Copper crystallises into a fcc lattice with edge length $3.61\times10^{-8}$ cm. Show that the calculated density is in agreement with its measured value of 8.92 g cm$^{-3}$.

Copper crystallises into a fcc lattice with edge length 3.61×10⁻⁸ cm. Show that the calculated density is in a

Exercises · 1.15

3.61\times10^{-8}

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Step 1 – Data.

fcc $\Rightarrow z = 4$ ; molar mass of copper $M = 63.5$ g mol $^{-1}$ ; $a = 3.61\times10^{-8}$ cm.

Step 2 – Cell volume.

a^3 = (3.61\times10^{-8})^3 = 4.70\times10^{-23}\text{ cm}^3

Step 3 – Density.

d = \frac{zM}{a^3 N_A} = \frac{4\times 63.5}{4.70\times10^{-23}\times 6.022\times10^{23}}

d = \frac{254}{28.33} = 8.97\text{ g cm}^{-3}

Step 4 – Compare. …