Complete the table below:
Answer the following for a body centered unit cell.
(Hint: Helpful information can be found by going to the "Lattice" menu, choosing "Cubic", and then choosing "Body-Centered" in the Crystalline Solids program.)
Crystalline Solids Program
Answers should be numerical, set r = 8.0.
A Answer
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
first part is 2r = 16
second part is 16 * square root of 2
third part is 6 * square root of 3
Sheila your answer relates to Primitive Cubic Unit Cell, and the "third part" should read "third part is 16 * square root of 3," not "third part is 6 * square root of 3."
To complete the table for a body-centered unit cell, we need to find the edge, face diagonal, and body diagonal in terms of the lattice point radius.
1. Edge in terms of r (the lattice point radius):
In a body-centered unit cell, the lattice points are located at the corners and in the center of the cell. The body diagonal connects two opposite corners of the unit cell, passing through the center.
To find the edge in terms of r, we need to consider that the body diagonal is equal to twice the edge length of the unit cell. Therefore, the edge length can be found by dividing the body diagonal length (2r) by the square root of 3 (since the body diagonal forms a right triangle with two edges of equal length).
Thus, the edge length in terms of r can be calculated as:
edge = (2r) / (sqrt(3))
2. Face diagonal in terms of r (the lattice point radius):
In a body-centered unit cell, the face diagonal connects two opposite corners of a face of the unit cell. Since the face diagonal passes through the center of the face, it is equal to the diagonal of a square formed by two edges of the unit cell.
To find the face diagonal in terms of r, we can use the Pythagorean theorem to calculate the length. The face diagonal is equal to the square root of 2 times the edge length.
Thus, the face diagonal in terms of r can be calculated as:
face diagonal = (sqrt(2)) * edge = (sqrt(2)) * (2r / sqrt(3))
3. Body diagonal in terms of r (the lattice point radius):
In a body-centered unit cell, the body diagonal connects two opposite corners of the unit cell, passing through the center. It is the longest diagonal in the unit cell.
The body diagonal length can be calculated using the Pythagorean theorem with three edges forming a right triangle. The body diagonal is equal to the square root of 3 times the edge length.
Thus, the body diagonal in terms of r can be calculated as:
body diagonal = (sqrt(3)) * edge = (sqrt(3)) * (2r / sqrt(3))
By substituting the given value of r (8.0), we can calculate the numerical values for edge, face diagonal, and body diagonal.