Question

In: Chemistry

Assuming atoms of radius of 1.00 Å and atoms just touching one another, calculate the percentage...

Assuming atoms of radius of 1.00 Å and atoms just touching one another, calculate the percentage of the volume taken up in a face-centered cubic unit cell by those atoms.

Expert Solution

Ans:

In FCC, along with the atoms in the 8 corner of a unit cell, we will have 1 atom sitting at the centre of each face.
Atoms present at the corner will contribute 1/8 to unit cell
Atoms present at the centre of face contribute 1/2 to unit cell
A cube will have 8 corners and 6 faces.
Number of atoms per unit cell of FCC, Z = (8 x 1/8) + (6 x 1/2) = 4
In FCC, atoms along the face diagonal touch each other.

In triangle ABC, using Pythagorean theorem we can write

AC² = AB² + BC²

F² = a² + a² = 2a²

We can also see from the diagram that, F = 4r. So,

(4r)² = 2a²

16r² = 2a²

a =

Packing efficiency = x 100

Packing efficiency = x 100 = x 100

Packing efficiency = 74%

74% of the cube volume is occupied by the atoms

queen_honey_blossom answered 2 years ago

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