Please help!
Answer the following for a body centered unit cell.
Crystalline Solids Program
Answers should be numerical,
set r = 4.0.
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:
8
11.31
for a body centered cell,
edge(a): a=sqrt(8) x r
face(b): b=sqrt((a^2) + (a^2))
body(c): c=sqrt((a^2) + (b^2))
r=4, so plug it in (:
I plug in your equations and get 11.31, 16, and 19.6, and i still get the answers wrong
never mind, calculation error. Thanks!!
To answer these questions, we need to understand the geometry of a body-centered unit cell in a crystalline solid. Let's break it down:
1. Edge in terms of r, the lattice point radius:
In a body-centered unit cell, there is one lattice point at each corner and another lattice point at the center of the cube. The edge length of the unit cell can be calculated as the sum of two radii of adjacent lattice points.
To find the edge length in terms of r, we are given that r = 4.0. So, the edge length would be:
Edge Length = 2 * r + 2 * r = 2 * 4.0 + 2 * 4.0 = 8.0 + 8.0 = 16.0
Therefore, the edge length in terms of r, the lattice point radius, is 16.0.
2. Face diagonal in terms of r, the lattice point radius:
The face diagonal of a body-centered unit cell connects two opposite corners of a face. This diagonal can be calculated using the Pythagorean theorem, adding the diagonal formed by a single edge and the diagonal from the center of the face.
To find the face diagonal in terms of r, we can use the edge length we already calculated. The face diagonal length would be:
Face Diagonal Length = √(2 * (Edge Length)^2) = √(2 * (16.0)^2) = √(2 * 256.0) = √(512.0)
Therefore, the face diagonal in terms of r, the lattice point radius, is √(512.0).
3. Body diagonal in terms of r, the lattice point radius:
The body diagonal of a body-centered unit cell connects two opposite corners of the cube. This diagonal can also be calculated using the Pythagorean theorem, adding the diagonal formed by a single edge and the diagonal from the body center.
To find the body diagonal in terms of r, we can again use the edge length we already calculated. The body diagonal length would be:
Body Diagonal Length = √(3 * (Edge Length)^2) = √(3 * (16.0)^2) = √(3 * 256.0) = √(768.0)
Therefore, the body diagonal in terms of r, the lattice point radius, is √(768.0).
So, the answers are:
Edge in terms of r, the lattice point radius: 16.0
Face diagonal in terms of r, the lattice point radius: √(512.0)
Body diagonal in terms of r, the lattice point radius: √(768.0)