Chemistry: What is the edge length of a face-centered cubic unit cell that is made of of atoms, each with a radius of 154 pm

What is the edge length of a face-centered cubic

tiwaribianca475

30.01.2022

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:

$8*\frac{1}{8} + 6*\frac{1}{2} = 4 atoms$

In a face-centered cubic unit cell, to find the edge length we need to use Pythagorean Theorem:

$a^{2} + a^{2} = (4R)^{2}$ (1)

Where:

a: is the edge length

R: is the radius of each atom = 154 pm

By solving equation (1) for "a" we have:

$a = 2R\sqrt{2} = 2*154 pm*\sqrt{2} = 435.6 pm$

Therefore, the edge length of a face-centered cubic unit cell is 435.6 pm.

I hope it helps you!

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