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30/12/2021 6:33 pm
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Copper crystallises into a fcc lattice with edge length 3.61 x 10-8 cm. Show that the calculated density is in agreement with its measured value of 8.92 g cm-3.
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30/12/2021 6:38 pm
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 = \(\frac{zM}{a^3N_A}\)
= \(\frac{4 \times 63.5gmol^{-1}}{(3.61 \times 10^{-8} cm)^3 \times 6.022 \times 10^{23}mol^{-1}}\)
= 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.