Aluminium Crystallises in a Cubic Close–packed Structure. Its Met Exercise Chapter 1 the Solid State Chemistry Class

Question 24: Aluminium crystallises in a cubic close–packed structure. Its metallic radius is 125 pm.
(i) What is the length of the side of the unit cell?
(ii) How many unit cells are there in 1.00 cm³ of aluminum?

Answer
For the cubic close–packed structure Let a is the edge of the cube and r is the radius of atom
Given that r = 125 pm
               a = 2√2 r
Plug the value of r we get
                  = 2 x 1.414 x125 pm
                  = 354 pm (approximately)
Volume of one unit cell = side³ = (354 pm)³
                          1 pm = 10^–10 cm
                                  = (354 x 10^–10 cm)³
                                  = (3.54 x 10^–8 cm)³
                                  = 44.36 x 10^–24 cm³
                                  = 4.4 × 10⁻²³ cm³
Total number of unit cells in 1.00 cm³
                                  = total volume / size of each cell
                                  =  (1.00cm³)/( 4.4 × 10⁻²³ cm³)
                                  = 2.27 × 1022 unit cell