Question

What is the length of one side of the crystal unit cell for aluminum? (show your work)

I've seen multiple answers for this, and I've attempted to get this on my own with no luck. I saw one that said the formula to get the length of one side for a unit cell side for FCC crystal lattice is 8^0.5 x radius. Is this correct? Don't just write answer I want to fully understand this so I need to know how and why. Not just how :)

Answer 1

Two approaches to find out unit cell edge length is shown below, where the former contains standard inputs taken from internet and the later is shown geometrically :

- 3 Molecular weight of Al A(M) = 27 g/mol = 27x10 kg/mol. Density of Al (%) = 2-7 g/cc = 2700 kg/m3 Avogadro Number (NA) = 6-023X1023 Aluminium forms a FCC structure. No. of atoms/ unit cell (2) = 18*178) + (0X72) = 4. Corner atoms contribute 78th of its volume to unit cella face atoms contribute Y2 of its volume to the unit cell.

we knowo- 2M 193 where, a= length of the unit cell. > a = 2 ZM > a = 4+278103 6-023X1023x 2700 -> as 4.058 1010 m > = 4:05 Å] Ara. Alternatively, $ AC = Sep (2rtytr) = 4r AC = ABV2 = av2. (2-0) .: Ar = arz az 2v2r radius is provided we can also find a. If