29_InstSolManual_PDF_Part1

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

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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 ...
View Full Document

Ask a homework question - tutors are online