Question

Show if lead is an FCC or a BCC crystal structure.

Lead (Pb) has an atomic radius of 0.175 nm and a density of 11.35 g/cm3 . Use this information to determine whether it has an FCC or a BCC crystal structure.

Please also provide the correct units.

Answer 1

We know density , d = (Z x atomic mass) / ( No x a³ x 10^-30 cm³ )   

Where Z = No . of atoms in a unit cell = ?

           atomic mass of lead = 207.2 g

           N_o = avagadro number = 6.023x10²³

           a = edge length = in pm

For fcc arrangement radius , r = (√2 / 4 ) a

a = 4r / √2 radius = r = 0.175 nm = 175 pm

= 495 pm

Plug these values in (1) we get

Z = d x No x a³ x 10^-30 cm³ / atomic mass

= 4

Since the number of atoms in a unit cell = 4 so it is an FCC structure