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 `1.00cm^(3)` of aluminium?

Explanation

(i) A ccp structure has fcc unit cell. In case of fcc unit cell, the relation between the radius ( r) of atoms and the edge-length (a) of unit cell is `r=a/(2sqrt2)`
Given : r = 125 pm
`therefore" "a=2sqrt2xx125`pm = 353.5 pm
(ii) Volume of each unit cell = `a^(3)=(353.5xx10^(-10)cm)^(3)`
`=4.42xx10^(-23)cm^(3)`
`therefore" "` Number of unit cells in `1.00cm^(3)` of aluminium
`1/(4.42xx10^(-23))=2.26xx10^(22)`