The density of the unit cell of Platinum in a face-centered cubic unit cell is 2.88 × 10²⁴ g/m³
<h3>What is a face-centered cubic unit cell?</h3>
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 }](https://tex.z-dn.net/?f=%5Cmathbf%7B%3D%20%5Cdfrac%7B16%7D%7B3%7D%5Cpi%20r%20%5E3%20%7D)
- Given that the atomic radius (r) = 139 pm
The volume of the FCC unit cell in platinum = ![\mathbf{= \dfrac{16}{3}\pi (139) ^3 }](https://tex.z-dn.net/?f=%5Cmathbf%7B%3D%20%5Cdfrac%7B16%7D%7B3%7D%5Cpi%20%28139%29%20%5E3%20%7D)
= 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:
brainly.com/question/26382596