Calculating the Mass of an Aluminum Unit Cell

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SUMMARY

The mass of an aluminum unit cell in a face-centered cubic (FCC) crystal lattice is calculated to be 1.792 x 10-22 g/unit cell. This value is derived by multiplying the mass of a single aluminum atom, 4.480 x 10-23 g, by the total number of atoms per unit cell, which is 4. In FCC geometry, atoms are located at the corners and face centers of the cube, contributing fractions of their mass to the unit cell, resulting in a total of 4 atoms per unit cell.

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  • Understanding of face-centered cubic (FCC) crystal lattice structure
  • Knowledge of atomic mass calculations
  • Familiarity with density and its application in material science
  • Basic geometry related to unit cell dimensions
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Aluminum has a density of 2.699 g/cm3 , and the atoms are packed in a face-centered cubic crystal lattice. Find the mass of a unit cell.

-----I already know the answer is 1.792*10^-22g/unit cell

I have a question about how you get the answer:
I know you multiply 4.480*10^-23g * 4 atoms/1 unit cell= the answer

where does the 4 atoms come from?
 
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Geometry of the cell. In fcc all atoms lie on the cell walls, so they are only partially belong to the cell. Sum these fractions.
 
Borek said:
Geometry of the cell. In fcc all atoms lie on the cell walls, so they are only partially belong to the cell. Sum these fractions.

got it, thanks!
 

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