CHEM...Calculation ..structure

Cu has abcabc.... close-packed structure.
The unit cell of Cu is face-centred cubic.

In each unit cell :
No. of Cu atoms at the corners = 8 x (1/8) = 1
No. of Cu atoms on the surfaces = 6 x (1/2) = 3
Total no. of Cu atom in the unit cell = 1 + 3 = 4
Volume of the unit cell = (3.58 x 10-8)3 cm3

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Method I for the calculation of the density of Cu :
(The method used in the question)

Consider 1 mol of unit cells. There are 4 mol of Cu atoms.
(This is because there are 4 Cu atom in each unit cell.)


No. of unit cells = 6.02 x 1023
Total volume = (6.02 x 1023) x (3.58 x 10-8)3 cm3
Mass of 4 mol of Cu atoms = 4 x (63.5) g

Density
= Mass / Volume
= 4 x (63.5) / [(6.02 x 1023) x (3.58 x 10-8)3] g cm-3

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Method II for the calculation of the density of Cu :

Consider 1 unit cell. There are 4 Cu atoms.

Volume = (3.58 x 10-8)3 cm3
Mass of 6.02 x 1023 Cu atoms = 63.5 g
Mass of 4 Cu atoms = 4 x (63.5) / (6.02 x 1023) g

Density
= Mass / Volume
= 4 x (63.5) / [(6.02 x 1023) x (3.58 x 10-8)3] g cm-3

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Both the methods give the same answer.