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 = MVmol 


d = density (g.m-3)

M = mass molar (g.mol-1)

Vmol = molar volume (m3.mol-1)

 

Vmol = Vunit cellN 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 = MVmol

 ⇒ Vmol = Md 

⇒ Vunit cell = M × Nd × NA

 

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

⇒ Vunit cell63.55 × 48.96 × 106 × 6.022 × 1023

⇒ 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 = L2 = 4 x crystallographic radii (r)

⇒ r = L22 = 128 pm