Question

# Show if lead is an FCC or a BCC crystal structure. Lead (Pb) has an atomic...

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.

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

No = 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

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