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Chemistry: Principles and Practice
Chemistry: Principles and Practice
3rd Edition
ISBN:9780534420123
Author:Daniel L. Reger, Scott R. Goode, David W. Ball, Edward Mercer
Publisher:Daniel L. Reger, Scott R. Goode, David W. Ball, Edward Mercer
Chapter11: Liquids And Solids
Section: Chapter Questions
Problem 11.74QE
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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: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 ****
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
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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