Chapter 1 Problems 1, 2 , 3 = straightforward, intermediate, challenging Section 1.2 Matter and Model-Building Note : Consult the endpapers, appendices, and tables in the text whenever necessary in solving problems. For this chapter, Appendix B.3 may be particularly useful. Answers to odd-numbered problems appear in the back of the book. 1. A crystalline solid consists of atoms stacked up in a repeating lattice structure. Consider a crystal as shown in Figure P1.1a. The atoms reside at the corners of cubes of side L = 0.200 nm. One piece of evidence for the regular arrangement of atoms comes from the flat surfaces along which a crystal separates, or cleaves, when it is broken. Suppose this crystal cleaves along a face diagonal, as shown in Figure P1.1b. Calculate the spacing d between two adjacent atomic planes that separate when the crystal cleaves. Figure P1.1 Section 1.3 Density and Atomic Mass 2. Use information on the endpapers of this book to calculate the average density of the Earth. Where does the value fit among those listed in Tables 1.5 and 14.1? Look up the density of a typical surface rock like granite in another source and compare also to it. 3. The standard kilogram is a platinum-iridium cylinder 39.0 mm in height and 39.0 mm in diameter. What is the density of the material? 4. A major motor company displays a die-cast model of its first automobile, made from 9.35 kg of iron. To celebrate its hundredth year in business, a worker will recast the model in gold from the original dies. What mass of gold is needed to make the new model?
5. What mass of a material with density ρ is required to make a hollow spherical shell having inner radius r 1 and outer radius r 2 ? 6. Two spheres are cut from a certain uniform rock. One has radius 4.50 cm. The mass of the other is five times greater. Find its radius. 7. Calculate the mass of an atom of (a) helium, (b) iron, and (c) lead. Give your answers in grams. The atomic masses of these atoms are 4.00 u, 55.9 u, and 207 u, respectively. 8. The paragraph preceding Example 1.1 in the text mentions that the atomic mass of aluminum is 27.0 u = 27.0 × 1.66 × 10-27 kg. Example 1.1 itself says that 27.0 g of aluminum contains 6.02 × 10 23 atoms. (a) Prove that each one of these two statements implies the other. (b) What If? What if it’s not aluminum? Let M represent the numerical value of the mass of one atom of any chemical element in atomic mass units. Prove that
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