The density of the unit cell of Platinum in a face-centered cubic unit cell is 2.88 × 10²⁴ g/m³
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.
The mass of an atom = molar mass/Avogadro's number
Now, the mass of a unit cell = 3.24 × 10²⁴ × 4
In an FCC unit cell, the volume of a unit cell is:
[tex]\mathbf{= \dfrac{16}{3}\pi r ^3 }[/tex]
The volume of the FCC unit cell in platinum = [tex]\mathbf{= \dfrac{16}{3}\pi (139) ^3 }[/tex]
= 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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