Aluminium crystallises in a cubic close-packed structure. Its metallic radius is 125 pm.
(a) What is the length of the side of the unit cell? (b) How many unit cells are there in 1.00 `cm^(3)` of aluminium?

Explanation

For fcc structure, radius of atom `=("edge length")/(2sqrt2)`
Edge length `=125xx2sqrt(2)=354"pm"`
Volume of unit cell `=a^(3)=(354xx10^(-12))^(3)m^(3)=4.436xx10^(-29)m^(3)=4.436xx10^(-23)cm^(3)`
No. of unit cell in 1 `cm^(3)=(1)/(4.436xx10^(-23))=2.25xx10^(22)` unit cell.