First slide

Crystal lattices and unit cells

Question

A crystalline solid of a pure substance has a face centred cubic structure with a cell edge of 400 pm. If the density of the substance in the crystal is 8 g cm^-3, then the number of atoms present in 256 g of the crystal is N × 10²⁴. The value of N is:

Moderate

Solution

$\begin{array}{l} d = \frac{Z \times M}{N_{A} \times a^{3}} \\ 8 = \frac{4 \times M}{6 .022 \times 10^{22} \times {(400 \times 10^{- 10})}^{3}} \\ M = 76 .8 g {mol}^{- 1} \\ 76 .8 g contain = 6 \times 10^{23} atoms \\ ∴ 256 g will contain = 20 \times 10^{23} atoms = 2 \times 10^{24} atoms \\ ∴ N = 2 \end{array}$

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