Aluminium crystallizes in a cubic close packed structure. Its metallic radius is 125 pm.
(a) What is the length of side of 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=(sqrt(2)a)/(4)`
`a=(4r)/(sqrt(2))=(4xx125)/(1.414)=353.5` pm
`therefore` Volume of unit cell `= a^(3)=(353.3xx10^(-10))^(3)cm^(3)=4.42xx10^(-23)cm^(3)`
Number of unit cells in `1cm^(3)=(1)/(4.42xx10^(-23))=2.26xx10^(22)` unit cells.