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Copper crystallises into a fcc lattice with edge length 3.61 \times 10^{-8} \mathrm{~cm}. Show that the calculated density is in agreement with its measured value of 8.92 \mathrm{~g} \mathrm{~cm}^{-3}
Chemistry | Previous Year Question Papers
Copper crystallises into a fcc lattice with edge length 3.61 \times 10^{-8} \mathrm{~cm}. Show that the calculated density is in agreement with its measured value of 8.92 \mathrm{~g} \mathrm{~cm}^{-3}

Ans: Edge length, a=3.61 \times 10^{-6} \mathrm{~cm}
As the lattice is fcc type, the number of atoms per unit cell, z=4
Atomic mass, \mathrm{M}=63.5 \mathrm{~g} \mathrm{~mol}^{-1}
We also know that, \mathrm{N}_{\mathrm{A}}=6.022 \times 10^{23} \mathrm{~mol}^{-1}
Using the relation:

    \[\begin{aligned} d &=\frac{z \mathrm{M}}{\mathrm{a}^{3} \mathrm{~N}_{\mathrm{A}}} \\ &=\frac{4 \times 63.5 \mathrm{gmol}^{-1}}{\left(3.61 \times 10^{-5} \mathrm{~cm}\right) \times 6.022 \times 10^{23} \mathrm{~mol}^{-1}} \\ &=8.97 \mathrm{~g} \mathrm{~cm}^{-3} \end{aligned}\]

The measured value of density is given as 8.92 \mathrm{~g} \mathrm{~cm}^{3}. Hence, the calculated density 8.97 \mathrm{~g} \mathrm{~cm}^{-3} is in agreement with its measured value.

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