Aluminium crystallizes in a cubic close-packed structre. Its metallic radius is `125 ppm`
a. What is the length of the side of the unit cell?
b. How many unit cell are there in `1.00 cm^(3)` of aluminium?

Explanation

For `f.c.c.` structure,
radius of atom `=("Edge length") /(2sqrt(2))`
`:.` Edge length `=125xx2sqrt(2)=354pm`
Volume of unit cell `=a^(3)`
`=(354xx10^(-12))^(3)m^(3)`
`=4.436xx10^(-29)m^(3)`
`=4.436xx10^(-23)cm^(3)`
`:.` No . of unit cell in `1 cm^(3)`
`=(1)/(4.436xx10^(-23))`
`=2.25xx10^(22)`unit cell