Answer :
To find the length of the edge of a face-centered cubic unit cell with 4 formula units, consider the contributions of atoms at corners and faces, calculate the volume in cubic centimeters, and then determine the density by dividing mass by volume.
The length of the edge of the unit cell in a face-centered cubic element with 4 formula units can be calculated by taking into account the contributions of atoms at corners and faces of the unit cell.
The volume of the unit cell can be determined by using the edge length and then by converting it to cubic centimeters.
Finally, by dividing the mass by the volume, you can calculate the density of the unit cell.
The length of the edge of the unit cell is approximately 4.08 angstroms.
A face-centered cubic (FCC) unit cell contains 4 atoms. The density of the unit cell is given by the formula:
[tex]\[ \text{Density} = \frac{\text{Mass of Unit Cell}}{\text{Volume of Unit Cell}} \][/tex]
Given that the density is[tex]\(6.2 \text{ g/cm}^3\)[/tex] and the atomic mass is [tex]\(60.2 \text{ amu}\)[/tex], we can find the mass of the unit cell:
[tex]\[ \text{Mass of Unit Cell} = 4 \times 60.2 \text{ amu} = 240.8 \text{ amu} \][/tex]
To calculate the volume of the unit cell, we first need to find the volume of one atom in the FCC lattice. Each atom in an FCC lattice is shared among 4 unit cells, so the volume of one atom is:
[tex]\[ \text{Volume of Atom} = \frac{4}{3} \times \pi \times (\frac{a}{2})^3 \][/tex]
Where \(a\) is the length of the edge of the unit cell. Thus, the volume of the unit cell is:
[tex]\[ \text{Volume of Unit Cell} = 4 \times \text{Volume of Atom} \][/tex]
Setting the formula for density equal to the mass of the unit cell divided by the volume of the unit cell, we can solve for \(a\). Solving the equation, we find \(a \approx 4.08\) angstroms.
