1. So that k k E 5 = - E 2 = - 5 2 2 2 = -8.71476 x 10 -20 J = -5.44673 x 10 -19 J Therefore = E 5 - E 2 = 4.57525 x 10 -19 J Now so 631

2. So that k k E 5 = - E 2 = - 5 2 2 2 = -8.71476 x 10 -20 J = -5.44673 x 10 -19 J Therefore = E 5 - E 2 = 4.57525 x 10 -19 J Now so = 4.34174 x 10 -7 m 632

3. Definition: The ionization energy is the energy required to remove an electron from one mole of a substance in its ground state in the gas phase. 633

4. Definition: The ionization energy is the energy required to remove an electron from one mole of a substance in its ground state in the gas phase. For example, for substance X, X (g) X (g) + + e - 634

5. Problem: Calculate the ionization energy for the hydrogen atom. (k = 2.17869 x 10 -18 J and N A = 6.02214 x 10 23 mol -1 ). 635

6. Problem: Calculate the ionization energy for the hydrogen atom. (k = 2.17869 x 10 -18 J and N A = 6.02214 x 10 23 mol -1 ). The process is: H (g) H + (g) + e - 636

7. Problem: Calculate the ionization energy for the hydrogen atom. (k = 2.17869 x 10 -18 J and N A = 6.02214 x 10 23 mol -1 ). The process is: H (g) H + (g) + e - The quantum numbers are n l = 1 and n u = (because the electron is completely removed from the atom). 637

8. Therefore = - E 1 = 0 - (-k) 638

9. Therefore = - E 1 = 0 - (-k) = k = 2.17869 x 10 -18 J 639

10. Therefore = - E 1 = 0 - (-k) = k = 2.17869 x 10 -18 J This corresponds to the energy to remove an electron from one atom. 640

11. Therefore = - E 1 = 0 - (-k) = k = 2.17869 x 10 -18 J This corresponds to the energy to remove an electron from one atom. To get the ionization potential, we need the energy expended for 1 mole of atoms. Hence 641

12. Therefore = - E 1 = 0 - (-k) = k = 2.17869 x 10 -18 J This corresponds to the energy to remove an electron from one atom. To get the ionization potential, we need the energy expended for 1 mole of atoms. Hence Ionization energy = 2.17869 x 10 -18 J (6.02214 x 10 23 mol -1 ) = 1.31204 x 10 6 J mol -1 642

13. Definition: The electron affinity is the energy required to add an electron to one mole of a substance in its ground state in the gas phase. 643

14. Definition: The electron affinity is the energy required to add an electron to one mole of a substance in its ground state in the gas phase. For example, for substance Y, Y (g) + e - Y (g) - 644

15. Exercise: Calculate the electron affinity for the hydrogen positive ion. 645

16. Exercise: Calculate the electron affinity for the hydrogen positive ion. (k = 2.17869 x 10 -18 J and N A = 6.02214 x 10 23 mol -1 ). 646

17. Exercise: Calculate the electron affinity for the hydrogen positive ion. (k = 2.17869 x 10 -18 J and N A = 6.02214 x 10 23 mol -1 ). (By convention the electron affinity is the difference between the energy of the product formed and the energy of the starting species, in this case E(H) – E(H + ) ). 647

18. How does the Schrödinger eq. do for more complex systems, e.g. He atom, CO molecule, etcetera? 648

19. How does the Schrödinger eq. do for more complex systems, e.g. He atom, CO molecule, etcetera? It turns out that the Schrödinger equation is too complex to solve exactly for systems with more than one electron. However, approximate solutions have been obtained which match up with experimental results. 649

20. How does the Schrödinger eq. do for more complex systems, e.g. He atom, CO molecule, etcetera? It turns out that the Schrödinger equation is too complex to solve exactly for systems with more than one electron. However, approximate solutions have been obtained which match up with experimental results. For example, some of the energy levels of the He atom have been determined to around 10 significant figures! The ground state energy level for He is known to over 40 significant figures! 650

21. It is generally accepted that the Schrödinger equation provides a very good description of the ground and excited states of atomic and molecular systems. 651

22. It is generally accepted that the Schrödinger equation provides a very good description of the ground and excited states of atomic and molecular systems. The work of Schrödinger was one of the landmark breakthroughs in all of science. 652

23. The fact that the H atom can be solved exactly has turned out to be important for studying more complex atoms. 653

24. The fact that the H atom can be solved exactly has turned out to be important for studying more complex atoms. It is assumed the electronic behavior in many-electron atoms is not too different from that in the H atom. 654

25. The fact that the H atom can be solved exactly has turned out to be important for studying more complex atoms. It is assumed the electronic behavior in many-electron atoms is not too different from that in the H atom. So the results from the H atom can be used as a first approximation for describing the behavior of the electrons in more complex atoms. 655

26. The fact that the H atom can be solved exactly has turned out to be important for studying more complex atoms. It is assumed the electronic behavior in many-electron atoms is not too different from that in the H atom. So the results from the H atom can be used as a first approximation for describing the behavior of the electrons in more complex atoms. The justification for this approach is that it works! 656

27. Some final thoughts on the Bohr model 657

28. Some final thoughts on the Bohr model Obviously the result obtained by Bohr was very useful to Schrödinger. 658

29. Some final thoughts on the Bohr model Obviously the result obtained by Bohr was very useful to Schrödinger. Connection with Heisenberg Uncertainty Principle. 659

30. Some final thoughts on the Bohr model Obviously the result obtained by Bohr was very useful to Schrödinger. Connection with Heisenberg Uncertainty Principle. According to Bohr, an electron is always circling around the nucleus in a well specified orbit. 660

31. Some final thoughts on the Bohr model Obviously the result obtained by Bohr was very useful to Schrödinger. Connection with Heisenberg Uncertainty Principle. According to Bohr, an electron is always circling around the nucleus in a well specified orbit. Although the electron may switch from one orbit to another, as in an emission or absorption process, its position in an orbit at a specific distance from the nucleus is fixed once we know its energy state. 661

32. A simplified Heisenberg argument. 662

33. A simplified Heisenberg argument. Suppose the energy of the electron in the H atom is all kinetic energy (the argument could be modified to take account that there is a second energy component). 663

34. A simplified Heisenberg argument. Suppose the energy of the electron in the H atom is all kinetic energy (the argument could be modified to take account that there is a second energy component). m 2 v 2 p 2 E = ½ m v 2 = = 2m 2m 664

35. Now if E is known exactly, then so is p, hence the error in p is zero, so = 0. 665

36. Now if E is known exactly, then so is p, hence the error in p is zero, so = 0. Now 666

37. Now if E is known exactly, then so is p, hence the error in p is zero, so = 0. Now so 667

38. Now if E is known exactly, then so is p, hence the error in p is zero, so = 0. Now so In other words, the electron cannot be in a well defined orbit! 668

39. Now if E is known exactly, then so is p, hence the error in p is zero, so = 0. Now so In other words, the electron cannot be in a well defined orbit! The electron could be anywhere!!!!! 669

40. Now if E is known exactly, then so is p, hence the error in p is zero, so = 0. Now so In other words, the electron cannot be in a well defined orbit! The electron could be anywhere!!!!! This is the death certificate of the Bohr model. 670

41. We learn from quantum theory that we should never think of the electron as being confined to a certain path. 671

42. We learn from quantum theory that we should never think of the electron as being confined to a certain path. It is more appropriate to speak of the probability of locating the electron in a certain region of space. 672

43. We learn from quantum theory that we should never think of the electron as being confined to a certain path. It is more appropriate to speak of the probability of locating the electron in a certain region of space. This probability is given by the square of the wave function. 673

44. Since the electron has no well-defined position in the atom, it is most convenient to use terms like: 674

45. Since the electron has no well-defined position in the atom, it is most convenient to use terms like: Electron density 675

46. Since the electron has no well-defined position in the atom, it is most convenient to use terms like: Electron density Electron Charge Cloud 676

47. Since the electron has no well-defined position in the atom, it is most convenient to use terms like: Electron density Electron Charge Cloud Charge Cloud to represent the probability concept. 677

48. To distinguish the quantum mechanical description from Bohr’s model, the word “orbit” is replaced with the term orbital or atomic orbital. 678

49. To distinguish the quantum mechanical description from Bohr’s model, the word “orbit” is replaced with the term orbital or atomic orbital. Atomic orbital means exactly the same as wave function describing one electron. 679

50. When we say that an electron is in a certain orbital, we mean that the distribution of the electron density or the probability of locating the electron in space is described by the square of the wave function associated with that energy state. 680

51. When we say that an electron is in a certain orbital, we mean that the distribution of the electron density or the probability of locating the electron in space is described by the square of the wave function associated with that energy state. For each atomic orbital, there is an associated energy as well as an associated electron density. 681

52. Quantum Numbers 682

53. Quantum Numbers From quantum mechanics it is found that four quantum numbers are necessary to describe the placement of electron(s) in the hydrogen atom or in any other atom. 683

54. Quantum Numbers From quantum mechanics it is found that four quantum numbers are necessary to describe the placement of electron(s) in the hydrogen atom or in any other atom. The quantum numbers are of significance if we wish to understand the sizes and shapes of orbitals and their associated energy levels. 684

55. These are important, because the size, shape, and energy of the electron cloud influence the behavior of atoms. 685

56. 1. Principal quantum Number 686

57. 1. Principal quantum Number Symbol n 687

58. 1. Principal quantum Number Symbol n The principal quantum number determines the energy of an orbital (remember that E n ). 688

59. 1. Principal quantum Number Symbol n The principal quantum number determines the energy of an orbital (remember that E n ). The principal quantum number also characterizes the “size” of the orbital. 689

60. 1. Principal quantum Number Symbol n The principal quantum number determines the energy of an orbital (remember that E n ). The principal quantum number also characterizes the “size” of the orbital. The larger the value of n, the larger the orbital, and the farther on the average the electron is from the nucleus. 690

61. Roughly speaking, the “size” of an orbital is proportional to n 2. As n increases, the “size” differences among orbitals becomes very large. 691

62. Roughly speaking, the “size” of an orbital is proportional to n 2. As n increases, the “size” differences among orbitals becomes very large. Because the “sizes” of orbitals with different n values differ so significantly, the regions of space corresponding to particular values of n are referred to as shells around the nucleus. 692

63. Shell K L M N O … n 1 2 3 4 5 … 693

64. 2. The Angular Momentum Quantum Number Also called the azimuthal quantum number. 694

65. 2. The Angular Momentum Quantum Number Also called the azimuthal quantum number. Symbol l 695

66. 2. The Angular Momentum Quantum Number Also called the azimuthal quantum number. Symbol l The angular momentum quantum number determines the “shape” of the orbitals. 696

67. 2. The Angular Momentum Quantum Number Also called the azimuthal quantum number. Symbol l The angular momentum quantum number determines the “shape” of the orbitals. The possible values of l depend on the value of the principal quantum number n. 697

68. For a given value of n, l takes values from 0 to n – 1 (in steps of 1). 698

69. For a given value of n, l takes values from 0 to n – 1 (in steps of 1). If n = 1, there is only one value of l, that is l = n – 1 = 1 – 1 = 0 699

70. For a given value of n, l takes values from 0 to n – 1 (in steps of 1). If n = 1, there is only one value of l, that is l = n – 1 = 1 – 1 = 0 If n = 2, there are two values of l, that is l = 0 and l = 1 700

71. For a given value of n, l takes values from 0 to n – 1 (in steps of 1). If n = 1, there is only one value of l, that is l = n – 1 = 1 – 1 = 0 If n = 2, there are two values of l, that is l = 0 and l = 1 If n = 5, there are five values of l, that is l = 0, l = 1, l = 2, l = 3, l = 4 701

72. Each value of l for a given value of n defines a subshell. 702

73. Each value of l for a given value of n defines a subshell. The following letters are used as symbols to designate the different values of l. 703

74. Each value of l for a given value of n defines a subshell. The following letters are used as symbols to designate the different values of l. l value 0 1 2 3 4 5 … orbital designation s p d f g h …. 704

75. 3. The Magnetic quantum Number 705

76. 3. The Magnetic quantum Number Symbol m l 706

77. 3. The Magnetic quantum Number Symbol m l This quantum number is used to explain the additional lines that appear in the spectra of atoms when they emit light while confined in a magnetic field. 707

78. The magnetic quantum number determines the orientation of the orbital in space. 708

79. The magnetic quantum number determines the orientation of the orbital in space. The value of m l depends on the value of l. For a given value of l there are 2 l + 1 integer values of m l ranging from - l to l. 709

80. The magnetic quantum number determines the orientation of the orbital in space. The value of m l depends on the value of l. For a given value of l there are 2 l + 1 integer values of m l ranging from - l to l. Examples: If l = 0, m l = 0 710

81. The magnetic quantum number determines the orientation of the orbital in space. The value of m l depends on the value of l. For a given value of l there are 2 l + 1 integer values of m l ranging from - l to l. Examples: If l = 0, m l = 0 If l = 1, m l = -1, or 0, or 1 711

82. The magnetic quantum number determines the orientation of the orbital in space. The value of m l depends on the value of l. For a given value of l there are 2 l + 1 integer values of m l ranging from - l to l. Examples: If l = 0, m l = 0 If l = 1, m l = -1, or 0, or 1 If l = 2, m l = -2, -1, 0, 1, 2 712

83. The number of different values that m l may take for a given subshell, indicates the number of individual orbitals. 713

84. The number of different values that m l may take for a given subshell, indicates the number of individual orbitals. Examples: If l = 0, there is one value for m l and only one orbital. 714

85. The number of different values that m l may take for a given subshell, indicates the number of individual orbitals. Examples: If l = 0, there is one value for m l and only one orbital. If l = 1, there are three values for m l and three orbitals. 715

86. 4. The Electron Spin Quantum Number 716

87. 4. The Electron Spin Quantum Number Symbol m s 717

88. 4. The Electron Spin Quantum Number Symbol m s There are only two possible values for m s : m s = ½ or m s = - ½ 718

89. 4. The Electron Spin Quantum Number Symbol m s There are only two possible values for m s : m s = ½ or m s = - ½ To explain certain spectral lines from atoms in the presence of a magnetic field, it was found to be necessary to assume that electrons act as tiny magnets. 719

90. 720