X-ray diffraction studies show that copper crystallises in an fcc unit cell with cell edge of $3.608\times10^{-8}$ cm. In a separate experiment, copper is determined to have a density of 8.92 g/cm$^3$, calculate the atomic mass of copper.

X-ray diffraction studies show that copper crystallises in an fcc unit cell with cell edge of 3.608×10⁻⁸ cm. I

Worked Examples · Example 1.4

3.608\times10^{-8}

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Step 1 – Density relation.

d = \frac{zM}{a^3 N_A}\ \Rightarrow\ M = \frac{d\,a^3 N_A}{z}

For an fcc unit cell $z = 4$ .

Step 2 – Cell volume.

a^3 = (3.608\times10^{-8})^3 = 4.697\times10^{-23}\text{ cm}^3

Step 3 – Substitute.

$M = \frac{8.92\times 4.697\times10^{-23}\times 6.022\times10^{23}}{4}$ …