A. Crystal Structures. (Indicate solution.) 1. The second-order diffraction (n = 2) for a gold crystal is at an angle of 22.20 for X rays of 154 pm. What is the spacing between these crystal planes? 2. A topaz crystal has an interplanar spacing (d) of 1.36 (1 = 1 x 10-16 m). Calculate the wavelength of the X ray that should be used if e = 15.0 (assume n = 1). 3. Xrays of wavelength 2.63 were used to analyze a crystal. The angle of first-order diffraction (n = 1 in the Bragg equation) was 15.55 degrees. What is the spacing between crystal planes, and what would be the angle for second-order diffraction (n = 2)? 4. Calcium has a cubic closest packed structure as a solid. Assuming that calcium has an atomic radius of 197 pm, calculate the density of solid calcium. 5. A certain form of lead has a cubic closest packed structure with an edge length of 492 pm. Calculate the value of the atomic radius and the density of lead. 6. You are given a small bar of an unknown metal X. You find the density of the metal to be 10.5 g/cm'. An X-ray diffraction experiment measures the edge of the face- centered cubic unit cell as 4.09 (1 X = 100 m). Identify X. 7. The radius of gold is 144 pm, and the density is 19.32 g/cm. Does elemental gold have a face-centered cubic structure or a body-centered cubic structure? B. Metallurgy 1. Iron is present in the earth's crust in many types of minerals. The iron oxide minerals are hematite (Fe 0 ) and magnetite (Fe3O4). What is the oxidation state of iron in each mineral? The iron ions in magnetite are a mixture of Fe2+ and Fetions. What is the ratio of Fe3 to Feions in magnetite? The formula for magnetite is often written as Feo. Fe2O3. Does this make sense? Explain. 2. Silver is sometimes found in nature as large nuggets more often it is found mixed with other metals and their ores. Cyanide ion is often used to extract the silver by the following reaction that occurs in basic solutions I Ag(s) + CN (aq) + 0,(g) Ag(CN), (aq) Balance this equation by using the half-reaction method