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The Central Themes of VB Theory

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1 The Central Themes of VB Theory
Basic Principle A covalent bond forms when the orbitals of two atoms overlap and are occupied by a pair of electrons that have the highest probability of being located between the nuclei. Themes These overlapping orbitals can have up to two electrons that must have opposite spins (Pauli principle). The valence orbitals in a molecule are different from those in isolated atoms. Copyright © Houghton Mifflin Company. All rights reserved.

2 Figure 12.18: Three representations of the hydrogen 1s
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3 Figure 13.1: (a) The interaction of two hydrogen atoms (b) Energy profile as a function of the distance between the nuclei of the hydrogen atoms. Copyright © Houghton Mifflin Company. All rights reserved.

4 Figure 13.1: (a) The interaction of two hydrogen atoms (b) Energy profile as a function of the distance between the nuclei of the hydrogen atoms. Copyright © Houghton Mifflin Company. All rights reserved.

5 Figure 12.19b: Representation of the 2p orbitals.
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6 Hydrogen, H2 Hydrogen fluoride, HF Fluorine, F2
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7 Figure 14.1: (a) Lewis structure of the methane molecule (b) the tetrahedral molecular geometry of the methane molecule. Copyright © Houghton Mifflin Company. All rights reserved.

8 Figure 14.2: valence orbitals on a free carbon atom
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9 Figure 14.1: (a) Lewis structure of the methane molecule (b) the tetrahedral molecular geometry of the methane molecule. Copyright © Houghton Mifflin Company. All rights reserved.

10 Figure 14.3: native 2s and three 2p atomic orbitals characteristic of a free carbon atome are combined to form a new set of four sp3 orbitals. Copyright © Houghton Mifflin Company. All rights reserved.

11 Carbon 1s22s22p2 Carbon could only make two bonds
if no hybridization occurs. However, carbon can make four equivalent bonds. B A sp3 hybrid orbitals Energy px py pz sp3 s C atom of CH4 orbital diagram Copyright © Houghton Mifflin Company. All rights reserved. Brown, LeMay, Bursten, Chemistry The Central Science, 2000, page 321

12 Figure 14.4: Cross section of an sp3 orbital
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13 The four sp3 hybrid orbitals in CH4
Promotion Copyright © Houghton Mifflin Company. All rights reserved.

14 relatively even distribution of electron density over all s bonds
Figure 11.9 The s bonds in ethane. both C are sp3 hybridized s-sp3 overlaps to s bonds sp3-sp3 overlap to form a s bond relatively even distribution of electron density over all s bonds Rotation about C-C bond allowed. (Greek sigma) bonds have axial symmetry and good overlap Copyright © Houghton Mifflin Company. All rights reserved.

15 Figure 14.6: Tetrahedral set of four sp3 orbitals on the carbon atom
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16 Figure 14.7: The nitrogen atom in ammonia is sp3 hybridized.
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17 The four sp3 hybrid orbitals in CH4
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18 The four sp3 hybrid orbitals in CH4
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19 N The four sp3 hybrid orbitals in NH3 Promotion
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20 N The four sp3 hybrid orbitals in NH3 Promotion
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21 The sp3 hybrid orbitals in H2O
Figure 11.5 The sp3 hybrid orbitals in H2O Lone pairs Copyright © Houghton Mifflin Company. All rights reserved.

22 Diamond - sp3 hybridized C
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23 NB: The remaining p orbital can be empty or serve another function
Figure 14.8: The hybridization of the s, px, and py atomic orbitals results in the formation of three sp2 orbitals centered in the xy plane. NB: The remaining p orbital can be empty or serve another function Copyright © Houghton Mifflin Company. All rights reserved.

24 The three sp2 hybrid orbitals in BF3
Promotion Note the single left over Unhybridized p orbital on B Region of overlap Copyright © Houghton Mifflin Company. All rights reserved.

25 sp2 hybrid orbitals shown together
Ground-state B atom 2s 2p 2s 2p B atom with one electron “promoted” sp2 hybrid orbitals Energy sp2 2p px py pz s B atom of BH3 orbital diagram p orbitals H B three sps hybrid orbitals sp2 hybrid orbitals shown together (large lobes only) hybridize s orbital Copyright © Houghton Mifflin Company. All rights reserved.

26 Figure 14.10: When one s and two p oribitals are mixed to form a set of three sp2 orbitals, one p orbital remains unchanged and is perpendicular to the plane of the hybrid orbitals. Copyright © Houghton Mifflin Company. All rights reserved.

27 Figure 14. 13: (a) The orbitals used to form the bonds in ethylene
Figure 14.13: (a) The orbitals used to form the bonds in ethylene. (b) The Lewis structure for ethylene. Copyright © Houghton Mifflin Company. All rights reserved.

28 The plastics shown here were manufactured with ethylene.
Source: Comstock - Mountainside, NJ Copyright © Houghton Mifflin Company. All rights reserved.

29 Figure 14.11: The s bonds in ethylene.
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30 Figure 14.12: A carbon-carbon double bond consists of a s bond and a p bond.
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31 Figure 14.48: The benzene molecule consists of a ring of six carbon atoms with one hydrogen atom bound to each carbon; all atoms are in the same plane. Sp2 hybridized Copyright © Houghton Mifflin Company. All rights reserved.

32 Graphite – sp2 hybridized C
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33 Fullerene-C60 and Fullerene-C70 What hybridization of C describes the structures?
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34 Figure 14.14: When one s orbital and one p orbital are hybridized, a set of two sp orbitals oriented at 180 degrees results. Copyright © Houghton Mifflin Company. All rights reserved.

35 The sp hybrid orbitals in gaseous BeCl2
Promote to create two half filled orbitals that participate in bond formation Promotion Filled 2s orbital can’t bond to Cl Why are sp hybrids invoked? Because if Be made one bond with its 2s and one bond with a 2p orbital, then the two Be-Cl bonds would have different strengths & lengths. But both bonds are identical. Copyright © Houghton Mifflin Company. All rights reserved.

36 The two sp hybrid orbitals in gaseous BeCl2
Note the two “leftover” p orbitals of Be Region of overlap Copyright © Houghton Mifflin Company. All rights reserved.

37 Figure 14.15: The hybrid orbitals in the CO2 molecule
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38 Figure 14.16: orbital energy level diagram for the formation of sp hybrid orbitals of carbon.
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39 Figure 14.17: Orbitals of an sp hybridized carbon atom
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40 Figure 14.18: Orbital arrangement for an sp2 hybridized oxygen atom
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41 Figure 14.19: (a) Orbitals predicted by the LE model to describe (b) The Lewis structure for carbon dioxide Copyright © Houghton Mifflin Company. All rights reserved.

42 Hybrid Orbitals Types of Hybrid Orbitals sp sp2 sp3 sp3d sp3d2
Shapes: linear triangular tetrahedral trig. bipyram. Octahedral # orbitals: Copyright © Houghton Mifflin Company. All rights reserved.

43 Figure 14.20: (a) An sp hybridized nitrogen atom (b) The s bond in the N2 molecule (c) the two p bonds in N2 are formed Copyright © Houghton Mifflin Company. All rights reserved.

44 N The four sp3 hybrid orbitals in NH3 Promotion
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45 The four sp3 hybrid orbitals in NH3
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46 Molecular shape and e- group arrangement
The conceptual steps from molecular formula to the hybrid orbitals used in bonding. Step 1 Step 2 Step 3 Molecular shape and e- group arrangement Molecular formula Lewis structure Hybrid orbitals Copyright © Houghton Mifflin Company. All rights reserved.

47 sp3 hybridization of a carbon atom
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48 sp3 hybridization of a carbon atom
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49 sp3 hybridization of a nitrogen atom
3 tetrahedral bonds with 1 lone pair sp 3 Copyright © Houghton Mifflin Company. All rights reserved.

50 sp3 hybridization of a nitrogen atom
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51 sp3 hybridization of a oxygen atom
2 tetrahedral bonds with 2 lone pairs sp 3 Copyright © Houghton Mifflin Company. All rights reserved.

52 sp3 hybridization of a oxygen atom
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53 sp2 hybridization of a carbon atom
4 hybridized orbitals sp 2 px 3 trigonal Bonds + 1 for a pi bond sp 2 px Copyright © Houghton Mifflin Company. All rights reserved.

54 Copyright © Houghton Mifflin Company. All rights reserved.

55 Copyright © Houghton Mifflin Company. All rights reserved.

56 Copyright © Houghton Mifflin Company. All rights reserved.

57 Copyright © Houghton Mifflin Company. All rights reserved.

58 sp2 hybridization of an oxygen atom
4 hybridized orbitals sp 2 px 1 trigonal Bond with 2 lone pairs + 1 for a pi bond sp 2 px Copyright © Houghton Mifflin Company. All rights reserved.

59 Figure 14.19: (a) Orbitals predicted by the LE model to describe (b) The Lewis structure for carbon dioxide Copyright © Houghton Mifflin Company. All rights reserved.

60 sp hybridization of a carbon atom
4 hybridized orbitals sp px py 2 linear bonds + 2 for pi bonds sp px py Copyright © Houghton Mifflin Company. All rights reserved.

61 Copyright © Houghton Mifflin Company. All rights reserved.

62 sp hybridization of an nitrogen atom
4 hybridized orbitals sp px py 1 linear Bonds with 1 lone pair + 2 for pi bonds sp px py Copyright © Houghton Mifflin Company. All rights reserved.

63 Figure 14.20: (a) An sp hybridized nitrogen atom (b) The s bond in the N2 molecule (c) the two p bonds in N2 are formed Copyright © Houghton Mifflin Company. All rights reserved.

64 Figure 14.21: A set of dsp3 hybrid orbitals on a phosphorous atom
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65 Hybridization Involving d Orbitals
promote 3s p d s p d unhybridized P atom P = [Ne]3s23p3 vacant d orbitals hybridize A Be Ba F P five sp3d orbitals 3d degenerate orbitals (all EQUAL) Trigonal bipyramidal Copyright © Houghton Mifflin Company. All rights reserved.

66 The five sp3d hybrid orbitals in PCl5
Figure 11.6 The five sp3d hybrid orbitals in PCl5 Copyright © Houghton Mifflin Company. All rights reserved.

67 Figure 14.22: The orbitals used to form the bonds in the PCL5 molecule
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68 Figure 14.23: An octahedral set of d2sp3 orbitals on a sulfur atom
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69 The six sp3d2 hybrid orbitals in SF6
Figure 11.7 The six sp3d2 hybrid orbitals in SF6 Copyright © Houghton Mifflin Company. All rights reserved.

70 Figure 14.24: The relationship among the number of effective pairs, their spatial arrangement, and the hybrid orbital set required Copyright © Houghton Mifflin Company. All rights reserved.

71 Figure 14.24: The relationship among the number of effective pairs, their spatial arrangement, and the hybrid orbital set required (cont’d) Copyright © Houghton Mifflin Company. All rights reserved.

72 Molecular shape and e- group arrangement
Figure 11.8 The conceptual steps from molecular formula to the hybrid orbitals used in bonding. Figure 10.1 Step 1 Figure 10.12 Step 2 Step 3 Table 11.1 Molecular shape and e- group arrangement Molecular formula Lewis structure Hybrid orbitals Copyright © Houghton Mifflin Company. All rights reserved.

73 Figure 13.1: (a) The interaction of two hydrogen atoms (b) Energy profile as a function of the distance between the nuclei of the hydrogen atoms. Copyright © Houghton Mifflin Company. All rights reserved.

74 Figure 13.1: (a) The interaction of two hydrogen atoms (b) Energy profile as a function of the distance between the nuclei of the hydrogen atoms. Copyright © Houghton Mifflin Company. All rights reserved.

75 Figure 14.25: The combination of hydrogen 1s atomic orbitals to form MOs
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76 Figure 14.25: The combination of hydrogen 1s atomic orbitals to form MOs
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77 10.6 Copyright © Houghton Mifflin Company. All rights reserved.

78  (- sign flips phase of the sound wave function)
 -  = 0 Auto mufflers use destructive interference of sound waves to reduce engine noises. Copyright © Houghton Mifflin Company. All rights reserved.

79 Bose is $200. Want to do it yourself? See Web site.
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80 Copyright © Houghton Mifflin Company. All rights reserved.

81 NOTE: +/- signs show PHASES of waves, NOT CHARGES!
An analogy between light waves and atomic wave functions. Amplitudes of wave functions added NOTE: +/- signs show PHASES of waves, NOT CHARGES! Amplitudes of wave functions subtracted. Copyright © Houghton Mifflin Company. All rights reserved.

82 Figure 14.26: (a) The MO energy-level diagram for the H2 molecule (b) The shapes of the Mos are obtained by squaring the wave functions for MO1 and MO2. Copyright © Houghton Mifflin Company. All rights reserved.

83 Figure 14.27: Bonding and anitbonding MOs
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84 Figure 14.30: The MO energy-level diagram for the He2+ ion.
# ANTIBONDING e’s = 1 # BONDING e’s = 2 Bond order = ½(2-1) = ½ Copyright © Houghton Mifflin Company. All rights reserved.

85 Figure 14.31: The MO energy-level diagram for the H2+ ion
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86 Figure 14.28: MO energy-level diagram for the H2 molecule
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87 Figure 14.29: The MO energy-level diagram for the He2 molecule
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88 Figure 14.30: The MO energy-level diagram for the He2+ ion.
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89 Figure 14.31: The MO energy-level diagram for the H2+ ion
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90 Figure 14.32: The MO energy-level diagram for the H2- ion
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91 Copyright © Houghton Mifflin Company. All rights reserved.

92 Figure 14.33: The relative sizes of the lithium 1s and 2s atomic orbitals
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93 Figure 14.34: The MO energy-level diagram for the Li2 molecule
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94 Figure 14.35: The three mutually perpendicular 2p orbitals on tow adjacent boron atoms.
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95 Figure 14.36: The two p oribitals on the boron atom that overlap head-on combine to form bonding and antibonding orbitals. Copyright © Houghton Mifflin Company. All rights reserved.

96 Figure 14.37: The expected MO energy-level diagram for the combustion of the 2P orbitals on two boron atoms. Copyright © Houghton Mifflin Company. All rights reserved.

97 Figure 14.37: The expected MO energy-level diagram for the combustion of the 2P orbitals on two boron atoms. Copyright © Houghton Mifflin Company. All rights reserved.

98 Figure 14.38: The expected MO energy-level diagram for the B2 molecule
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99 Figure 14.39: An apparatus used to measure the paramagnetism of a sample
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100 Figure 14.40: The correct MO energy-level diagram for the B2 molecule.
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101 Figure 14.41: The MO energy-level diagrams, bond orders, bond energies, and bond lengths for the diatomic molecules, B2 through F2. Copyright © Houghton Mifflin Company. All rights reserved.

102 Figure 14.42: When liquid oxygen is poured into the space between the poles of a strong magnet, it remains there until it boils away. Source: Donald Clegg Copyright © Houghton Mifflin Company. All rights reserved.

103 Figure 14.43: The MO energy-level diagram for the NO molecule
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104 Figure 14.44: The MO energy-level diagram for both the NO+ and CN- ions
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105 Figure 14.45: A partial MO energy-level diagram for the HF molecule
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106 Figure 14.46: The electron probability distribution in the bonding MO of the HF molecule
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107 Figure 14.47: The resonance structures for O3 and NO3-
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108 Figure 14.48: The benzene molecule consists of a ring of six carbon atoms with one hydrogen atom bound to each carbon; all atoms are in the same plane. Copyright © Houghton Mifflin Company. All rights reserved.

109 Figure 14.49: The s bonding system in the benzene molecule
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110 Figure 14.50: The MO system in benzene is formed by combining the six p orbitals
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111 Figure 14.51: The p orbitals used to form the bonding system in the NO3- ion
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112 Copyright © Houghton Mifflin Company. All rights reserved.

113 λ ν Electromagnetic spectrum
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114 Copyright © Houghton Mifflin Company. All rights reserved.

115 Copyright © Houghton Mifflin Company. All rights reserved.

116 Copyright © Houghton Mifflin Company. All rights reserved.

117 λν=c Copyright © Houghton Mifflin Company. All rights reserved.

118 Copyright © Houghton Mifflin Company. All rights reserved.

119 Copyright © Houghton Mifflin Company. All rights reserved.

120 Copyright © Houghton Mifflin Company. All rights reserved.

121 Copyright © Houghton Mifflin Company. All rights reserved.

122 Copyright © Houghton Mifflin Company. All rights reserved.

123 Copyright © Houghton Mifflin Company. All rights reserved.

124 Figure 14.52: Schematic representation of two electronic energy levels in a molecule
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125 Figure 14.53: The various types of transitions are shown by vertical arrows.
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126 Figure 14. 54: Spectrum corresponding to the changes indicated in Fig
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127 Figure 14.55: The molecular orbital diagram for the ground state of NO+
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128 The molecular structure of beta-carotene
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129 Figure 14.57: The electronic absorption spectrum of beta-carotene.
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130 VIBRATIONS

131 VIBRATIONS

132 Figure 14.58: The potential curve for a diatomic molecule
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133 Figure 14.59: Morse energy curve for a diatomic molecule.
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134 Figure 14.60: The three fundamental vibrations for sulfur dioxide
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135 Figure 14.61: The infrared spectrum of CH2Cl2.
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136 Copyright © Houghton Mifflin Company. All rights reserved.

137 Copyright © Houghton Mifflin Company. All rights reserved.

138 Figure 14.62: Representations of the two spin states of the proton interacting
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139 Figure 14.63: The molecular structure of bromoethane
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140 Figure 14.64: The expected NMR spectrum for bromoethane
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141 Figure 14.65: The spin of proton Hy can by "up" or "down"
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142 Figure 14.66: The spins for protons Hy can be "up", can be opposed (in 2 ways) or can both be "down"
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143 Figure 14.67: The spins for the protons Hy can by arranged as shown in (a) leading to four different magnetic environments Copyright © Houghton Mifflin Company. All rights reserved.

144 Figure 14.68: The NMR spectrum of CH3CH2Br (bromoethane) with TMS reference
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145 Figure 14.69: The molecule (2-butanone)
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146 Fullerene-C60 and Fullerene-C70
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147 Fullerene-C60 and Fullerene-C70
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148 Figure 14.70: A technician speaks to a patient before heis moved intot eh cavity of a magnetic resonance imaging (MRI) machine. Copyright © Houghton Mifflin Company. All rights reserved.

149 Figure 14.71: A colored Magnetic Resonance Imaging (MRI) scan through a human head, showing a healthy brain in side view. Copyright © Houghton Mifflin Company. All rights reserved.


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