CHAPTER 9:

THE STRUCTURE OF SOLIDS

The following information is often presented on the first page of exams covering this chapter under the heading: “potentially useful information.”

          R+/R-                      CN                           1 cm = 10⁷ nm

0.732 - 18d_face = √2 a

          0.414 - 0.732           6                              d_body = √3 a

          0 - 0.414                  4

The Structure of Solids: General

9-1. Which of the following descriptions of hydrogen bonding is incorrect?

(a) It involves a type of van der Waals force.

(b) It is primarily an electrostatic interaction.

(c) It results in specific orientations of molecules in solids.

           (d) It is important when hydrogen is bonded to N, O, or F.

           (e) All of the above statements are correct.

Answer: (e)

9-2. The bonding in diamond involves sp³ hybridized carbon. Diamond is an example of a:

(a) molecular solid (b) a covalent solid (c) an ionic solid

          (d) a solid solution (e) a metallic solid

Answer: (b)

9-3. Rare gases, such as xenon, can be frozen to form solids. The intermolecular forces responsible for maintaining the solid are best described as:

          (a) hydrogen-bonding forces        (b) van der Waal's forces

          (c) dipole-dipole forces                (d) dipole-induced dipole forces

           (e) induced dipole-induced dipole forces

Answer: (e)

9-4. SiO₂ is a covalent solid. Which of the following is most likely to be true of SiO₂?

          (a) SiO₂ would have a low melting point and would conduct electricity when melted.

(b) SiO₂ would conduct electricity as a solid and its melting point cannot be predicted.

          (c) SiO₂ would have a high melting point and would conduct electricity when melted.

(d) SiO₂ would have a high melting point and wouldn’t conduct electricity when melted.

(e) SiO₂ would have a low melting point and wouldn’t conduct electricity when melted.

Answer: (d)

9-5. Which of the following types of solids is most likely to be soft, have a low melting point, and not conduct electricity when melted?

          (a) ionic (b) molecular (c) covalent (d) metallic (e) none of the above

Answer: (b)

9-6. Which solid is held together by an extended network of covalent bonds?

          (a) sodium chloride (b) gold (c) calcium carbonate (d) diamond

          (e) dry ice (solid CO₂)

Answer: (d)

9-7. Which force makes the most important contribution to the lattice energy of solid CO₂?

          (a) metallic bonding (b) ionic bonding (c) hydrogen bonding

           (d) van der Waal's forces (e) all of the above

Answer: (d)

9-8. A compound that is a poor conductor of electricity when solid, but a very good conductor when molten is most likely to fit into which category?

          (a) molecular solid (b) covalent solid (c) ionic solid (d) metallic solid

          (e) any of the above

Answer: (c)

Packing

9-9. Sodium crystallizes in a structure in which the coordination number is 8. Which structure best describes this crystal?

          (a) simple cubic (b) body-centered cubic (c) cubic closest packed

           (d) hexagonal closest packed (e) none of the above

Answer: (b)

9-10. Cubic holes can be found in which structure?

           (a) simple cubic (b) body-centered cubic (c) cubic closest packed

          (d) hexagonal closest packed (e) none of the above

Answer: (a)

9-11. In which of the following structures would a Xe atom be able to form the largest number of induced dipole-induced dipole interactions?

          (a) simple cubic (b) body-centered cubic (c) cubic closest packing

          (d) hexagonal closest packing (e) either cubic or hexagonal closest packing

Answer: (e)

Radius Ratio Rules

9-12. In KF, the K⁺ and F^- ions are almost exactly the same size: 0.134 nm. Which would be larger: a neutral potassium atom or a neutral fluorine atom?

Answer: neutral K atom

9-13. The crystal structure of CoO would be expected to be most like which of the following crystals? (Radii: Co²⁺ = 0.072 nm; O^2- = 0.140 nm)

           (a) NaCl (b) ZnS (c) CsCl (d) CaF₂ (e) TiO₂

Answer: (a)

9-14. The crystal structure of CaTe (Ca²⁺ = 0.099 nm; Te^2- = 0.221 nm) is most like which of the following?

          (a) CaF₂ (b) CsCl (c) Cu₂O (d) NaCl (e) ZnS

Answer: (d)

Filling of Holes

9-15. What is the coordination number of a cation packed in an octahedral hole?

          (a) 2 (b) 4 (c) 6 (d) 8 (e) 12

Answer: (c)

9-16. Which of the following compounds could be described as a closest packed array of anions with lithium atoms in all of the tetrahedral holes?

          (a) Li₄C (b) Li₃N (c) Li₂S (d) LiF

Answer: (c)

9-17. What is the formula of a compound of niobium and nitrogen that crystallizes in a hexagonal closest packed array of nitrogen atoms with niobium atoms in half of the tetrahedral holes?

          (a) Nb₄N (b) Nb₂N (c) NbN (d) NbN₂ (e) NbN₄

Answer: (c)

9-18. What is the coordination number of the niobium atoms in the compound in the previous question?

           (a) 4 (b) 6 (c) 8 (d) 12 (e) 14

Answer: (a)

9-19. Scandium oxide, Sc₂O₃, crystallizes with the oxide ions in a closest packed array with the scandium ions in octahedral holes. What fraction of the octahedral holes are filled?

          (a) all (b) 2/3 (c) 1/2 (d) 1/3 (e) 1/4

Answer: (b)

9-20. Titanium carbide is a high melting, chemically inert compound that is almost as hard as diamond. The crystal structure can be described as a closely-packed array of carbon atoms with titanium atoms in all of the octahedral holes. What is the empirical formula of this compound?

          (a) Ti₂C (b) TiC (c) TiC₂ (d) Ti₂C₃ (e) TiC₄

Answer: (b)

9-21. Pyrite crystallizes in a structure that could be described as a closely-packed array of positive ions with negative ions in all of the octahedral holes. What is the best formulation of this mineral: [Fe⁴⁺] [S^2-] or [Fe²⁺][S₂^2-]? Explain why.

Answer: [Fe²⁺][S₂^2-] because this would have to be a 1:1 salt

9-22. What is the formula of an oxide of titanium that crystallizes as a closely packed array of oxygen atoms with titanium atoms in two-thirds of the octahedral holes?

          (a) TiO (b) TiO₂ (c) Ti₂O₃ (d) Ti₃O₂ (e) none of the above

Answer: (c)

9-23. Cadmium iodide crystallizes in a structure that could be described as a closely-packed array of iodide atoms with cadmium atoms in half of the octahedral holes. What is the oxidation state of cadmium in this compound?

          (a) 0 (b) +1 (c) +2 (d) + 3 (e) +4

Answer: (c)

9-24. Which compound is most likely to crystallize in a simple cubic array of Cl^- ions with metal ions in half of the cubic holes?

           (a) LiCl (b) CsCl (c) BeCl₂ (d) BaCl₂ (e) SCl₂

Answer: (d)

9-25. What is the oxidation state of cobalt in a compound that crystallizes in a closest-packed array of oxide ions with cobalt ions in 1/8th of the tetrahedral holes and 1/2 of the octahedral holes?

          (a) 5/8 (b) 3/2 (c) 2 (d) 2²/₃ (e) 3

Answer: (d)

9-26. Thallium cyanide, Ti(CN)_x , crystallizes as a simple cubic array of CN^- ions with thallium ions in all of the cubic holes. What is the oxidation state of thallium in this compound?

          (a) -1 (b) 0 (c) +1 (d) +2 (e) +3

Answer: (c)

Coordination Numbers

9-27. Thallium iodide (TlI) crystallizes with the same structure as CsCl. How many nearest neighbor I^- ions does each Tl⁺ ion have?

          (a) 1 (b) 4 (c) 6 (d) 8 (e) 12

Answer: (d)

9-28. Which of the following correctly describes a body-centered cubic structure?

          (a) CN = 6, 1 atom per unit cell               (b) CN = 6, 2 atoms per unit cell

          (c) CN = 6, 4 atoms per unit cell              (d) CN = 8, 1 atom per unit cell

           (e) CN = 8, 2 atoms per unit cell

Answer: (e)

9-29. Which of the following correctly describes the structure of CaF₂?

           (a) CN of Ca²⁺ = 8, CN of F^- = 4, 4 Ca²⁺ and 8 F^- per unit cell

          (b) CN of Ca²⁺ = 4, CN of F^- = 8, 8 Ca²⁺ and 4 F^- per unit cell

          (c) CN of Ca²⁺ = 4, CN of F^- = 8, 4 Ca²⁺ and 8 F^- per unit cell

          (d) CN of Ca²⁺ = 8, CN of F^- = 4, 8 Ca²⁺ and 4 F^- per unit cell

          (e) CN of Ca²⁺ = 4, CN of F^- = 4, 4 Ca²⁺ and 8 F^- per unit cell

Answer: (a)

9-30. Diamond crystallizes in a cubic unit cell with carbon atoms at the following coordinates:

          0,0,0; 1/2,1/2,0; 1/2,0,1/2; 0,1/2,1/2; 1/4,1/4,1/4; 1/4,3/4,3/4; 3/4,1/4,3/4; 3/4,3/4,1/4.

What is the coordination number of the carbon atom in diamond?

          (a) 2 (b) 4 (c) 6 (d) 8 (e) 10

Answer: (b)

Unit Cells

9-31. What is the ratio of the length of the body diagonal of a cube to the face diagonal of the cube?

           (a) 0.817 (b) 1.00 (c) 1.22 (d) 1.41 (e) 1.73

Answer: (c)

9-32. What is the relationship between the unit cell edge length (a) and the radius of a metal atom (r) when the metal crystallizes in a face-centered cubic unit cell?

          (a) r = √2 a (b) r = (√2 a)/4 (c) r = (√2 a)/2 (d) r = (√3 a)/4

          (e) none of the above

Answer: (b)

9-33. Calcium titanate crystallizes in a cubic unit cell with titanium atoms at the corners of the cell, oxygen atoms in the middle of the edges of the cell, and a calcium atom in the center of the cell. What is the formula of calcium titanate?

          (a) CaTiO (b) CaTiO₃ (c) CaTiO₄ (d) Ca₂TiO₄ (e) CaTi₈O₂

Answer: (b)

9-34. At very low temperatures, argon crystallizes in a structure in which unique Ar atoms are located at the following positions: 0,0,0; 0,1/2,1/2; 1/2,0,1/2; 1/2,1/2,0. What is the unit cell?

(a) simple cubic (b) body-centered cubic (c) face-centered cubic

          (d) it is impossible to determine the unit cell of argon from this information.

Answer: (c)

9-35. The mineral cuprite crystallizes in a structure with unique oxygen atoms at 0,0,0 and 1/2,1/2,1/2 and unique copper atoms at 1/4,1/4,1/4; 1/4,3/4,3/4; 3/4,1/4,3/4 and 3/4,3/4,1/4. What is the unit cell of cuprite?

          (a) simple cubic (b) body-centered cubic (c) face-centered cubic

          (d) it is impossible to determine the unit cell of cuprite from this information.

Answer: (b)

9-36. What is the empirical formula for the mineral cuprite, whose structure was described in the previous question?

           (a) Cu₂O (b) CuO (c) CuO₂ (d) Cu₂O₃ (e) Cu₃O₂

Answer: (a)

9-37. Gallium arsenide is a semiconductor with several advantages over silicon. It crystallizes in a structure with unique gallium atoms at 0,0,0; 1/2,1/2,0; 1/2,0,1/2 and 0,1/2,1/2 and unique arsenic atoms at 1/4,1/4,1/4; 1/4,3/4,3/4; 3/4,1/4,3/4 and 3/4,3/4,1/4. Describe the unit cell of this compound, the kind of holes in which the arsenic atoms are found, the fraction of the holes occupied, and the empirical formula of this compound.

Answer: FCC, tetrahedral, half, GaAs

9-38. The mineral perovskite crystallizes in a cubic unit cell with a unique titanium atom at 0,0,0; a unique calcium atom at 1/2,1/2,1/2; and unique oxygen atoms at 1/2,0,0; 0,1/2,0 and 0,0,1/2. Describe the unit cell and calculate the empirical formula of this compound.

Answer: SC, CaTiO₃

Number of Atoms per Unit Cell

9-39. Calculate the number of chloride and ammonium ions per unit cell if NH₄Cl is a simple cubic unit cell of NH₄⁺ ions with a Cl^- ion in the center of the unit cell.

           (a) 1 NH₄⁺ ion and 1 Cl^- ion                    (b) 2 NH₄⁺ ions and 2 Cl^- ions

          (c) 4 NH₄⁺ ions and 4 Cl^- ions      (d) 8 NH₄⁺ ions and 8 Cl^- ions

          (e) none of the above

Answer: (a)

9-40. Which of the following correctly describes the structure of NaOH if this compound crystallizes in the same structure as CsCl?

          (a) Na⁺ CN = 6, 1 Na⁺ and 1 OH^- per unit cell

          (b) Na⁺ CN = 6, 2 Na⁺ and 2 OH^- per unit cell

           (c) Na⁺ CN = 8, 1 Na⁺ and 1 OH^- per unit cell

          (d) Na⁺ CN = 8, 2 Na⁺ and 2 OH^- per unit cell

          (e) Na⁺ CN = 8, 4 Na⁺ and 4 OH^- per unit cell

Answer: (c)

Unit Cell Calculations

9-41. Potassium metal has a density of 0.862 g/cm³ and a cell edge of 0.532 nm. What is the lattice type for potassium metal? (AW: K = 39.1 amu)

          (a) simple cubic (b) body-centered cubic (c) face-centered cubic

          (d) the NaCl structure (e) the ZnS structure

Answer: (b)

9-42. CdO crystallizes in a cubic unit cell with a cell edge of 0. 47 nm. The density of CdO is 8.2 g/cm³. How many Cd and O atoms are present in a single unit cell. (AW: O = 16.0, Cd = 112 amu)

(a) 1 Cd and 1 O (b) 2 Cd and 2 O (c) 3 Cd and 3 O

           (d) 4 Cd and 4 O (e) 8 Cd and 8 O

Answer: (d)

9-43. Pyrite, FeS₂, crystalizes in a cubic unit cell with a cell edge of 0.541 nm. The density of pyrite is 5.02 g/cm³. How many Fe²⁺ and S₂^2- ions are present in a single unit cell? (AW: S = 32.1, Fe = 55.8 amu)

          (a) 1 Fe²⁺ and 1 S₂^2-                    (b) 2 Fe²⁺ and 2 S₂^2-

           (c) 4 Fe²⁺ and 4 S₂^2-                    (d) 6 Fe²⁺ and 6 S₂^2-

          (e) 8 Fe²⁺ and 8 S₂^2-

Answer: (c)

9-44. What is the density of sodium if this metal crystallizes in a body-centered cubic unit cell with a cell edge of 0.429 nm? (AW: Na = 23.0 amu; 1 cm = 10⁷ nm)

          (a) 0.484 g/cm³ (b) 0.582 g/cm³ (c) 0.967 g/cm³

          (d) 1.94 g/cm³ (e) 9.67 x 10^-25 g/cm³

Answer: (c)

9-45. What is the approximate density of titanium metal if the atomic radius of a titanium atom is 0.145 nm and the atoms form a body-centered cubic unit cell? (AW: Ti = 47.9 amu)

          (a) 0.1 g/cm³ (b) 1 g/cm³ (c) 5 g/cm³ (d) 25 g/cm³ (e) 30 g/cm³

Answer: (c)

9-46. Determine whether molybdenum crystallizes in a simple cubic, body centered cubic or face-centered cubic unit cell if the unit cell edge length is 0.3147 nm and the density of this metal is 10.2 g/cm³. (AW: Mo = 95.94 amu)

          (a) simple cubic (b) body-centered cubic (c) face-centered cubic

          (e) impossible to determine from the information given

Answer: (b)

9-47. Which of the following metals crystallizes in a face-centered cubic unit cell with a cell edge length of 0.3608 nm if the density of the metal is 8.95 g/cm³?

          (a) Na, 23.0 g/mol (b) Ca, 40.1 g/mol (c) Ti, 47.9 g/mol

           (d) Cu, 63.5 g/mol (e) Au, 197.0 g/mol

Answer: (d)

9-48. Tungsten crystallizes in a cubic unit cell with a cell edge of 0.3981 nm. The density of tungsten is 19.35 g/cm³. Calculate the number of atoms per unit cell. (AW: W = 183.85 g/mol)

          (a) 1 (b) 2 (c) 3 (d) 4 (e) 8

Answer: (d)

9-49. Iron crystallizes in a cubic unit cell with a cell edge of 0.2866 nm. The density of iron is 7.875 g/cm³. Calculate the number of atoms per unit cell. (AW: Fe = 55.847 g/mol)

          (a) 1 (b) 2 (c) 3 (d) 4 (e) 8

Answer: (b)

9-50. Diamond crystallizes in a cubic unit cell with unique carbon atoms at the positions 0,0,0; 1/2,1/2,0; 1/2,0,1/2; 0,1/2,1/2; 1/4,1/4,1/4; 1/4,3/4,3/4; 3/4,1/4,3/4 and 3/4,3/4,1/4. If the density of diamond is 3.515 g/cm³, calculate the unit cell edge length

Answer: This structure suggests 8 carbon atoms per unit cell,

when this is combined with the atomic weight of carbon and the density

of diamond, we get a unit cell volume that gives a unit cell edge of 0.3567 nm.

9-51. The metal chromium has an atomic weight of 52.0 amu and crystallizes in a body-centered cubic structure with a density of 7.12 g/cm³. What is the volume of the unit cell?

          (a) 1.21 x 10^-23 cm³ (b) 2.43 x 10^-23 cm³ (c) 4.86 x 10^-23 cm³

          (d) 14.6 cm³ (e) 7.32 cm³

Answer: (b)

9-52. Use the answer to the previous question to determine the metallic radius of a chromium atom.

(a) 2.90 x 10^-8 cm (b) 1.45 x 10^-8 cm (c) 1.26 x 10^-8 cm

          (d) 1.79 x 10^-8 cm (e) 2.05 x 10^-8 cm

Answer: (c)

9-53. Calculate the atomic radius of an argon atom if argon crystallizes at low temperature in a face-centered cubic unit cell with a density of 1.623 g/cm³.

Answer: 0.1933 nm

9-54. Calculate the atomic radius of the Ag atom if silver crystallizes in a face-centered cubic unit cell with a cell edge of 0.4086 nm.

Answer: 0.1445 nm

9-55. Cesium iodide consists of a simple cubic lattice of l^- ions with Cs⁺ ions in the cubic holes. If the cell edge length is 0.445 nm, what is the Cs—I interatomic distance?

           (a) 0.193 nm (b) 0.314 nm (c) 0.385 nm (d) 0.629 nm (e) 0.770 nm

Answer: (c)

9-56. NaH crystallizes with a structure similar to NaCl. If the unit cell edge length in this crystal is 0.4880 nm, calculate the average Na—H bond length in this crystal.

Answer: The average Na-H bond length is half the unit cell = 0.244 nm

Integrated Questions

Use the following information to answer questions 57-59.

Barium sulfide crystallizes in a cubic unit cell with an edge length of 0.638 nm with atoms in the following positions: S^2- = 0,0,0; 1/2,1/2,0; 1/2,0,1/2; 0,1/2,1/2 and Ba²⁺ = 1/2,1/2,1/2; 1/2,0,0; 0,1/2,0; 0,0,1/2

9-57. This unit cell would best be described as:

          (a) simple cubic (b) body-centered cubic (c) face-centered cubic

          (d) hexagonal closest packed (e) none of the above

Answer: (c)

9-58. Each unit cell contains how many Ba²⁺ and S^2- ions?

          (a) 1 Ba²⁺ and 1 S^2-           (b) 2 Ba²⁺ and 2 S^2-

          (c) 2 Ba²⁺ and 4 S^2-           (d) 4 Ba²⁺ and 2 S^2-

           (e) 4 Ba²⁺ and 4 S^2-

Answer: (e)

9-59. What is the radius of the Ba²⁺ ion? Assume that the Ba²⁺ and S^2- ions touch and that the radius of the S^2- ion is 0.184 nm.

           (a) 0.135 nm (b) 0.267 nm (c) 0.270 nm (d) 0.276 nm (e) 0.368 nm

Answer: (a)

9-60. A compound of unknown formula crystallizes in a body-centered cubic unit cell with M atoms at 0,0,0 and 1/2,1/2,1/2 and with X atoms on the six faces. What is the empirical formula of this compound?

          (a) MX (b) M₂X (c) MX₂ (d) M₂X₃ (e) M₃X₂

Answer: (d)

9-61. What is the coordination number of the M atom in the previous question?

          (a) 2 (b) 4 (c) 6 (d) 8 (e) 12

Answer: (c)

9-62. What is the shortest distance between two X atoms in this structure?

           (a) a/√2 (b) a (c) √2 a (d) (2 √2) a (e) none of these

Answer: (a)

9-63. Cuprite is the name of a mineral that crystallizes in a cubic unit cell for which the cell edge is 0.4270 nm. The positions of the unique atoms are described by the following coordinates: O = 0,0,0 and 1/2, 1/2,1/2 and Cu = 1/4,1/4,1/4; 1/4,3/4,3/4; 3/4,1/4,3/4; 3/4,3/4,1/4 How many net atoms of each type are contained within the unit cell? What is the empirical formula of this compound? What is the oxidation number of the Cu atom in this compound? What are the coordination numbers of the Cu and O atoms in this compound? Is this a simple cubic, body-centered cubic, or face-centered cubic unit cell? What is the Cu—O interatomic distance in nm?

9-64. Rhenium oxide crystallizes in a cubic unit cell for which the cell edge is 0.3751 nm. The positions of the unique atoms are described by the following coordinates: Re = 0,0,0 and O = 0,0,1/2; 0,1/2,0; 1/2,0,0 How many net atoms of each type are contained within the unit cell? What is the empirical formula of this compound? What is the oxidation number of the Re atom in this compound? What are the coordination numbers of the Re and O atoms in this compound? Is this a simple cubic, body-centered cubic, or face-centered cubic unit cell? What is the Re—O interatomic distance in nm?

9-65. Potassium magnesium fluoride crystallizes in a cubic unit cell for which the cell edge is 0.3973 nm. The positions of the unique atoms are described by the following coordinates: K = 0,0,0; Mg = 1/2,1/2,1/2; and F = 0,1/2,1/2; 1/2,0,1/2; 1/2,1/2,0 How many net atoms of each type are contained within the unit cell? What is the empirical formula of this compound? What is the oxidation number of the Mg atom in this compound? What are the coordination numbers of the K and Mg atoms in this compound? Is this a simple cubic, body-centered cubic, or face-centered cubic unit cell? What is the Mg—F inter-atomic distance in nm?

9-66. Zirconium carbide crystallizes in a cubic unit cell for which the cell edge is 0.4683 nm. The positions of the unique atoms are described by the following coordinates: Zr = 0,0,0; 0,1/2,1/2; 1/2,0,1/2; 1/2,1/2,0 and C = 1/2,1/2,1/2; 1/2,0,0; 0,1/2,0; 0,0,1/2 How many net atoms of each type are contained within the unit cell? What is the empirical formula of this compound? What is the oxidation number of the Zr atom in this compound? What are the coordination numbers of the Zr and C atoms in this compound? Is this a simple cubic, body-centered cubic, or face-centered cubic unit cell? What is the Zr—C inter-atomic distance in nm?

9-67. Gallium arsenide is a light-sensitive compound used in photocells, which crystallizes in a cubic unit cell for which the cell edge is 0.5653 nm. The positions of the unique atoms are described by the following coordinates: Ga = 0,0,0; 0,1/2,1/2; 1/2,0,1/2; 1/2,1/2,0 and As = 1/4,1/4,1/4; 1/4,3/4,3/4; 3/4,1/4,3/4; 3/4,3/4,1/4. How many net atoms of each type are contained within the unit cell? What is the empirical formula of this compound? If gallium is in Group IlIA and arsenic is in Group VA of the periodic table, what is the oxidation number of the Ga atom in this compound? What are the coordination numbers of the Ga and As atoms in this compound? Is this a simple cubic, body-centered cubic, or face-centered cubic unit cell? What is the Ga—As interatomic distance in nm?

9-68. Cuprous nitride crystallizes in a cubic unit cell for which the cell edge is 0.3814 nm. The positions of the unique atoms are described by the following coordinates: N = 0,0,0 and Cu = 0,0,1/2; 0,1/2,0; 1/2, 0 How many net atoms of each type are contained within the unit cell? What is the empirical formula of this compound? What is the oxidation number of the Cu atom in this compound? What are the coordination numbers of the Cu and N atoms in this compound? Is this a simple cubic, body-centered cubic, or face-centered cubic unit cell? What is the Cu—N interatomic distance in nm?

9-69. A compound that contains only copper and gold atoms crystallizes in a cubic unit cell for which the cell edge is 0.3748 nm. The positions of the unique atoms are described by the following coordinates: Au = 0,0,0 and Cu = 0,1/2,1/2; 1/2,0,1/2; 1/2,1/2,0 How many net atoms of each type are contained within the unit cell? What is the empirical formula of this compound? What is the coordination number of the Au atoms? There is no atom at 1/2,1/2,1/2 in this unit cell. If there were, what would be its coordination number? Is this a simple cubic, body-centered cubic, or face-centered cubic unit cell? What is the shortest distance between Cu atoms in this unit cell?