Aluminium crystallizes 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 cell are there in `1.00 cm^(3)` of aluminium?

Explanation

Aluminum crystallizes in a cubic closed-packed form, which is a given.
The metallic radius of this object is 125 pm.

(i) For cubic close-packed structure
`"a"=2sqrt 2x=2sqrt 2 xx125=354"pm"`
Here, a is the edge length of the unit cells and r is the atomic radius.

(ii) Volume of one unit cell
`=a^3=(354"pm")^3=4.4xx10^-23"cm"^3`
`(1"pm"=10^-10"cm")`
Number of unit cells in`1.00cm_3=frac{1.00cm^3}{4.4xx10^-23"cm"^3}=2.27xx10^22`