Question:
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 aluminium?
Solution:
(i) For cubic close-packed structure:
$a=2 \sqrt{2} r$
$=2 \sqrt{2} \times 125 \mathrm{pm}$
= 353.55 pm
= 354 pm (approximately)
(ii) Volume of one unit cell = (354 pm)3
= 4.4 × 107 pm3
= 4.4 × 107 × 10−30 cm3
= 4.4 × 10−23 cm3
Therefore, number of unit cells in $1.00 \mathrm{~cm}^{3}=\frac{1.00 \mathrm{~cm}^{3}}{4.4 \times 10^{-23} \mathrm{~cm}^{3}}$
= 2.27 × 1022
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