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2) For a face-centered cube, show the calculation to determine the number of atoms per cell and the total number of atoms in 6 unit cells. Page 541

2) For a face-centered cube, show the calculation to determine the number of atoms per cell and the total number of atoms in 6 unit cells. Page 541

General Chemistry - Standalone book (MindTap Course List)
General Chemistry - Standalone book (MindTap Course List)
11th Edition
ISBN:9781305580343
Author:Steven D. Gammon, Ebbing, Darrell Ebbing, Steven D., Darrell; Gammon, Darrell Ebbing; Steven D. Gammon, Darrell D.; Gammon, Ebbing; Steven D. Gammon; Darrell
Publisher:Steven D. Gammon, Ebbing, Darrell Ebbing, Steven D., Darrell; Gammon, Darrell Ebbing; Steven D. Gammon, Darrell D.; Gammon, Ebbing; Steven D. Gammon; Darrell
Chapter11: States Of Matter; Liquids And Solids
Section: Chapter Questions
Problem 11.113QP
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2) For a face-centered cube, show the calculation to determine the number of atoms per cell and the total number of atoms in 6 unit cells. Page 541
Transcribed Image Text:2) For a face-centered cube, show the calculation to determine the number of atoms per cell and the total number of atoms in 6 unit cells. Page 541
12.3 Unit Cells and Basic Structures 541 RELATIONSHIPS USED: V = 1³ (Volume of a cube) 4r (Edge length of body-centered cubic unit cell) V3 1 = %3D SOLVE SOLUTION Solve the equation for the volume of a cube for I and substitute in the given value for V to find I. V = 13 1 = Vv = V4.32 × 10-23 cm 3.5088 x 10-8 cm %3D Solve the equation for the edge length of a body-centered cubic unit cell for r and substitute in the value of 1 (from the 4r 1 = V3 previous step) to find r. V31 V3 (3.5088 × 10 8 cm) = 1.5193 x 10-8 cm 4 4 Convert r from cm to m and then to pm. 0.01 m 1 pm 1.5193 X 10-8 cm x 152 pm %3D 1 cm W Z1-0 CHECK The units of the answer (pm) are correct. The magnitude is reasonable because atomic radii range roughly from 50 to 200 pm. FOR PRACTICE 12.3 An atom has radius of 138 pm and crystallizes in the body-centered cubic unit cell. What is the volume of the unit cell in cm³? The face-centered cubic unit cell (Figure 12.7▼) is a cube Face-centered cubic with one atom at each corner and one atom (of the same kind) in the center of each cube face. Note that in the face-centered unit cell (like the body-centered unit cell), the atoms do not touch along each edge of the cube. Instead, the atoms touch along the face diagonal. The edge length in terms of the atomic radius is therefore I = 2V2r, as shown here. 62 = 12 + 1? = 21² b = 4r (4r)2 = 212 (4r)2 %3D %3D 12 4r %3D V2 In the face-centered cubic lattice, the atoms touch along a face diagonal. The edge length is 2V2r. = 2V2r Face-Centered Cubic Unit Cell Coordination number = 12 Atoms/unit = x 8) + (G x 6) = 4 atom atom at 8 cornerS at 6 faces A FIGURE 12.7 Face-Centered Cubic Crystal Structure The different colors used on the atoms in this figure are for clarity only. All atoms within the structure are identical.
Transcribed Image Text:12.3 Unit Cells and Basic Structures 541 RELATIONSHIPS USED: V = 1³ (Volume of a cube) 4r (Edge length of body-centered cubic unit cell) V3 1 = %3D SOLVE SOLUTION Solve the equation for the volume of a cube for I and substitute in the given value for V to find I. V = 13 1 = Vv = V4.32 × 10-23 cm 3.5088 x 10-8 cm %3D Solve the equation for the edge length of a body-centered cubic unit cell for r and substitute in the value of 1 (from the 4r 1 = V3 previous step) to find r. V31 V3 (3.5088 × 10 8 cm) = 1.5193 x 10-8 cm 4 4 Convert r from cm to m and then to pm. 0.01 m 1 pm 1.5193 X 10-8 cm x 152 pm %3D 1 cm W Z1-0 CHECK The units of the answer (pm) are correct. The magnitude is reasonable because atomic radii range roughly from 50 to 200 pm. FOR PRACTICE 12.3 An atom has radius of 138 pm and crystallizes in the body-centered cubic unit cell. What is the volume of the unit cell in cm³? The face-centered cubic unit cell (Figure 12.7▼) is a cube Face-centered cubic with one atom at each corner and one atom (of the same kind) in the center of each cube face. Note that in the face-centered unit cell (like the body-centered unit cell), the atoms do not touch along each edge of the cube. Instead, the atoms touch along the face diagonal. The edge length in terms of the atomic radius is therefore I = 2V2r, as shown here. 62 = 12 + 1? = 21² b = 4r (4r)2 = 212 (4r)2 %3D %3D 12 4r %3D V2 In the face-centered cubic lattice, the atoms touch along a face diagonal. The edge length is 2V2r. = 2V2r Face-Centered Cubic Unit Cell Coordination number = 12 Atoms/unit = x 8) + (G x 6) = 4 atom atom at 8 cornerS at 6 faces A FIGURE 12.7 Face-Centered Cubic Crystal Structure The different colors used on the atoms in this figure are for clarity only. All atoms within the structure are identical.
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