Question:
Copper crystallises into a fcc lattice with edge length 3.61 × 10−8 cm. Show that the calculated density is in agreement with its measured value of 8.92 g cm−3.
Solution:
Edge length, a = 3.61 × 10−8 cm
As the lattice is fcc type, the number of atoms per unit cell, z = 4
Atomic mass, M = 63.5 g mol−1
We also know that, NA = 6.022 × 1023 mol−1
Applying the relation:
$d=\frac{z \mathrm{M}}{a^{3} \mathrm{~N}_{\mathrm{A}}}$
$=\frac{4 \times 63.5 \mathrm{~g} \mathrm{~mol}^{-1}}{\left(3.61 \times 10^{-8} \mathrm{~cm}\right)^{3} \times 6.022 \times 10^{23} \mathrm{~mol}^{-1}}$
= 8.97 g cm−3
The measured value of density is given as 8.92 g cm−3. Hence, the calculated density 8.97 g cm−3 is in agreement with its measured value.