrm{d}}$

⇒ Vunit cell =

Face-centered cubic lattice: 4 atoms per unit cell ⇒ N = 4

⇒ Vunit cell

⇒ Vunit cell = 4.71 x 10-29 m3

If L = length of the edge

⇒ Vunit cell = L3

⇒ L = 3.61 x 10-10 m = 361 pm

Face-centered cubic lattice:

length of a diagonal of a face = L$\sqrt{2}$ = 4 x crystallographic radii (r)

⇒ r = $\frac{\mathrm{L}}{2\sqrt{2}}$ = 128 pm