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Copyright © Houghton Mifflin Company. All rights reserved. 14a–1 The Central Themes of VB Theory Basic Principle A covalent bond forms when the orbitals.

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Presentation on theme: "Copyright © Houghton Mifflin Company. All rights reserved. 14a–1 The Central Themes of VB Theory Basic Principle A covalent bond forms when the orbitals."— Presentation transcript:

1 Copyright © Houghton Mifflin Company. All rights reserved. 14a–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.

2 Copyright © Houghton Mifflin Company. All rights reserved. 14a–2 Figure 12.18: Three representations of the hydrogen 1s

3 Copyright © Houghton Mifflin Company. All rights reserved. 14a–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.

4 Copyright © Houghton Mifflin Company. All rights reserved. 14a–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.

5 Copyright © Houghton Mifflin Company. All rights reserved. 14a–5 Figure 12.19b: Representation of the 2p orbitals.

6 Copyright © Houghton Mifflin Company. All rights reserved. 14a–6 Hydrogen, H 2 Hydrogen fluoride, HFFluorine, F 2

7 Copyright © Houghton Mifflin Company. All rights reserved. 14a–7 Figure 14.1: (a) Lewis structure of the methane molecule (b) the tetrahedral molecular geometry of the methane molecule.

8 Copyright © Houghton Mifflin Company. All rights reserved. 14a–8 Figure 14.2: valence orbitals on a free carbon atom

9 Copyright © Houghton Mifflin Company. All rights reserved. 14a–9 Figure 14.1: (a) Lewis structure of the methane molecule (b) the tetrahedral molecular geometry of the methane molecule.

10 Copyright © Houghton Mifflin Company. All rights reserved. 14a–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.

11 Copyright © Houghton Mifflin Company. All rights reserved. 14a–11 s pxpx pypy pzpz Carbon 1s 2 2s 2 2p 2 Carbon could only make two bonds if no hybridization occurs. However, carbon can make four equivalent bonds. sp 3 hybrid orbitals Energy sp 3 C atom of CH 4 orbital diagram B A B B B Brown, LeMay, Bursten, Chemistry The Central Science, 2000, page 321

12 Copyright © Houghton Mifflin Company. All rights reserved. 14a–12 Figure 14.4: Cross section of an sp3 orbital

13 Copyright © Houghton Mifflin Company. All rights reserved. 14a–13 The four sp 3 hybrid orbitals in CH 4 Promotion

14 Copyright © Houghton Mifflin Company. All rights reserved. 14a–14 Figure 11.9 The bonds in ethane. both C are sp 3 hybridized s-sp 3 overlaps to bonds sp 3 -sp 3 overlap to form a bond relatively even distribution of electron density over all bonds (Greek sigma) bonds have axial symmetry and good overlap Rotation about C-C bond allowed.

15 Copyright © Houghton Mifflin Company. All rights reserved. 14a–15 Figure 14.6: Tetrahedral set of four sp 3 orbitals on the carbon atom

16 Copyright © Houghton Mifflin Company. All rights reserved. 14a–16 Figure 14.7: The nitrogen atom in ammonia is sp 3 hybridized.

17 Copyright © Houghton Mifflin Company. All rights reserved. 14a–17 The four sp 3 hybrid orbitals in CH 4 Promotion

18 Copyright © Houghton Mifflin Company. All rights reserved. 14a–18 The four sp 3 hybrid orbitals in CH 4 Promotion

19 Copyright © Houghton Mifflin Company. All rights reserved. 14a–19 The four sp 3 hybrid orbitals in NH 3 Promotion N

20 Copyright © Houghton Mifflin Company. All rights reserved. 14a–20 The four sp 3 hybrid orbitals in NH 3 Promotion N

21 Copyright © Houghton Mifflin Company. All rights reserved. 14a–21 Figure 11.5 The sp 3 hybrid orbitals in H 2 O Lone pairs

22 Copyright © Houghton Mifflin Company. All rights reserved. 14a–22 Diamond - sp 3 hybridized C

23 Copyright © Houghton Mifflin Company. All rights reserved. 14a–23 Figure 14.8: The hybridization of the s, p x, and p y atomic orbitals results in the formation of three sp 2 orbitals centered in the xy plane. NB: The remaining p orbital can be empty or serve another function

24 Copyright © Houghton Mifflin Company. All rights reserved. 14a–24 The three sp 2 hybrid orbitals in BF 3 Promotion Region of overlap Note the single left over Unhybridized p orbital on B

25 Copyright © Houghton Mifflin Company. All rights reserved. 14a–25 Hybrid Orbitals 2s2s2p2p Ground-state B atom s pxpx pypy pzpz Energy sp 2 2p2p B atom of BH 3 orbital diagram hybridize s orbital 2s2s2p2p B atom with one electron promoted sp 2 hybrid orbitals p orbitals sp 2 hybrid orbitals shown together (large lobes only) three sp s hybrid orbitals H H H B

26 Copyright © Houghton Mifflin Company. All rights reserved. 14a–26 Figure 14.10: When one s and two p oribitals are mixed to form a set of three sp 2 orbitals, one p orbital remains unchanged and is perpendicular to the plane of the hybrid orbitals.

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

28 Copyright © Houghton Mifflin Company. All rights reserved. 14a–28 The plastics shown here were manufactured with ethylene. Source: Comstock - Mountainside, NJ

29 Copyright © Houghton Mifflin Company. All rights reserved. 14a–29 Figure 14.11: The s bonds in ethylene.

30 Copyright © Houghton Mifflin Company. All rights reserved. 14a–30 Figure 14.12: A carbon-carbon double bond consists of a s bond and a p bond.

31 Copyright © Houghton Mifflin Company. All rights reserved. 14a–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

32 Copyright © Houghton Mifflin Company. All rights reserved. 14a–32 Graphite – sp 2 hybridized C

33 Copyright © Houghton Mifflin Company. All rights reserved. 14a–33 Fullerene-C 60 and Fullerene-C 70 What hybridization of C describes the structures?

34 Copyright © Houghton Mifflin Company. All rights reserved. 14a–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.

35 Copyright © Houghton Mifflin Company. All rights reserved. 14a–35 The sp hybrid orbitals in gaseous BeCl 2 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. Promotion Promote to create two half filled orbitals that participate in bond formation Filled 2s orbital cant bond to Cl

36 Copyright © Houghton Mifflin Company. All rights reserved. 14a–36 The two sp hybrid orbitals in gaseous BeCl 2 Note the two leftover p orbitals of Be Region of overlap

37 Copyright © Houghton Mifflin Company. All rights reserved. 14a–37 Figure 14.15: The hybrid orbitals in the CO 2 molecule

38 Copyright © Houghton Mifflin Company. All rights reserved. 14a–38 Figure 14.16: orbital energy level diagram for the formation of sp hybrid orbitals of carbon.

39 Copyright © Houghton Mifflin Company. All rights reserved. 14a–39 Figure 14.17: Orbitals of an sp hybridized carbon atom

40 Copyright © Houghton Mifflin Company. All rights reserved. 14a–40 Figure 14.18: Orbital arrangement for an sp 2 hybridized oxygen atom

41 Copyright © Houghton Mifflin Company. All rights reserved. 14a–41 Figure 14.19: (a) Orbitals predicted by the LE model to describe (b) The Lewis structure for carbon dioxide

42 Copyright © Houghton Mifflin Company. All rights reserved. 14a–42 Hybrid Orbitals spsp 2 sp 3 sp 3 dsp 3 d 2 Types of Hybrid Orbitals Shapes: linear triangular tetrahedral trig. bipyram. Octahedral # orbitals:

43 Copyright © Houghton Mifflin Company. All rights reserved. 14a–43 Figure 14.20: (a) An sp hybridized nitrogen atom (b) The s bond in the N 2 molecule (c) the two p bonds in N 2 are formed

44 Copyright © Houghton Mifflin Company. All rights reserved. 14a–44 The four sp 3 hybrid orbitals in NH 3 Promotion N

45 Copyright © Houghton Mifflin Company. All rights reserved. 14a–45 The four sp 3 hybrid orbitals in NH 3 Promotion

46 Copyright © Houghton Mifflin Company. All rights reserved. 14a–46 The conceptual steps from molecular formula to the hybrid orbitals used in bonding. Molecular formula Lewis structure Molecular shape and e - group arrangement Hybrid orbitals Step 1Step 2Step 3

47 Copyright © Houghton Mifflin Company. All rights reserved. 14a–47 sp 3 hybridization of a carbon atom

48 Copyright © Houghton Mifflin Company. All rights reserved. 14a–48 sp 3 hybridization of a carbon atom

49 Copyright © Houghton Mifflin Company. All rights reserved. 14a–49 sp 3 hybridization of a nitrogen atom 3 tetrahedral bonds with 1 lone pair sp 3

50 Copyright © Houghton Mifflin Company. All rights reserved. 14a–50 sp 3 hybridization of a nitrogen atom N

51 Copyright © Houghton Mifflin Company. All rights reserved. 14a–51 sp 3 hybridization of a oxygen atom 2 tetrahedral bonds with 2 lone pairs sp 3

52 Copyright © Houghton Mifflin Company. All rights reserved. 14a–52 sp 3 hybridization of a oxygen atom

53 Copyright © Houghton Mifflin Company. All rights reserved. 14a–53 sp 2 hybridization of a carbon atom 3 trigonal Bonds + 1 for a pi bond sp 2 pxpx 4 hybridized orbitals sp 2 pxpx

54 Copyright © Houghton Mifflin Company. All rights reserved. 14a–54

55 Copyright © Houghton Mifflin Company. All rights reserved. 14a–55

56 Copyright © Houghton Mifflin Company. All rights reserved. 14a–56

57 Copyright © Houghton Mifflin Company. All rights reserved. 14a–57

58 Copyright © Houghton Mifflin Company. All rights reserved. 14a–58 sp 2 hybridization of an oxygen atom 1 trigonal Bond with 2 lone pairs + 1 for a pi bond sp 2 pxpx 4 hybridized orbitals sp 2 pxpx

59 Copyright © Houghton Mifflin Company. All rights reserved. 14a–59 Figure 14.19: (a) Orbitals predicted by the LE model to describe (b) The Lewis structure for carbon dioxide

60 Copyright © Houghton Mifflin Company. All rights reserved. 14a–60 sp hybridization of a carbon atom 4 hybridized orbitals sp 2 linear bonds + 2 for pi bonds sp pypy pypy pxpx pxpx

61 Copyright © Houghton Mifflin Company. All rights reserved. 14a–61

62 Copyright © Houghton Mifflin Company. All rights reserved. 14a–62 sp hybridization of an nitrogen atom 4 hybridized orbitals sp 1 linear Bonds with 1 lone pair + 2 for pi bonds sp pypy pypy pxpx pxpx

63 Copyright © Houghton Mifflin Company. All rights reserved. 14a–63 Figure 14.20: (a) An sp hybridized nitrogen atom (b) The s bond in the N 2 molecule (c) the two p bonds in N 2 are formed

64 Copyright © Houghton Mifflin Company. All rights reserved. 14a–64 Figure 14.21: A set of dsp 3 hybrid orbitals on a phosphorous atom

65 Copyright © Houghton Mifflin Company. All rights reserved. 14a–65 Hybridization Involving d Orbitals 3s 3p 3d promote five sp 3 d orbitals 3d3d F F F P F F A BeBe BeBe BeBe BaBa BaBa Trigonal bipyramidal hybridize degenerate orbitals (all EQUAL) unhybridized P atom P = [Ne]3s 2 3p 3 vacant d orbitals

66 Copyright © Houghton Mifflin Company. All rights reserved. 14a–66 Figure 11.6 The five sp 3 d hybrid orbitals in PCl 5

67 Copyright © Houghton Mifflin Company. All rights reserved. 14a–67 Figure 14.22: The orbitals used to form the bonds in the PCL 5 molecule

68 Copyright © Houghton Mifflin Company. All rights reserved. 14a–68 Figure 14.23: An octahedral set of d 2 sp 3 orbitals on a sulfur atom

69 Copyright © Houghton Mifflin Company. All rights reserved. 14a–69 Figure 11.7 The six sp 3 d 2 hybrid orbitals in SF 6

70 Copyright © Houghton Mifflin Company. All rights reserved. 14a–70 Figure 14.24: The relationship among the number of effective pairs, their spatial arrangement, and the hybrid orbital set required

71 Copyright © Houghton Mifflin Company. All rights reserved. 14a–71 Figure 14.24: The relationship among the number of effective pairs, their spatial arrangement, and the hybrid orbital set required (contd)

72 Copyright © Houghton Mifflin Company. All rights reserved. 14a–72 Figure 11.8 The conceptual steps from molecular formula to the hybrid orbitals used in bonding. Molecular formula Lewis structure Molecular shape and e - group arrangement Hybrid orbitals Figure 10.1 Step 1 Figure Step 2Step 3 Table 11.1

73 Copyright © Houghton Mifflin Company. All rights reserved. 14a–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.

74 Copyright © Houghton Mifflin Company. All rights reserved. 14a–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.

75 Copyright © Houghton Mifflin Company. All rights reserved. 14a–75 Figure 14.25: The combination of hydrogen 1s atomic orbitals to form MOs

76 Copyright © Houghton Mifflin Company. All rights reserved. 14a–76 Figure 14.25: The combination of hydrogen 1s atomic orbitals to form MOs

77 Copyright © Houghton Mifflin Company. All rights reserved. 14a–

78 Copyright © Houghton Mifflin Company. All rights reserved. 14a–78 Auto mufflers use destructive interference of sound waves to reduce engine noises. - ( - sign flips phase of the sound wave function) - = 0

79 Copyright © Houghton Mifflin Company. All rights reserved. 14a–79 Bose is $200. Want to do it yourself? See Web site.

80 Copyright © Houghton Mifflin Company. All rights reserved. 14a–80

81 Copyright © Houghton Mifflin Company. All rights reserved. 14a–81 Amplitudes of wave functions added An analogy between light waves and atomic wave functions. Amplitudes of wave functions subtracted. NOTE: +/- signs show PHASES of waves, NOT CHARGES!

82 Copyright © Houghton Mifflin Company. All rights reserved. 14a–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.

83 Copyright © Houghton Mifflin Company. All rights reserved. 14a–83 Figure 14.27: Bonding and anitbonding MOs

84 Copyright © Houghton Mifflin Company. All rights reserved. 14a–84 Figure 14.30: The MO energy-level diagram for the He 2 + ion. # BONDING es = 2 # ANTIBONDING es = 1 Bond order = ½(2-1) = ½

85 Copyright © Houghton Mifflin Company. All rights reserved. 14a–85 Figure 14.31: The MO energy-level diagram for the H 2 + ion

86 Copyright © Houghton Mifflin Company. All rights reserved. 14a–86 Figure 14.28: MO energy-level diagram for the H 2 molecule

87 Copyright © Houghton Mifflin Company. All rights reserved. 14a–87 Figure 14.29: The MO energy-level diagram for the He 2 molecule

88 Copyright © Houghton Mifflin Company. All rights reserved. 14a–88 Figure 14.30: The MO energy-level diagram for the He 2 + ion.

89 Copyright © Houghton Mifflin Company. All rights reserved. 14a–89 Figure 14.31: The MO energy-level diagram for the H 2 + ion

90 Copyright © Houghton Mifflin Company. All rights reserved. 14a–90 Figure 14.32: The MO energy-level diagram for the H 2 - ion

91 Copyright © Houghton Mifflin Company. All rights reserved. 14a–91

92 Copyright © Houghton Mifflin Company. All rights reserved. 14a–92 Figure 14.33: The relative sizes of the lithium 1s and 2s atomic orbitals

93 Copyright © Houghton Mifflin Company. All rights reserved. 14a–93 Figure 14.34: The MO energy-level diagram for the Li 2 molecule

94 Copyright © Houghton Mifflin Company. All rights reserved. 14a–94 Figure 14.35: The three mutually perpendicular 2p orbitals on tow adjacent boron atoms.

95 Copyright © Houghton Mifflin Company. All rights reserved. 14a–95 Figure 14.36: The two p oribitals on the boron atom that overlap head-on combine to form bonding and antibonding orbitals.

96 Copyright © Houghton Mifflin Company. All rights reserved. 14a–96 Figure 14.37: The expected MO energy-level diagram for the combustion of the 2 P orbitals on two boron atoms.

97 Copyright © Houghton Mifflin Company. All rights reserved. 14a–97 Figure 14.37: The expected MO energy-level diagram for the combustion of the 2 P orbitals on two boron atoms.

98 Copyright © Houghton Mifflin Company. All rights reserved. 14a–98 Figure 14.38: The expected MO energy-level diagram for the B 2 molecule

99 Copyright © Houghton Mifflin Company. All rights reserved. 14a–99 Figure 14.39: An apparatus used to measure the paramagnetism of a sample

100 Copyright © Houghton Mifflin Company. All rights reserved. 14a–100 Figure 14.40: The correct MO energy-level diagram for the B 2 molecule.

101 Copyright © Houghton Mifflin Company. All rights reserved. 14a–101 Figure 14.41: The MO energy-level diagrams, bond orders, bond energies, and bond lengths for the diatomic molecules, B 2 through F 2.

102 Copyright © Houghton Mifflin Company. All rights reserved. 14a–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

103 Copyright © Houghton Mifflin Company. All rights reserved. 14a–103 Figure 14.43: The MO energy-level diagram for the NO molecule

104 Copyright © Houghton Mifflin Company. All rights reserved. 14a–104 Figure 14.44: The MO energy-level diagram for both the NO+ and CN- ions

105 Copyright © Houghton Mifflin Company. All rights reserved. 14a–105 Figure 14.45: A partial MO energy-level diagram for the HF molecule

106 Copyright © Houghton Mifflin Company. All rights reserved. 14a–106 Figure 14.46: The electron probability distribution in the bonding MO of the HF molecule

107 Copyright © Houghton Mifflin Company. All rights reserved. 14a–107 Figure 14.47: The resonance structures for O 3 and NO 3 -

108 Copyright © Houghton Mifflin Company. All rights reserved. 14a–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.

109 Copyright © Houghton Mifflin Company. All rights reserved. 14a–109 Figure 14.49: The s bonding system in the benzene molecule

110 Copyright © Houghton Mifflin Company. All rights reserved. 14a–110 Figure 14.50: The MO system in benzene is formed by combining the six p orbitals

111 Copyright © Houghton Mifflin Company. All rights reserved. 14a–111 Figure 14.51: The p orbitals used to form the bonding system in the NO 3 - ion

112 Copyright © Houghton Mifflin Company. All rights reserved. 14a–112

113 Copyright © Houghton Mifflin Company. All rights reserved. 14a–113 Electromagnetic spectrum λ ν

114 Copyright © Houghton Mifflin Company. All rights reserved. 14a–114

115 Copyright © Houghton Mifflin Company. All rights reserved. 14a–115

116 Copyright © Houghton Mifflin Company. All rights reserved. 14a–116

117 Copyright © Houghton Mifflin Company. All rights reserved. 14a–117 λν=c

118 Copyright © Houghton Mifflin Company. All rights reserved. 14a–118

119 Copyright © Houghton Mifflin Company. All rights reserved. 14a–119

120 Copyright © Houghton Mifflin Company. All rights reserved. 14a–120

121 Copyright © Houghton Mifflin Company. All rights reserved. 14a–121

122 Copyright © Houghton Mifflin Company. All rights reserved. 14a–122

123 Copyright © Houghton Mifflin Company. All rights reserved. 14a–123

124 Copyright © Houghton Mifflin Company. All rights reserved. 14a–124 Figure 14.52: Schematic representation of two electronic energy levels in a molecule

125 Copyright © Houghton Mifflin Company. All rights reserved. 14a–125 Figure 14.53: The various types of transitions are shown by vertical arrows.

126 Copyright © Houghton Mifflin Company. All rights reserved. 14a–126 Figure 14.54: Spectrum corresponding to the changes indicated in Fig

127 Copyright © Houghton Mifflin Company. All rights reserved. 14a–127 Figure 14.55: The molecular orbital diagram for the ground state of NO +

128 Copyright © Houghton Mifflin Company. All rights reserved. 14a–128 The molecular structure of beta-carotene

129 Copyright © Houghton Mifflin Company. All rights reserved. 14a–129 Figure 14.57: The electronic absorption spectrum of beta-carotene.

130 VIBRATIONS

131

132 Copyright © Houghton Mifflin Company. All rights reserved. 14a–132 Figure 14.58: The potential curve for a diatomic molecule

133 Copyright © Houghton Mifflin Company. All rights reserved. 14a–133 Figure 14.59: Morse energy curve for a diatomic molecule.

134 Copyright © Houghton Mifflin Company. All rights reserved. 14a–134 Figure 14.60: The three fundamental vibrations for sulfur dioxide

135 Copyright © Houghton Mifflin Company. All rights reserved. 14a–135 Figure 14.61: The infrared spectrum of CH 2 Cl 2.

136 Copyright © Houghton Mifflin Company. All rights reserved. 14a–136

137 Copyright © Houghton Mifflin Company. All rights reserved. 14a–137

138 Copyright © Houghton Mifflin Company. All rights reserved. 14a–138 Figure 14.62: Representations of the two spin states of the proton interacting

139 Copyright © Houghton Mifflin Company. All rights reserved. 14a–139 Figure 14.63: The molecular structure of bromoethane

140 Copyright © Houghton Mifflin Company. All rights reserved. 14a–140 Figure 14.64: The expected NMR spectrum for bromoethane

141 Copyright © Houghton Mifflin Company. All rights reserved. 14a–141 Figure 14.65: The spin of proton H y can by "up" or "down"

142 Copyright © Houghton Mifflin Company. All rights reserved. 14a–142 Figure 14.66: The spins for protons H y can be "up", can be opposed (in 2 ways) or can both be "down"

143 Copyright © Houghton Mifflin Company. All rights reserved. 14a–143 Figure 14.67: The spins for the protons H y can by arranged as shown in (a) leading to four different magnetic environments

144 Copyright © Houghton Mifflin Company. All rights reserved. 14a–144 Figure 14.68: The NMR spectrum of CH 3 CH 2 B r (bromoethane) with TMS reference

145 Copyright © Houghton Mifflin Company. All rights reserved. 14a–145 Figure 14.69: The molecule (2-butanone)

146 Copyright © Houghton Mifflin Company. All rights reserved. 14a–146 Fullerene-C 60 and Fullerene-C 70

147 Copyright © Houghton Mifflin Company. All rights reserved. 14a–147 Fullerene-C 60 and Fullerene-C 70

148 Copyright © Houghton Mifflin Company. All rights reserved. 14a–148 Figure 14.70: A technician speaks to a patient before heis moved intot eh cavity of a magnetic resonance imaging (MRI) machine.

149 Copyright © Houghton Mifflin Company. All rights reserved. 14a–149 Figure 14.71: A colored Magnetic Resonance Imaging (MRI) scan through a human head, showing a healthy brain in side view.


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