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.
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14a–1
Figure 12.18: Three representations
of the hydrogen 1s
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14a–2
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.
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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.
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14a–4
Figure 12.19b: Representation of
the 2p orbitals.
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14a–5
Hydrogen, H2
Hydrogen fluoride, HF
Fluorine, F2
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14a–6
Figure 14.1: (a) Lewis structure of the methane
molecule (b) the tetrahedral molecular geometry
of the methane molecule.
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14a–7
Figure 14.2: valence orbitals on a free
carbon atom
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14a–8
Figure 14.1: (a) Lewis structure of the methane
molecule (b) the tetrahedral molecular geometry
of the methane molecule.
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14a–9
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.
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14a–10
Carbon
1s22s22p2
Carbon could only make two bonds
if no hybridization occurs. However,
carbon can make four equivalent bonds.
B
A
B
B
Energy
hybrid orbitals
px
py
B
pz
s
Brown, LeMay, Bursten, Chemistry The Central Science, 2000, page 321
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sp3
sp3
C atom of CH4 orbital diagram
14a–11
Figure 14.4: Cross section of an sp3 orbital
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14a–12
The four sp3 hybrid orbitals in CH4
Promotion
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14a–13
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
Rotation about C-C
bond allowed.
s (Greek sigma) bonds
have axial symmetry and
good overlap
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relatively even
distribution of electron
density over all s
bonds
14a–14
Figure 14.6: Tetrahedral set of four sp3
orbitals on the carbon atom
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14a–15
Figure 14.7: The nitrogen atom in ammonia
is sp3 hybridized.
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14a–16
The four sp3 hybrid orbitals in CH4
Promotion
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14a–17
The four sp3 hybrid orbitals in CH4
Promotion
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14a–18
The four sp3 hybrid orbitals in NH3
Promotion
N
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14a–19
The four sp3 hybrid orbitals in NH3
Promotion
N
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14a–20
Figure 11.5
The sp3 hybrid orbitals in H2O
Lone pairs
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14a–21
Diamond - sp3 hybridized C
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14a–22
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
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14a–23
The three sp2 hybrid orbitals in
BF3
Promotion
Note the single left over
Unhybridized p orbital on B
Region of overlap
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14a–24
Hybrid Orbitals
Ground-state B atom
2s
2p
B atom with one electron “promoted”
2s
2p
Energy
hybrid orbitals
px
py
pz
sp2
sp2
s
2p
B atom of BH3 orbital diagram
H
hybridize
B
s orbital
H
p orbitals
three sps hybrid orbitals
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sp2
hybrid orbitals shown together
(large lobes only)
H
14a–25
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.
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14a–26
Figure 14.13: (a) The orbitals used to form the bonds in
ethylene. (b) The Lewis structure for ethylene.
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14a–27
The plastics shown here were
manufactured with ethylene.
Source: Comstock - Mountainside, NJ
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14a–28
Figure 14.11: The s bonds in ethylene.
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14a–29
Figure 14.12: A carbon-carbon double bond
consists of a s bond and a p bond.
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14a–30
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
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14a–31
Graphite – sp2 hybridized C
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14a–32
Fullerene-C60 and Fullerene-C70
What hybridization of C describes the structures?
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14a–33
Figure 14.14: When one s orbital and one
p orbital are hybridized, a set of two sp
orbitals oriented at 180 degrees results.
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14a–34
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.
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14a–35
The two sp hybrid orbitals in gaseous BeCl2
Note the two “leftover” p orbitals of Be
Region of overlap
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14a–36
Figure 14.15: The hybrid orbitals in the
CO2 molecule
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14a–37
Figure 14.16: orbital energy level diagram for
the formation of sp hybrid orbitals of carbon.
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14a–38
Figure 14.17: Orbitals of an sp hybridized
carbon atom
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14a–39
Figure 14.18: Orbital arrangement for an sp2
hybridized oxygen atom
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14a–40
Figure 14.19: (a) Orbitals predicted by the LE model to
describe (b) The Lewis structure for carbon dioxide
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14a–41
Hybrid Orbitals
Types of Hybrid Orbitals
sp
Shapes: linear
# orbitals: 2
sp2
triangular
3
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sp3
sp3d
sp3d2
tetrahedral trig. bipyram. Octahedral
4
5
6
14a–42
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
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14a–43
The four sp3 hybrid orbitals in NH3
Promotion
N
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14a–44
The four sp3 hybrid orbitals in NH3
2p
2p
sp
sp
Promotion
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14a–45
The conceptual steps from molecular formula to the hybrid orbitals
used in bonding.
Step 1
Molecular
formula
Step 2
Lewis
structure
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Step 3
Molecular shape
and e- group
arrangement
Hybrid
orbitals
14a–46
sp3 hybridization of a carbon atom
4 atomic
orbitals
s
p
4 hybridized
orbitals
sp3
4 tetrahedral
bonds
sp3
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14a–47
sp3 hybridization of a carbon atom
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14a–48
sp3 hybridization of a nitrogen atom
4 atomic
orbitals
s
p
4 hybridized
orbitals
sp3
3 tetrahedral
bonds with
1 lone pair
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sp3
14a–49
sp3 hybridization of a nitrogen atom
N
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14a–50
sp3 hybridization of a oxygen atom
4 atomic
orbitals
s
p
4 hybridized
orbitals
sp3
2 tetrahedral
bonds with
2 lone pairs
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sp3
14a–51
sp3 hybridization of a oxygen atom
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14a–52
sp2 hybridization of a carbon atom
4 atomic
orbitals
s
p
4 hybridized
orbitals
3 trigonal
Bonds
+ 1 for a pi bond
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sp2
px
sp2
px
14a–53
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14a–54
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14a–55
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14a–56
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14a–57
sp2 hybridization of an oxygen atom
4 atomic
orbitals
s
p
4 hybridized
orbitals
1 trigonal
Bond with
2 lone pairs
+ 1 for a pi bond
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sp2
px
sp2
px
14a–58
Figure 14.19: (a) Orbitals predicted by the LE model to
describe (b) The Lewis structure for carbon dioxide
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14a–59
sp hybridization of a carbon atom
4 atomic
orbitals
s
p
4 hybridized
orbitals
2 linear
bonds
+ 2 for pi bonds
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sp
px
py
sp
px
py
14a–60
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14a–61
sp hybridization of an nitrogen atom
4 atomic
orbitals
s
p
4 hybridized
orbitals
1 linear
Bonds with
1 lone pair
+ 2 for pi bonds
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sp
px
py
sp
px
py
14a–62
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
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14a–63
Figure 14.21: A set of dsp3 hybrid orbitals
on a phosphorous atom
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14a–64
Hybridization Involving d Orbitals
promote
3s
3p
3d
unhybridized P atom
P = [Ne]3s23p3
3s
3p
3d
vacant d orbitals
hybridize
Ba
F
Be
F
P
five sp3d orbitals
F
3d
Be
F
Be
F
Ba
degenerate
orbitals
(all EQUAL)
Trigonal bipyramidal
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14a–65
Figure 11.6
The five sp3d hybrid orbitals in PCl5
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14a–66
Figure 14.22: The orbitals used to form the
bonds in the PCL5 molecule
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14a–67
Figure 14.23: An octahedral set of d2sp3
orbitals on a sulfur atom
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14a–68
Figure 11.7
The six sp3d2 hybrid orbitals in SF6
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14a–69
Figure 14.24: The relationship among the number
of effective pairs, their spatial arrangement,
and the hybrid orbital set required
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14a–70
Figure 14.24: The relationship among the number
of effective pairs, their spatial arrangement,
and the hybrid orbital set required (cont’d)
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14a–71
Figure 11.8
The conceptual steps from molecular formula to the hybrid orbitals
used in bonding.
Step 1
Molecular
formula
Step 2
Lewis
structure
Figure 10.1
Step 3
Molecular shape
and e- group
arrangement
Figure 10.12
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Hybrid
orbitals
Table 11.1
14a–72
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.
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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.
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14a–74
Figure 14.25: The combination of hydrogen
1s atomic orbitals to form MOs
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14a–75
Figure 14.25: The combination of hydrogen
1s atomic orbitals to form MOs
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14a–76
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10.6
14a–77

- (- sign flips phase of
the sound wave function)
-=0
Auto mufflers use destructive interference
of sound waves to reduce engine noises.
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14a–78
Bose is
$200. Want to
do it yourself?
See Web site.
http://www.headwize.com/projects/noise_prj.htm
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14a–79
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14a–80
An analogy between light waves and atomic wave functions.
NOTE: +/- signs show
PHASES of waves, NOT
CHARGES!
Amplitudes of wave
functions added
Amplitudes of wave
functions subtracted.
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14a–81
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.
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14a–82
Figure 14.27: Bonding and anitbonding MOs
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14a–83
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
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14a–84
Figure 14.31: The MO energy-level
diagram for the H2+ ion
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14a–85
Figure 14.28: MO energy-level diagram
for the H2 molecule
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14a–86
Figure 14.29: The MO energy-level
diagram for the He2 molecule
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14a–87
Figure 14.30: The MO energy-level diagram
for the He2+ ion.
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14a–88
Figure 14.31: The MO energy-level
diagram for the H2+ ion
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14a–89
Figure 14.32: The MO energy-level diagram
for the H2- ion
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14a–90
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14a–91
Figure 14.33: The relative sizes of the lithium
1s and 2s atomic orbitals
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14a–92
Figure 14.34: The MO energy-level diagram
for the Li2 molecule
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14a–93
Figure 14.35: The three mutually perpendicular
2p orbitals on tow adjacent boron atoms.
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14a–94
Figure 14.36: The two p oribitals on the boron
atom that overlap head-on combine to form
bonding and antibonding orbitals.
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14a–95
Figure 14.37: The expected MO energy-level
diagram for the combustion of the 2P orbitals
on two boron atoms.
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14a–96
Figure 14.37: The expected MO energy-level
diagram for the combustion of the 2P orbitals
on two boron atoms.
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14a–97
Figure 14.38: The expected MO energy-level
diagram for the B2 molecule
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14a–98
Figure 14.39: An apparatus used to measure
the paramagnetism of a sample
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14a–99
Figure 14.40: The correct MO energy-level
diagram for the B2 molecule.
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14a–100
Figure 14.41: The MO energy-level diagrams, bond
orders, bond energies, and bond lengths for the
diatomic molecules, B2 through F2.
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14a–101
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
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14a–102
Figure 14.43: The MO energy-level diagram
for the NO molecule
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14a–103
Figure 14.44: The MO energy-level diagram
for both the NO+ and CN- ions
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14a–104
Figure 14.45: A partial MO energy-level
diagram for the HF molecule
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14a–105
Figure 14.46: The electron probability distribution
in the bonding MO of the HF molecule
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14a–106
Figure 14.47: The resonance structures
for O3 and NO3-
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14a–107
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.
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14a–108
Figure 14.49: The s bonding system in
the benzene molecule
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14a–109
Figure 14.50: The MO system in benzene is
formed by combining the six p orbitals
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14a–110
Figure 14.51: The p orbitals used to form the
bonding system in the NO3- ion
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14a–111
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14a–112
Electromagnetic spectrum
ν
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λ
14a–113
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14a–114
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14a–115
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14a–116
λν=c
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14a–117
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14a–118
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14a–119
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14a–120
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14a–121
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14a–122
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14a–123
Figure 14.52: Schematic representation of
two electronic energy levels in a molecule
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14a–124
Figure 14.53: The various types of
transitions are shown by vertical arrows.
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14a–125
Figure 14.54: Spectrum corresponding to the
changes indicated in Fig. 14.53.
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14a–126
Figure 14.55: The molecular orbital diagram
for the ground state of NO+
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14a–127
The molecular
structure of
beta-carotene
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14a–128
Figure 14.57: The electronic absorption
spectrum of beta-carotene.
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14a–129
VIBRATIONS
VIBRATIONS
Figure 14.58: The potential curve for a
diatomic molecule
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14a–132
Figure 14.59: Morse energy curve for a
diatomic molecule.
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14a–133
Figure 14.60: The three fundamental
vibrations for sulfur dioxide
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14a–134
Figure 14.61: The infrared spectrum of
CH2Cl2.
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14a–135
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14a–136
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14a–137
Figure 14.62: Representations of the two
spin states of the proton interacting
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14a–138
Figure 14.63: The molecular structure of
bromoethane
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14a–139
Figure 14.64: The expected NMR
spectrum for bromoethane
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14a–140
Figure 14.65: The spin of proton Hy
can by "up" or "down"
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14a–141
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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14a–142
Figure 14.67:
The spins for the
protons Hy can
by arranged as
shown in (a)
leading to four
different
magnetic
environments
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14a–143
Figure 14.68: The NMR spectrum of
CH3CH2Br (bromoethane) with TMS reference
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14a–144
Figure 14.69: The molecule (2-butanone)
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14a–145
Fullerene-C60 and Fullerene-C70
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14a–146
Fullerene-C60 and Fullerene-C70
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14a–147
Figure 14.70: A technician speaks to a patient
before heis moved intot eh cavity of a magnetic
resonance imaging (MRI) machine.
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14a–148
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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14a–149