The volume of a unit cell of diamond is 0.0454 nm³, and the density of diamond is 3.52 g/cm³. Find the number of carbon atoms in a unit cell of diamond.

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Convert the volume of the unit cell from nm³ to cm³ by using the conversion factor: 1 nm = 10⁻⁷ cm.

Calculate the mass of the unit cell using the formula: mass = density × volume.

Use the molar mass of carbon (12.01 g/mol) to convert the mass of the unit cell to moles of carbon atoms.

Use Avogadro's number (6.022 × 10²³ atoms/mol) to convert moles of carbon atoms to the number of carbon atoms.

Determine the number of carbon atoms in the unit cell by considering the structure of diamond, which is a face-centered cubic lattice with additional atoms inside the cell.

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