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 a c.c.p length of the side of unit cell is related to radius r = `(sqrt2a)/(4)`
`a = (4r)/(sqrt2) = (4 xx 125)/(1.414) = 353.5 `pm
`therefore ` volume of unit cell `(a^3)`
` = (353 xx 10^(-10) )^3 cm^3 = 4.42 xx 10^(-23) cm^2`
Number of unit cell in `1cm^3`
` = (1)/(4.42 xx 10^(-23) ) = 2.26 xx 10^22`