Copper which crystallizes as a face – centred cubic lattice has a density of 8.93g/cm3 at 20o C. calculate the length of the unit cell.

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Solution

Cu has a FCC structure , so the value of Z = 4.
Molar mass of Cu = 63.5 g
Density = 8.93 g cm^-3
$Volume of unit cell = \frac{Molar mass×Z}{{Density×N}_{A}} Volume = \frac{63.5 \times 4}{8.93 \times 6.022 \times 10^{23}} = 1.1808 \times 10^{- 23} {cm}^{3} {Volume = a}^{3} = 2.277 \times 10^{- 8} {cm}^{3} a = 2.277 \times 10^{- 8} cm = 227.7 pm$

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