Question

Platinum has atomic radius 139 pm and crystallizes with a face-centered cubic unit cell. Calculate its density.

Answer 1

The density of the unit cell of Platinum in a face-centered cubic unit cell is 2.88 × 10²⁴ g/m³

What is a face-centered cubic unit cell?

Face-centered cubic is a type of atom arrangement found in nature.  A face-centered cubic unit cell is made up of atoms organized in a cube with a portion of an atom in each corner and six extra whole atoms in the middle of each cube face.

• An fcc unit cell contains 4 atoms

The mass of an atom = molar mass/Avogadro's number

• The mass of an atom = 195.084/6.022 × 10²³
• The mass of an atom = 3.24 × 10²⁴ grams

Now, the mass of a unit cell = 3.24 × 10²⁴ × 4

• The mass of a unit cell = 1.296×10²⁵ grams

In an FCC unit cell, the volume of a unit cell is:

$\mathbf{= \dfrac{16}{3}\pi r ^3 }$

• Given that the atomic radius (r) = 139 pm

The volume of the FCC unit cell in platinum = $\mathbf{= \dfrac{16}{3}\pi (139) ^3 }$

= 44997978.24 pm³

= 4.49 m³

Therefore, the density of an FCC unit cell = mass of a unit cell/ volume of a unit cell

The density of a unit cell = 1.296×10²⁵ g/4.49 m³

The density of a unit cell = 2.88 × 10²⁴ g/m³

Learn more about Face centered cubic unit cells here:

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