29_InstSolManual_PDF_Part1

29_InstSolManual_PDF_Part1 - ATOMS, MOLECULES, AND SOLIDS...

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Unformatted text preview: ATOMS, MOLECULES, AND SOLIDS 29 7. B 8. C 9. C 10. D Answers to Multiple-Choice Problems 1. A, C 2. A, D 3. B, D 4. B 5. A, D 6. A, B, E Solutions to Problems 29.1. Set Up: l 5 0, 1, 2, c, n 2 1. ml 5 0, 61, 62, c, 6l. Solve: l 5 0: ml 5 0. l 5 1: ml 5 1, 0, 21. l 5 2: m l 5 2, 1, 0, 21, 22. There is one state for l 5 0, three for l 5 1, and five for l 5 2. The total number of states is 1 1 3 1 5 5 9. 29.2. Set Up: L z 5 mlU. ml 5 0, 61, 62, c, 6l. L 5 "l 1 l 1 1 2 U. cos u 5 L z / L. Solve: (a) The largest L z is for ml 5 3 and is L z 5 3U. (b) L 5 "3 1 3 1 1 2 U 5 2 "3 U 5 3.46U. L is larger than the maximum possible L z. 3U 2U (c) For L z 5 3U, cos u 5 and u 5 30.0°. For L z 5 2U, cos u 5 and u 5 54.7°. For L z 5 U, 2 "3 U 2 "3 U U 2U cos u 5 and u 5 73.2°. For L z 5 0, cos u 5 0 and u 5 90.0°. For L z 5 2U, cos u 5 and u 5 106.8°. 2 "3 U 2 "3 U 22U 23U For L z 5 22U, cos u 5 and u 5 125.3°. For L z 5 23U, cos u 5 and u 5 150.0°. 2 "3 U 2 "3 U Solve: (a) l 5 0: L 5 0, L z 5 0. l 5 1: L 5 "2 U, L z 5 U, 0, 2U. l 5 2: L 5 "6 U, L z 5 2U, U, 0, 2U, 22U. 114.1°, 144.7°. S Reflect: There is no state where L is totally aligned along the z axis. 29.3. Set Up: L 5 "l 1 l 1 1 2 U. L z 5 mlU. l 5 0, 1, 2, c, n 2 1. ml 5 0, 61, 62, c, 6l. cos u 5 L z / L. (b) In each case cos u 5 L z / L. L 5 0: u not defined. L 5 "2 U: 45.0°, 90.0°, 135.0°. L 5 "6 U: 35.3°, 65.9°, 90.0°, Solve: (a) l 5 0: L 5 0, L z 5 0. l 5 1: L 5 "2 U, L z 5 U, 0, 2U. l 5 2: L 5 "6 U, L z 5 2U, U, 0, 2U, 22U. l 5 3: (b) L 5 0: u not defined. L 5 "2 U: 45.0°, 90.0°, 135.0°. L 5 "6 U: 35.3°, 65.9°, 90.0°, 114.1°, 144.7°. L 5 2 "3 U: 153.4°. (c) The minimum angle is 26.6° and occurs for l 5 4, ml 5 14. The maximum angle is 153.4° and occurs for l 5 4, m l 5 24 54.7°, 73.2°, 90.0°, 106.8°, 125.3°, 150.0°. L 5 2 "5 U: 26.6°, 47.9°, 63.4°, 77.1°, 90.0°, 102.9°, 116.6°, 132.1°, L 5 2 "3 U, L z 5 3U, 2U, U, 0, 2U, 22U, 23U. l 5 4: L 5 2 "5 U, L z 5 4U, 3U, 2U, U, 0, 2U, 22U, 23U, 24U. 29.4. Set Up: L 5 "l 1 l 1 1 2 U. L z 5 mlU. l 5 0, 1, 2, c, n 2 1. ml 5 0, 61, 62, c, 6l. cos u 5 L z / L. 29-1 ...
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