Answer:
The edge length of a face-centered cubic unit cell is 435.6 pm.
Explanation:
In a face-centered cubic unit cell, each of the eight corners is occupied by one atom and each of the six faces is occupied by a single atom.
Hence, the number of atoms in an FCC unit cell is:
[tex] 8*\frac{1}{8} + 6*\frac{1}{2} = 4 atoms [/tex]
In a face-centered cubic unit cell, to find the edge length we need to use Pythagorean Theorem:
[tex] a^{2} + a^{2} = (4R)^{2} [/tex] (1)
Where:
a: is the edge length
R: is the radius of each atom = 154 pm
By solving equation (1) for "a" we have:
[tex] a = 2R\sqrt{2} = 2*154 pm*\sqrt{2} = 435.6 pm [/tex]
Therefore, the edge length of a face-centered cubic unit cell is 435.6 pm.
I hope it helps you!
