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Calculate the theoretical density (in g/cm3) of copper (Cu), given that it has the FCC structure. The atomic weight of Cu is 63.55 g/mol, and its atomic radius R is 0.1278 nm.

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Answer:

8.937g/cm³

Explanation:

To answer this question we need to know that, in 1 unit FCC cell you have:

Edge length = √8 * R

Volume = 8√8 * R³

And there are 4 atoms per unit cell

Mass of 4 atoms in g:

4 atom * (1mol / 6.022x10²³atom) * (63.55g / mol) = 4.221x10⁻²²g

Volume in cm³:

0.1278nm * (1x10⁻⁷cm / 1nm) = 1.278x10⁻⁸cm

Volume = 8√8 * (1.278x10⁻⁸cm)³

Volume = 4.723x10⁻²³cm³

And density is:

4.221x10⁻²²g / 4.723x10⁻²³cm³ =

8.937g/cm³

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