Answer the following for a face centered unit cell. r=6.0
edge in terms of r, the lattice pt radius
face diagonal in terms of r, the lattice
pt radius
body diagonal in terms of r, the lattice pt radius
Kacy or Stacy or whoever,
You will find here at Jiskha that long series of questions, posted with no evidence of effort or thought by the person posting, will not be answered. We will gladly respond to your future questions in which your thoughts are included.
In addition, please do not post any question more than once. It wastes everyone's time.
Thanks.
To find the answers for a face-centered unit cell with a lattice point radius of r = 6.0, we need to understand the relationships between the different measurements in the unit cell.
1. Edge in terms of r, the lattice point radius:
In a face-centered unit cell, each face has one lattice point at its center, and each edge contains two lattice points. The diagonal of a face-centered unit cell is equal to four times the radius (2r) of the lattice points. Therefore, the edge length of the unit cell can be obtained by subtracting twice the radius of the lattice points from the diagonal of a face:
Edge length = Diagonal - 2(r)
For a face-centered unit cell, the diagonal is given as:
Diagonal = 4r
Substituting the values into the formula, we get:
Edge length = (4r) - 2(r) = 2r
Hence, the edge length of the face-centered unit cell in terms of r, the lattice point radius, is 2r.
2. Face diagonal in terms of r, the lattice point radius:
The face diagonal is the distance from one corner of the face to the opposite corner. In a face-centered unit cell, the face diagonal is equal to four times the radius (2r) of the lattice points.
Face diagonal = 4r
Therefore, the face diagonal of the face-centered unit cell in terms of r, the lattice point radius, is 4r.
3. Body diagonal in terms of r, the lattice point radius:
The body diagonal is the distance from one corner of the unit cell to the farthest corner inside the unit cell, passing through the center. In a face-centered unit cell, the body diagonal is obtained by connecting opposite corners of the cube, forming a diagonal across the face diagonal.
Body diagonal = Square root of [(Face diagonal)^2 + (Edge length)^2]
Substituting the values of face diagonal and edge length calculated earlier:
Body diagonal = Square root of [(4r)^2 + (2r)^2]
= Square root of [16r^2 + 4r^2]
= Square root of [20r^2]
= Square root of (20) * r
= 2 * Square root of 5 * r
Hence, the body diagonal of the face-centered unit cell in terms of r, the lattice point radius, is 2 * Square root of 5 * r.