Aluminium crystallises in a cubic close-packed structure. Its metallic radius is 125 \mathrm{pm}.
Aluminium crystallises in a cubic close-packed structure. Its metallic radius is 125 \mathrm{pm}.

(i) What is the length of the side of the unit cell?
Ans: For cubic close-packed structure:

    \[\begin{array}{l} \mathrm{a}=2 \sqrt{2} \mathrm{r} \\ \Rightarrow 2 \sqrt{2}=125 \mathrm{pm} \\ =353.55 \mathrm{pm} \end{array}\]

Hence, the length of the side of the unit cell is 354 pm (approximately).
(ii) How many unit cells are there in 1.00 \mathrm{~cm}^{3} of aluminium?
Ans: Volume of one unit cell =(354 \mathrm{pm})^{3}

    \[\begin{array}{l} =4.4 \times 10^{7} \mathrm{pm}^{3} \\ =4.4 \times 10^{7} \times 10^{-30} \mathrm{~cm}^{3} \\ =4.4 \times 10^{-23} \mathrm{~cm}^{3} \end{array}\]

Therefore, number of unit cells in 1.00 \mathrm{~cm}^{3}=\frac{1.00 \mathrm{~cm}^{3}}{4.4 \times 10^{-2} \mathrm{~cm}^{-3}}=2.27 \times 10^{22}