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Chemistry
10th Edition
ISBN: 9781305957404
Author: Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher: Cengage Learning
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
Transcribed Image Text:Coordination number = 8
%3D
Atoms per unit cell=
Gx 8) + 1 = 2
atom at each
8.
of 8 corners
...............
1 atom
at center
through the middle of the cube, to the opposite corner. The edge length in terms of the
atomic radius is therefore 1 = 4r/V3 as shown here:
A FIGURE 12.6 Body-Centered
Cubic Crystal Structure The
%3D
different colors used for the atoms
in this figure are for clarity only.
Body-centered cubic
All atoms within the structure are
identical.
c2 = b2 + 1?
6? = 1² + 1?
b2 = 212
%3D
c = 4r
(4r)² = 21² + 1?
(4r)² = 31²
(4r)2
%3D
%3D
12
4r
In the body-centered cubic lattice, the
atoms touch only along the cube diagonal.
The edge length is 4r/V3.
V3
The body-centered unit cell contains two atoms per unit cell because the cente
atom is not shared with any other neighboring cells. The coordination number of th
body-centered cubic unit cell is 8, which we can see by examining the atom in the e
center of the cube, which touches eight atoms at the corners. The packing efficiency
the body-centered unit cell is 68%, significantly higher than for the simple cubic u
cell. Each atom in this structure strongly interacts with more atoms than each atom
the simple cubic unit cell.
Example 12.3
Relating Unit Cell Volume, Edge Length, and Atomic Radius
A body-centered cubic unit cell has a volume of 4.32 x 10-23 cm³. Find the radius of the atom in pm.
SORT You are given the volume of a unit cell and asked to
GIVEN: V = 4.32 X 10-23 cm³
%3D
find the radius of the atom.
FIND: r (in pm)
STRATEGIZE Use the given volume to find the edge length
CONCEPTUAL PLAN
of the unit cell.
V
V=
Then use the edge length to determine the radius of the
atom.
4r
V3
****

Transcribed Image Text:5) An atom has radius of 165 pm and crystallizes in the body-centered cubic unit cell. What is
the volume of the unit cell in cm³? You will need to use examples from your textbook to
help you. Pg 540-541
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