Aluminium crystallizes in an fcc structure. Atomic radius of the metal is 125 pm.
How many such unit cells are there in 1 `m^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=(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 cell in `1cm^3=1/(4.42xx10^(-23))`
`=2.26xx10^22` unit cells