1. Atomic Structure

2. Light n Made up of electromagnetic radiation. n Waves of electric and magnetic fields at right angles to each other.

3. Parts of a wave Wavelength Frequency = number of cycles in one second Measured in hertz 1 hertz = 1 cycle/second

4. Frequency = Frequency =

5. Kinds of EM waves n There are many different and different and n Radio waves, microwaves, x rays and gamma rays are all examples. n Light is only the part our eyes can detect. Gamma Rays Radio waves

6. The speed of light n in a vacuum is 2.998 x 10 8 m/s n = c c = c = n What is the wavelength of light with a frequency 5.89 x 10 5 Hz? n What is the frequency of blue light with a wavelength of 484 nm?

7. Early in the 20 th Century n Matter and energy were seen as different from each other in fundamental ways. n Matter was particles. n Energy could come in waves, with any frequency. n Max Planck found that as the cooling of hot objects couldn’t be explained by viewing energy as a wave.

8. Energy is Quantized Planck found  E came in chunks with size h Planck found  E came in chunks with size h  E = nh  E = nh n where n is an integer. n and h is Planck’s constant n h = 6.626 x 10 -34 J s these packets of h are called quantum these packets of h are called quantum

9. Einstein and his Work n Said electromagnetic radiation is quantized in particles called photons. Each photon has energy = h = hc/ Each photon has energy = h = hc/ n Combine this with E = mc 2 n You get the apparent mass of a photon. m = h / ( c) m = h / ( c)

10. Which is it, a particle or a wave? n Is energy a wave like light, or a particle? n Yes n Concept is called the Wave -Particle duality. n What about the other way, is matter a wave? n Yes

11. Matter as a wave Using the velocity v instead of the wavelength we get. Using the velocity v instead of the wavelength we get. De Broglie’s equation = h/mv De Broglie’s equation = h/mv n Can calculate the wavelength of an object.

12. Examples n The laser light of a CD is 7.80 x 10 -2 m. What is the frequency of this light? n What is the energy of a photon of this light? n What is the apparent mass of a photon of this light? n What is the energy of a mole of these photons?

13. What is the wavelength? n of an electron with a mass of 9.11 x 10 -31 kg traveling at 1.0 x 10 7 m/s? n Of a softball with a mass of 0.10 kg moving at 125 mi/hr?

14. Diffraction n When light passes through, or reflects off, a series of thinly spaced line, it creates a rainbow effect n because the waves interfere with each other.

15. A wave moves toward a slit.

16. Comes out as a curve

17. with two holes

18. Two Curves

19. with two holes Interfere with each other

20. Two Curves with two holes Interfere with each other crests add up

21. Several waves

22. Several Curves

23. Several waves Interference Pattern Several Curves

24. What will an electron do? n It has mass, so it is matter. n A particle can only go through one hole. n A wave through both holes. n An electron does go though both, and makes an interference pattern. n It behaves like a wave. n Other matter has wavelengths too short to notice.

25. Spectrum n The range of frequencies present in light. n White light has a continuous spectrum. n All the colors are possible. n A rainbow.

26. Hydrogen spectrum n Emission spectrum because these are the colors it gives off or emits. n Called a line spectrum. n There are just a few discrete lines showing 410 nm 434 nm 486 nm 656 nm

27. What this means n Only certain energies are allowed for the hydrogen atom. n Can only give off certain energies. Use  E = h  = hc / Use  E = h  = hc / n Energy in the in the atom is quantized.

28. Niels Bohr n Developed the quantum model of the hydrogen atom. n He said the atom was like a solar system. n The electrons were attracted to the nucleus because of opposite charges. n Didn’t fall in to the nucleus because it was moving around.

29. The Bohr Ring Atom n He didn’t know why but only certain energies were allowed. n He called these allowed energies energy levels. n Putting Energy into the atom moved the electron away from the nucleus. n From ground state to excited state. n When it returns to ground state it gives off light of a certain energy.

30. The Bohr Ring Atom n = 3 n = 4 n = 2 n = 1

31. The Bohr Model n n is the energy level n for each energy level the energy is n Z is the nuclear charge, which is +1 for hydrogen. n E = -2.178 x 10 -18 J (Z 2 / n 2 ) n n = 1 is called the ground state when the electron is removed, n =  when the electron is removed, n =  n E = 0

32. We are worried about the change n When the electron moves from one energy level to another.  E = E final - E initial  E = E final - E initial  E = -2.178 x 10 -18 J Z 2 (1/ n f 2 - 1/ n i 2 )  E = -2.178 x 10 -18 J Z 2 (1/ n f 2 - 1/ n i 2 )

33. Examples n Calculate the energy need to move an electron from its to the third energy level. n Calculate the energy released when an electron moves from n= 4 to n=2 in a hydrogen atom. n Calculate the energy released when an electron moves from n= 5 to n=3 in a He +1 ion

34. When is it true? n Only for hydrogen atoms and other monoelectronic species. n Why the negative sign? n To increase the energy of the electron you make it closer to the nucleus. n the maximum energy an electron can have is zero, at an infinite distance.

35. The Bohr Model n Doesn’t work. n Only works for hydrogen atoms. n Electrons don’t move in circles. n The quantization of energy is right, but not because they are circling like planets.

36. The Quantum Mechanical Model n A totally new approach. n De Broglie said matter could be like a wave. n De Broglie said they were like standing waves. n The vibrations of a stringed instrument.

38. What’s possible? n You can only have a standing wave if you have complete waves. n There are only certain allowed waves. n In the atom there are certain allowed waves called electrons. n 1925 Erwin Schroedinger described the wave function of the electron. n Much math but what is important are the solution.

39. Schroedinger’s Equation n The wave function is a F(x, y, z) n Solutions to the equation are called orbitals. n These are not Bohr orbits. n Each solution is tied to a certain energy. n These are the energy levels.

40. There is a limit to what we can know n We can’t know how the electron is moving or how it gets from one energy level to another. n The Heisenberg Uncertainty Principle. n There is a limit to how well we can know both the position and the momentum of an object.

41. Mathematically  x ·  (mv) > h/4   x ·  (mv) > h/4   x is the uncertainty in the position.  x is the uncertainty in the position.  (mv) is the uncertainty in the momentum.  (mv) is the uncertainty in the momentum. the minimum uncertainty is h/4  the minimum uncertainty is h/4 

42. Examples n What is the uncertainty in the position of an electron. mass 9.31 x 10 - 31 kg with an uncertainty in the speed of.100 m/s n What is the uncertainty in the position of a baseball, mass.145 kg with an uncertainty in the speed of.100 m/s

43. What does the wave Function mean? n nothing. n it is not possible to visually map it. n The square of the function is the probability of finding an electron near a particular spot. n best way to visualize it is by mapping the places where the electron is likely to be found.

44. Probability Distance from nucleus

45. Sum of all Probabilities Distance from nucleus

46. Defining the size n The nodal surface. n The size that encloses 90% to the total electron probability. n NOT at a certain distance, but a most likely distance. n For the first solution it is a a sphere.

47. Quantum Numbers n There are many solutions to Schroedinger’s equation n Each solution can be described with quantum numbers that describe some aspect of the solution. n Principal quantum number (n) size and energy of of an orbital. n Has integer values >0

48. Quantum numbers Angular momentum quantum number l. Angular momentum quantum number l. n shape of the orbital. n integer values from 0 to n-1 l = 0 is called s l = 0 is called s l = 1 is called p l = 1 is called p l =2 is called d l =2 is called d l =3 is called f l =3 is called f l =4 is called g l =4 is called g

49. S orbitals

50. P orbitals

51. P Orbitals

52. D orbitals

53. F orbitals

55. Quantum numbers Magnetic quantum number (m l ) Magnetic quantum number (m l ) integer values between - l and + l integer values between - l and + l n tells direction in each shape. Electron spin quantum number (m s ) Electron spin quantum number (m s ) n Can have 2 values. n either +1/2 or -1/2

56. Polyelectronic Atoms n More than one electron. n three energy contributions. n The kinetic energy of moving electrons. n The potential energy of the attraction between the nucleus and the electrons. n The potential energy from repulsion of electrons.

57. Polyelectronic atoms n Can’t solve Schroedinger’s equation exactly. n Difficulty is repulsion of other electrons. n Solution is to treat each electron as if it were effected by the net field of charge from the attraction of the nucleus and the repulsion of the electrons. n Effective nuclear charge

58. +10 11 electrons +10 10 other electrons e-e- Z eff

59. Effective Nuclear charge n Can be calculated from E = -2.178 x 10 -18 J (Z eff 2 / n 2 ) n and  E = -2.178 x 10 -18 J Z eff 2 (1/ n f 2 - 1/ n i 2 )  E = -2.178 x 10 -18 J Z eff 2 (1/ n f 2 - 1/ n i 2 )

60. The Periodic Table n Developed independently by German Julius Lothar Meyer and Russian Dmitri Mendeleev (1870”s). n Didn’t know much about atom. n Put in columns by similar properties. n Predicted properties of missing elements.

61. Aufbau Principle n Aufbau is German for building up. n As the protons are added one by one, the electrons fill up hydrogen- like orbitals. n Fill up in order of energy levels.

62. Increasing energy 1s 2s 3s 4s 5s 6s 7s 2p 3p 4p 5p 6p 3d 4d 5d 7p 6d 4f 5f He with 2 electrons

63. Details n Valence electrons- the electrons in the outermost energy levels (not d). n Core electrons- the inner electrons. n Hund’s Rule- The lowest energy configuration for an atom is the one have the maximum number of of unpaired electrons in the orbital. n C 1s 2 2s 2 2p 2

64. Fill from the bottom up following the arrows 1s 2s 2p 3s 3p 3d 4s 4p 4d 4f 5s 5p 5d 5f 6s 6p 6d 6f 7s 7p 7d 7f 1s 2 2 electrons 2s 2 4 2p 6 3s 2 12 3p 6 4s 2 20 3d 10 4p 6 5s 2 38 4d 10 5p 6 6s 2 56

65. Details n Elements in the same column have the same electron configuration. n Put in columns because of similar properties. n Similar properties because of electron configuration. n Noble gases have filled energy levels. n Transition metals are filling the d orbitals

66. Exceptions n Ti = [Ar] 4s 2 3d 2 n V = [Ar] 4s 2 3d 3 n Cr = [Ar] 4s 1 3d 5 n Mn = [Ar] 4s 2 3d 5 n Half filled orbitals. n Scientists aren’t sure of why it happens n same for Cu [Ar] 4s 1 3d 10

67. More exceptions n Lanthanum La: [Xe] 6s 2 5d 1 n Cerium Ce: [Xe] 6s 2 4f 1 5d 1 n Promethium Pr: [Xe] 6s 2 4f 3 5d 0 n Gadolinium Gd: [Xe] 6s 2 4f 7 5d 1 n Lutetium Pr: [Xe] 6s 2 4f 14 5d 1 n We’ll just pretend that all except Cu and Cr follow the rules.

68. More Polyelectronic n We can use Z eff to predict properties, if we determine it’s pattern on the periodic table. n Can use the amount of energy it takes to remove an electron for this. n Ionization Energy- The energy necessary to remove an electron from a gaseous atom.

69. Remember this n E = -2.18 x 10 -18 J(Z 2 /n 2 ) n was true for Bohr atom. n Can be derived from quantum mechanical model as well n for a mole of electrons being removed n E =(6.02 x 10 23 /mol)2.18 x 10 -18 J(Z 2 /n 2 ) n E= 1.13 x 10 6 J/mol(Z 2 /n 2 ) n E= 1310 kJ/mol(Z 2 /n 2 )

70. Example n Calculate the ionization energy of B +4

71. Remember our simplified atom +11 11 e- Z eff 1 e-

72. This gives us n Ionization energy = 1310 kJ/mol(Z eff 2 /n 2 ) n So we can measure Zeff n The ionization energy for a 1s electron from sodium is 1.39 x 10 5 kJ/mol. n The ionization energy for a 3s electron from sodium is 4.95 x 10 2 kJ/mol. n Demonstrates shielding.

73. Shielding n Electrons on the higher energy levels tend to be farther out. n Have to look through the other electrons to see the nucleus. n They are less effected by the nucleus. n lower effective nuclear charge n If shielding were completely effective, Z eff = 1 n Why isn’t it?

74. Penetration n There are levels to the electron distribution for each orbital. 2s

75. Graphically Penetration 2s Radial Probability Distance from nucleus

76. Graphically Radial Probability Distance from nucleus 3s

77. Radial Probability Distance from nucleus 3p

78. Radial Probability Distance from nucleus 3d

79. Radial Probability Distance from nucleus 4s 3d

80. Penetration effect n The outer energy levels penetrate the inner levels so the shielding of the core electrons is not totally effective. n from most penetration to least penetration the order is n ns > np > nd > nf (within the same energy level). n This is what gives us our order of filling, electrons prefer s and p.

81. How orbitals differ n The more positive the nucleus, the smaller the orbital. n A sodium 1s orbital is the same shape as a hydrogen 1s orbital, but it is smaller because the electron is more strongly attracted to the nucleus. n The helium 1s is smaller as well. n This provides for better shielding.

82. Z eff 1 2 4 5 1

83. 1 2 4 5 1 If shielding is perfect Z= 1

84. Z eff 1 2 4 5 1 No shielding Z = Z eff

85. Z eff 1 2 4 5 16

86. Periodic Trends n Ionization energy the energy required to remove an electron form a gaseous atom n Highest energy electron removed first. First ionization energy ( I 1 ) is that required to remove the first electron. First ionization energy ( I 1 ) is that required to remove the first electron. Second ionization energy ( I 2 ) - the second electron Second ionization energy ( I 2 ) - the second electron n etc. etc.

87. Trends in ionization energy n for Mg I 1 = 735 kJ/moleI 1 = 735 kJ/mole I 2 = 1445 kJ/moleI 2 = 1445 kJ/mole I 3 = 7730 kJ/moleI 3 = 7730 kJ/mole n The effective nuclear charge increases as you remove electrons. n It takes much more energy to remove a core electron than a valence electron because there is less shielding.

88. Explain this trend n For Al I 1 = 580 kJ/moleI 1 = 580 kJ/mole I 2 = 1815 kJ/moleI 2 = 1815 kJ/mole I 3 = 2740 kJ/moleI 3 = 2740 kJ/mole I 4 = 11,600 kJ/moleI 4 = 11,600 kJ/mole

89. Across a Period Generally from left to right, I 1 increases because Generally from left to right, I 1 increases because n there is a greater nuclear charge with the same shielding. As you go down a group I 1 decreases because electrons are farther away. As you go down a group I 1 decreases because electrons are farther away.

90. It is not that simple Z eff changes as you go across a period, so will I 1 Z eff changes as you go across a period, so will I 1 n Half filled and filled orbitals are harder to remove electrons from. n here’s what it looks like.

91. First Ionization energy Atomic number

92. First Ionization energy Atomic number

93. First Ionization energy Atomic number

94. Parts of the Periodic Table

95. The information it hides n Know the special groups n It is the number and type of valence electrons that determine an atoms chemistry. n You can get the electron configuration from it. n Metals lose electrons have the lowest IE n Non metals- gain electrons most negative electron affinities.

96. The Alkali Metals n Doesn’t include hydrogen- it behaves as a non-metal n decrease in IE n increase in radius n Decrease in density n decrease in melting point n Behave as reducing agents

97. Reducing ability n Lower IE< better reducing agents n Cs>Rb>K>Na>Li n works for solids, but not in aqueous solutions. n In solution Li>K>Na n Why? n It’s the water -there is an energy change associated with dissolving

98. Hydration Energy n It is exothermic n for Li + -510 kJ/mol n for Na + -402 kJ/mol n for K + -314 kJ/mol n Li is so big because of it has a high charge density, a lot of charge on a small atom. n Li loses its electron more easily because of this in aqueous solutions

99. The reaction with water n Na and K react explosively with water n Li doesn’t. Even though the reaction of Li has a more negative  H than that of Na and K Even though the reaction of Li has a more negative  H than that of Na and K n Na and K melt  H does not tell you speed of reaction  H does not tell you speed of reaction n More in Chapter 12.