Aluminium crystallises in a cubic close-packed structure. Its metallic radius is 125 pm. (i) What is the length of the side of the unit cell? (ii) How many unit cells are there in 1.00 cm3 of aluminium?

For the cubic close–packed structure
Let a is the edge of the cube and r is the radius of atom
Given that r = 125 pm
a = 2√2 r
plug the value of r we get
= 2 x 1.414 x125 pm
= 354 pm (approximately)
<>(ii) = (354 pm)3
1 pm = 10–10 cm
= (354 x 10–10 cm)3
= (3.54 x 10–8 cm)3
= 44.36 x 10–24 cm3
= 4.4 × 10−23 cm3
Total number of unit cells in 1.00 cm3
= total volume / size of each cell
= (1.00cm3)/( 4.4 × 10−23 cm3)
= 2.27 × 10^22 unit cell