Copper crystallises into a fcc lattice with edge length

Question:

Copper crystallises into a fcc lattice with edge length 3.61 × 10−8 cm. Show that the calculated density is in agreement with its measured value of 8.92 g cm−3.

Solution:

Edge length, a = 3.61 × 10−8 cm

As the lattice is fcc type, the number of atoms per unit cell, z = 4

Atomic mass, M = 63.5 g mol−1

We also know that, NA = 6.022 × 1023 mol−1

Applying the relation:

$d=\frac{z \mathrm{M}}{a^{3} \mathrm{~N}_{\mathrm{A}}}$

$=\frac{4 \times 63.5 \mathrm{~g} \mathrm{~mol}^{-1}}{\left(3.61 \times 10^{-8} \mathrm{~cm}\right)^{3} \times 6.022 \times 10^{23} \mathrm{~mol}^{-1}}$

= 8.97 g cm−3

 

The measured value of density is given as 8.92 g cm−3. Hence, the calculated density 8.97 g cm−3 is in agreement with its measured value.

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