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

Step I. Calculation of length of side of the unit cell
For f.c.c. unit cell, `a=2sqrt2r=2sqrt2(125"pm")=2xx1.4142xx(124"pm")=354"pm"`.
Step II. Calculation of no. of unit cells in `1.00cm^(3)` of aluminium.
Volume of one unit cell = `(354"pm")^(3)=(354xx10^(-10)cm)^(3)=44174155xx10^(-30)"cc"`.
No. of unit cells in 1.00 cc of Al metal = `(1("cc"))/(44174155xx10^(-30)("cc"))=2.26xx10^(22)`