1. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 1 Electromagnetic Radiation Radiant energy that exhibits wavelength-like behavior and travels through space at the speed of light in a vacuum.

2. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 2 Waves Waves have 3 primary characteristics: 1.Wavelength: distance between two peaks in a wave. 2.Frequency: number of waves per second that pass a given point in space. 3.Speed: speed of light is 3.0  10 8 m/s.

3. Figure 7.1: The nature of waves. Note that the radiation with the shortest wavelength has the highest frequency.

4. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 4 Wavelength and frequency can be interconverted. c = = frequency (s  1 ) hertz = wavelength (m) c = speed of light (m s  1 ) 2.9979x10 8 m/s

5. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 5 Figure 7.2: Classification of electromagnetic radiation.

6. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 6 Nature of Matter Max Planck studied the radiation emitted by solid bodies heated to incandescence. energy can be gained or lost only in whole- number multiples of the quantity h.

7. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 7 Planck’s Constant  E = change in energy, in J h = Planck’s constant, 6.626  10  34 J s = frequency, in s  1 (absorbed or emitted) = wavelength, in m Transfer of energy is quantized, and can only occur in discrete units, called quanta.

8. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 8 The Energy of a Photon The blue color in fireworks is often achieved by heating copper (I) chloride to about 1200°C. Then the compound emits blue light having a wavelength of 450nm. What is the increment of energy (the quantum) that is emitted at 4.50 x 10 2 nm by CuCl?

9. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 9 Solution Equation ΔE = h  = c/ 2.9979 x 10 8 m/s = 6.66x10 14 s -1 4.50 x 10 -7 m So ΔE = h = (6.66x10 -34 J·s)(6.66x10 14 s -1 ) = 4.41 x 10 -19 J

10. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 10 Albert Einstein Electromagnetic radiation is itself quantized. Viewed as a stream of “particles” called photons. The energy of a photon : E = h

11. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 11 Energy and Mass Energy has mass E = mc 2 E = energy m = mass c = speed of light

12. 12 Energy and Mass E = mc 2 then, m = E/c 2 E photon = hc/ then the mass is: m = E/c 2 = hc  = h/ c c 2 (Hence the dual nature of light.)

13. Figure 7.4: Electromagnetic radiation exhibits wave properties and particulate properties.

14. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 14 Does a photon really have mass? Only in the relative sense– it has no rest mass. Electromagnetic radiation exhibits wave properties and characteristics of particulate matter. dual nature of light

15. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 15 Plank and Einstein Energy is quantized. It can occur only in discrete units called quanta. Electromagnetic radiation is dual natured; behaves as a wave and has properties of particulate matter.

16. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 16 Is the opposite true? Does matter that is normally assumed to be particulate exhibit wave properties? m = h/  c  = h/ m  *  = velocity

17. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 17 Calculate the  of a particle = wavelength, in m h = Planck’s constant, 6.626  10  34 J s = kg m 2 s  1 m = mass, in kg = velocity de Broglie’s Equation

18. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 18 Calculations of Wavelength Compare the wavelength for an electron (mass= 9.11 x 10 -31 kg) traveling at a speed of 1.0 x 10 7 m/s with that for a ball (mass = 0.10 kg) traveling at 35 m/s.

19. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 19 Full Circle ER has particulate properties. Electrons (particles) have wavelengths associated with them. ***Matter and Energy are not distinct*** Energy is a form of matter, and all matter has both wave and particulate properties.

20. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 20 Atomic Spectrum of Hydrogen H 2 gas – high energy spark – absorbs energy H-H bonds are broken, hydrogen becomes excited. (e- move up) When they drop back down….emit light. This is known as…..

21. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 21 The emission spectrum of the hydrogen atom.

22. Figure 7.6: (a) A continuous spectrum containing all wavelengths of visible light. (b) The hydrogen line spectrum contains only a few discrete wavelengths.

23. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 23 The hydrogen emission spectrum is called a line spectrum.

24. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 24 Atomic Spectrum of Hydrogen Continuous spectrum: Contains all the wavelengths of light. Line (discrete) spectrum: Contains only some of the wavelengths of light. WHY???

25. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 25 A change in energy from a high to a lower level would give a wavelength of light that can be calculated from Planck’s equation.

26. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 26 Figure 7.7: A change between two discrete energy levels emits a photon of light.

27. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 27 What would happen if the electron could move and from any energy level?

28. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 28 Only certain energies are allowed for the e- in the hydrogen. Thus, the energy levels and therefore the energy of the e- is quantized.

29. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 29 Bohr knew… Particle in motion moves in a straight line; can travel in a circle only by force. (force of p+ in the nucleus) A charged particle under acceleration radiates energy. An e-; always changes direction– acceleration. Therefore: an e- should emit light, lose energy and be drawn into the nucleus.

30. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 30 Bohr Model (must also agree w/ the H-spectrum) Assumed that the angular momentum (mass x velocity x orbital radius) of the electron could only occur in certain increments. This gave the hydrogen atom energy levels consistent with the hydrogen emission spectrum.

31. Figure 7.8: Electronic transitions in the Bohr model for the hydrogen atom.

32. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 32 The Bohr Model E = energy of the levels in the H-atom z = nuclear charge (for H, z = 1) n = an integer (larger the integer the larger the orbital) The electron in a hydrogen atom moves around the nucleus only in certain allowed circular orbits.

33. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 33 (-) sign means: the energy of the e- bound to the nucleus is lower than it would be if the e- were at an infinite distance (n = ∞) from the nucleus, where there is no interaction and the energy is zero.

34. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 34 The Bohr Model Ground State: The lowest possible energy state for an atom (n = 1). (most negative energy)

35. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 35 Energy Changes in the Hydrogen Atom  E = E final state  E initial state (negative– lost energy by emitting photon and becomes more stable) Wavelength of the photon

36. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 36 Example Calculate the energy required to excite the hydrogen electron from level n = 1 to level n = 2. Calculate the wavelength of light that must be absorbed.

37. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 37

38. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 38 Two Important Things The model correctly fits the quantized energy levels of the H atom and postulates only certain allowed circular orbits for the electron. As the electron becomes more tightly bound, its energy becomes more (-) relative to the zero point of infinite distance. As the e - is brought closer to the nucleus it releases energy.

39. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 39 General equation for electrons moving  E = E final state  E initial state =-2.178 x 10 -18 J(1/n final 2 -1/n initial 2 )

40. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 40 Bohr Model INCORRECT!!!! Electrons do not move around the nucleus in circular orbits.

41. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 41 Wave-generating apparatus. Heisenberg, de Broglie, and Schrodinger Wave Mechanics or Quantum mechanics

42. Figure 7.9: The standing waves caused by the vibration of a guitar string fastened at both ends. Each dot represents a node (a point of zero displacement).

43. Figure 7.10: The hydrogen electron visualized as a standing wave around the nucleus. *Correspond to a whole number of wavelengths.*

44. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 44 Quantum Mechanics Based on the wave properties of the atom  = wave function = mathematical operator E = total energy of the atom A specific wave function is often called an orbital.

45. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 45 This is not a Bohr orbital by any means. The 1s orbital is not a circular orbit. How is the e- moving? I don’t know!!!

46. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 46 Heisenberg Uncertainty Principle x = position mv = momentum h = Planck’s constant The more accurately we know a particle’s position, the less accurately we can know its momentum.

47. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 47 Probability Distribution 4 square of the wave function 4 probability of finding an electron at a given position Radial probability distribution is the probability distribution in each spherical shell.

48. Figure 7.11: (a) The probability distribution for the hydrogen 1s orbital in three dimensional space. (b) The probability of finding the electron at points along a line drawn from the nucleus outward in any direction for the hydrogen 1s orbital.

49. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 49 Figure 7.12: (a) Cross section of the hydrogen 1s orbital probability distribution divided into successive thin spherical shells. (b) The radial probability distribution.

50. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 50 Quantum Numbers (QN) properties of the orbitals: 1.Principal QN (n = 1, 2, 3,...) - related to size and energy of the orbital. 2.Angular Momentum QN (l = 0 to n  1) - relates to shape of the orbital. [l = 0 is called s orbital, l= 1 is called p, l= 2 is called d, l= 3 is called f] (sometimes called subshell) 3.Magnetic QN (m l = l to  l, including 0) - relates to orientation of the orbital in space relative to other orbitals. 4.Electron Spin QN (m s = + 1 / 2,  1 / 2 ) - relates to the spin states of the electrons.

51. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 51

52. Figure 7.13: Two representations of the hydrogen 1s, 2s, and 3s orbitals. Nodes = area of Zero probability

53. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 53 Figure 7.14: Representation of the 2p orbitals. (a) The electron probability distributed for a 2p orbital. (b) The boundary surface representations of all three 2p orbitals.

54. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 54 Figure 7.16: Representation of the 3d orbitals.

55. Figure 7.17: Representation of the 4f orbitals in terms of their boundary surface.

56. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 56 Figure 7.19: A picture of the spinning electron.

57. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 57 degenerate All orbitals with the same value of n have the same energy. True??? Or not??

58. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 58 Pauli Exclusion Principle In a given atom, no two electrons can have the same set of four quantum numbers (n, l, m l, m s ). Therefore, an orbital can hold only two electrons, and they must have opposite spins.

59. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 59 Aufbau Principle As protons are added one by one to the nucleus to build up the elements, electrons are similarly added to these hydrogen-like orbitals.

60. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 60 Hund’s Rule The lowest energy configuration for an atom is the one having the maximum number of unpaired electrons allowed by the Pauli principle in a particular set of degenerate orbitals.

61. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 61 Valence Electrons The electrons in the outermost principle quantum level of an atom. Inner electrons are called core electrons.

62. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 62 Figure 7.25: The electron configurations in the type of orbital occupied last for the first 18 elements.

63. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 63 Figure 7.26: Electron configurations for potassium through krypton.

64. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 64 Broad Periodic Table Classifications Representative Elements (main group): filling s and p orbitals (Na, Al, Ne, O) Transition Elements: filling d orbitals (Fe, Co, Ni) Lanthanide and Actinide Series (inner transition elements): filling 4f and 5f orbitals (Eu, Am, Es)

65. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 65 Figure 7.27: The orbitals being filled for elements in various parts of the periodic table.

66. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 66 Figure 7.28: The periodic table with atomic symbols, atomic numbers, and partial electron configurations.

67. Figure 7.29: A diagram that summarizes the order in which the orbitals fill in polyelectronic atoms.

68. 68 Determine the expected electron configurations for each of the following: S Ba Ni 2+ Eu Ti + React 8 [Ar]3d 8 [Ne]3s 2 3p 4 [Xe]6s 2 [Xe]6s 2 5d 1 4f 6 [Ar]3d 3

69. 69 Z eff (Effective nuclear charge) Treat the e - as if it were moving in a field of charge that is the net result of the nuclear attraction and the average repulsions of all the other electrons. Shielded (screened) from the nuclear charge by the nuclear repulsion of the other e - As the # of e- between the nucleus and the valence electrons increases Z eff decreases

70. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 70 Polyelectronic atoms The orbitals are not degenerate, they vary in energy E ns < E np < E nd < E nf Penetration effect- small but significant amt of time near the nucleus (penetrates the nucleus more strongly)

71. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 71 Figure 7.20: A comparison of the radial probability distributions of the 2s and 2p orbitals.

72. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 72 Figure 7.21: (a) The radial probability distribution for an electron in a 3s orbital. (b) The radial probability distribution for the 3s, 3p, and 3d orbitals.

73. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 73 Figure 7.22: The orders of the energies of the orbitals in the first three levels of polyelectronic atoms.

74. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 74 The more effectively an orbital allows its e - to penetrate the shielding electrons to be close to the nuclear charge, the lower the energy of that orbital.

75. Three things that effect trends 1. Down a group: increase the value of n, and increase the # of core electrons; better shielding and weaker attraction between the nucleus and out shell electrons. 2. Across a period: larger nuclear charge (p+ increase), increase # of valence e-, but in the same shell (poor shielding), stronger interaction. 3. Type of orbital holding the shielding e-: best shielding s>p>d>f 75

76. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 76 Ionization Energy The quantity of energy required to remove an electron from the gaseous atom or ion.

77. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 77 Periodic Trends First ionization energy: increases from left to right across a period; decreases going down a group.

78. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 78 Figure 7.32: Trends in ionization energies (kJ/mol) for the representative elements.

79. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 79 Electron Affinity The energy change associated with the addition of an electron to a gaseous atom. X(g) + e   X  (g)

80. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 80 Periodic Trends Atomic Radii: decrease going from left to right across a period; increase going down a group.

81. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 81 Figure 7.34: The radius of an atom (r) is defined as half the distance between the nuclei in a molecule consisting of identical atoms.

82. Figure 7.35: Atomic radii (in picometers ) for selected atoms.

83. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 83 Information Contained in the Periodic Table 1.Each group member has the same valence electron configuration (these electrons primarily determine an atom’s chemistry). 2.The electron configuration of any representative element. 3.Certain groups have special names (alkali metals, halogens, etc). 4.Metals and nonmetals are characterized by their chemical and physical properties.