CH 29 - ATOMS MOLECULES AND SOLIDS 29 7 B 8 C 9 C 10 D...

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29-1 A TOMS , M OLECULES , AND S OLIDS 29 Answers to Multiple-Choice Problems 1. A, C 2. A, D 3. B, D 4. B 5. A, D 6. A, B, E 7. B 8. C 9. C 10. D Solutions to Problems 29.1. Set Up: 1, Solve: 0, 1, 0, There is one state for three for and five for The total number of states is 29.2. Set Up: Solve: (a) The largest is for and is (b) L is larger than the maximum possible (c) For and For and For and For and For and For and For and 29.3. Set Up: 1, Solve: (a) 0, 0, (b) In each case not defined. Reflect: There is no state where is totally aligned along the z axis. 29.4. Set Up: 1, Solve: (a) 0, 0, 0, 0, (b) not defined. (c) The minimum angle is and occurs for The maximum angle is and occurs for m l 5 2 4 l 5 4, 153.4° m l 5 1 4. l 5 4, 26.6° 153.4°. 132.1°, 116.6°, 102.9°, 90.0°, 77.1°, 63.4°, 47.9°, 26.6°, L 5 2 " 5 U : 150.0°. 125.3°, 106.8°, 90.0°, 73.2°, 54.7°, L 5 2 " 3 U : 144.7°. 114.1°, 90.0°, 65.9°, 35.3°, L 5 " 6 U : 135.0°. 90.0°, 45.0°, L 5 " 2 U : u L 5 0: 2 4 U . 2 3 U , 2 2 U , 2 U , U , 2 U , 3 U , L z 5 4 U , L 5 2 " 5 U , l 5 4: 2 3 U . 2 2 U , 2 U , U , 2 U , L z 5 3 U , L 5 2 " 3 U , l 5 3: 2 2 U . 2 U , U , L z 5 2 U , L 5 " 6 U , l 5 2: 2 U . L z 5 U , L 5 " 2 U , l 5 1: L z 5 0. L 5 0, l 5 0: cos u 5 L z / L . 6 l . 6 2, c , 6 1, m l 5 0, n 2 1. 2, c , l 5 0, L z 5 m l U . L 5 " l 1 l 1 1 2 U . L S 144.7°. 114.1°, 90.0°, 65.9°, 35.3°, L 5 " 6 U : 135.0°. 90.0°, 45.0°, L 5 " 2 U : u L 5 0: cos u 5 L z / L . 2 2 U . 2 U , U , L z 5 2 U , L 5 " 6 U , l 5 2: 2 U . L z 5 U , L 5 " 2 U , l 5 1: L z 5 0. L 5 0, l 5 0: cos u 5 L z / L . 6 l . 6 2, c , 6 1, m l 5 0, n 2 1. 2, c , l 5 0, L z 5 m l U . L 5 " l 1 l 1 1 2 U . u 5 150.0°. cos u 5 2 3 U 2 " 3 U L z 5 2 3 U , u 5 125.3°. cos u 5 2 2 U 2 " 3 U L z 5 2 2 U , u 5 106.8°. cos u 5 2 U 2 " 3 U L z 5 2 U , u 5 90.0°. cos u 5 0 L z 5 0, u 5 73.2°. cos u 5 U 2 " 3 U L z 5 U , u 5 54.7°. cos u 5 2 U 2 " 3 U L z 5 2 U , u 5 30.0°. cos u 5 3 U 2 " 3 U L z 5 3 U , L z . L 5 " 3 1 3 1 1 2 U 5 2 " 3 U 5 3.46 U . L z 5 3 U . m l 5 3 L z cos u 5 L z / L . L 5 " l 1 l 1 1 2 U . 6 l . 6 2, c , 6 1, m l 5 0, L z 5 m l U . 1 1 3 1 5 5 9. l 5 2. l 5 1, l 5 0, 2 2. 2 1, m l 5 2, l 5 2: 2 1. m l 5 1, l 5 1: m l 5 0. l 5 0: 6 l . 6 2, c , 6 1, m l 5 0, n 2 1. 2, c , l 5 0,
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29.5. Set Up: For the N shell Solve: (a) The smallest l is so (b) The largest l is so (c) Let the chosen direction be the z axis. The largest m is (d) The maximum value is (e) Reflect: The orbital and spin angular momenta are of comparable sizes. 29.6. Set Up: d means and means Solve: (a) There are ten 3 d states: with for each. (b) There are no states. These states would have But the maximum l is and doesn’t occur for 29.7. Set Up: g means with and Solve: (a) There are eighteen 5 g states: with for each. (b) The largest is for the most negative The most negative is and (c) The smallest is for the largest positive which is and Reflect: The minimum angle between and the z axis is for and for that 29.8. Set Up: Classically, For a solid uniform sphere, For an electron, Solve: gives Note that gives that a point on the surface has which greatly exceeds the speed of light. 29.9. Set Up: Solve: 29.10. Set Up: Solve: (a) (b) There are 25 combinations of l , values. For each, s can be or Therefore, electrons can be placed into the shell.
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