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Dr. Beverly A. Clement
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Dr. Beverly A. Clement
Copyright, 2007
CHAPTER 5
Periodicity an Atomic
Structure
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The Periodic Table
Developed in 1869 by Dmitri Mendeleev.
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Electromagnetic Radiation
wavelength
l
†
(Greek lower case lambda)
distance from the top (crest) of one wave to the
top of the next wave
units of distance

m, cm,
Å
1
Å =
1
–
10
m = 1
–
8
cm
frequency
(Greek lower case nu)
this is sometimes represented as
(italicized v)
number of crests (wavelengths) that pass a given
point per second
units of frequency = 1/time or s
–
1
or Hertz (Hz)
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Electromagnetic Radiation
Relationship for electromagnetic
radiation
c
=
l
c = velocity of light
3.00
8
m/s or 3
10
cm/s
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Electromagnetic Radiation
Example 1: What is the frequency of green light of
wavelength 5200
Å
? (c = 3.00
8
m/s)
First convert
Å
to
m
m
10
200
.
5
Å
m
0
1
1
Å
5200
7
10
l
l
c
c
m
10
5.200
10
3.00
7
s
m
8
1
14
s
10
5.77
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Atomic Spectra and Bohr Theory
Rydberg’s equation is an empirical equation that
relates the wavelengths of the lines in the
hydrogen spectrum.
m
n
constant)
s
(Rydberg'
m
10
1.097
R
1
7
H
of
spectrum
emission
the
in
lines
the
of
number
the
to
refer
n
and
m
2
2
2
2
n
1
m
1
c
R
or
n
1
m
1
R
1
l
You will encounter the universal gas constant
R
later.
Don’t confuse it with Rydberg’s constant R.
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Electromagnetic Radiation
Why worry about wavelength and
frequency?
These can be used to calculate energy.
Again, why?
Energy does lots of things both good and bad.
How much light at what frequency is needed to cause
cancer?
How many cells are required to work a calculator in dim
light?
How sensitive is a motion detector or electric eye timer?
How much light is required to darken light sensitive
glasses?
Etc.
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Electromagnetic Radiation
Max Planck calculated the energy that is
quantized in a photon.
The energy of light can be expressed as
l
c
or
h
E
h
E
s
J
10
6.626
constant
s
Planck’
34
h
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Electromagnetic Radiation
Example 2: What is energy of a photon of green light
with wavelength 5200 Å? (c = 3.00
8
m/s;
h =
6.626
10
–
34
J∙s
)
l
c
or
h
E
h
E
5200 Å = 5.200
–
7
m
m
10
200
.
5
)
10
s)(3.00
J
10
626
.
6
(
7
s
m
8
34
E
J/photon
10
83
.
3
19
E
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Electromagnetic Radiation
Example 3: What is energy of 1 mole of photons
of green light with wavelength 5200 Å?
From the previous example
J/photon
10
83
.
3
19
E
l)
photons/mo
10
6.02
(
J/photon)
10
83
.
3
(
23
19
E
kJ/mol
231
or
J/mol
10
31
.
2
5
E
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The Wave Nature of the Electron
Louis de Broglie postulated that electrons have
wave

like properties
The wavelengths of electrons are described by
the
de Broglie relationship.
v
h
m
l
constant
s
Planck’
h
kg)
(in
particle
of
mass
m
particle
of
velocity
v
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Photoelectric Effect
Albert Einstein explained that light had both particle
and energy characteristics.
The particle/energy unit of light was called a photon.
FYI.
Einstein won the 1921 Nobel Prize in Physics
for this discovery.
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Atomic Spectra and Bohr Theory
It had been known that an electric current passing
through a gas in a vacuum tube (at very low
pressure) caused the gas to emit light.
This light could be broken into its components and
was found to be a series of
bright
lines.
This is a
bright line
or
emission
spectrum
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Atomic Spectra and Bohr Theory
It was also known that if you passed a beam of
white light through a sample of gas, the spectrum
would show a series of dark lines where the specific
wavelengths of light had been absorbed.
This is
dark line
or
absorption
spectra.
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Atomic Spectra and Bohr Theory
These spectra are as characteristic as fingerprints
and can be used to identify elements.
This is commonly used to identify the elements in
individual stars and the atmospheres of their
planets.
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Atomic Spectra and Bohr Theory
The spectra of atoms provides quite a bit of
information about their internal structure.
Bohr, Schrodinger, and Heisenberg were some of
the first to translate the language of atoms.
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The Origin of Spectral Lines
Light of a characteristic wavelength (and
frequency) is absorbed when an electron
jumps from lower
E
(orbit) to higher
E
(orbit).
This jump in energy is the original
quantum
leap
.
This is the origin of absorption spectrum.
The energy is specifically characteristic of
the energy quantum levels available to the
electrons in an elements electron shell.
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The Wave Nature of the Electron
Electrons, all particles for that matter, have both
a particle and a wave like character.
Wave

particle duality is a fundamental property of
submicroscopic particles.
Newtonian physics (gravity, friction, etc.) deals
with regular objects.
Subatomic particles follow their own laws of
physics called
quantum mechanics
.
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Quantum Mechanical Picture
Heisenberg Uncertainty Principle
It is impossible to determine simultaneously both
the position and momentum of an electron.
Any device for detecting the motion of an electron
disturbs its position and/or momentum.
Therefore the positions and momentum of
electrons must be described in terms of probability
functions (
Ⱐ瑨攠䝲敥欠
psi
)
.
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Quantum Numbers
Basic Postulates of Quantum Theory
Atoms and molecules can exist only in certain
energy states. In each energy state, the atom or
molecule has a definite energy. When an atom
or molecule changes its energy state, it must
emit or absorb just enough energy to bring it to
the new energy state (the quantum condition).
The allowed energy states of atoms and
molecules can be described by sets of numbers
called
quantum numbers
.
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Quantum Numbers
Quantum numbers
are solutions of the
Schr
ö
dinger, Heisenberg & Dirac
equations
Four quantum numbers are necessary to
describe the energy states of electrons in
atoms
n
–
the principle quantum number
–
subsidiary quantum number
m
–
magnetic quantum number
m
s
–
spin quantum number
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Quantum Numbers
Principal Quantum Number
–
n
This is the first quantum number and describes the
shell or layer that the electrons are found in.
These are numbered sequentially with the
innermost level beginning with the number
1
.
n = 1, 2, 3, 4, ......
There is an alternate numbering system using
letters, the first level begins with letter
K
.
n = K, L, M, N, ......
The electron’s energy depends principally on n.
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Quantum Numbers
Subsidiary Quantum number
–
The subsidiary quantum number,
Ⱐ摥d捲楢敳c瑨t
shape of the orbital
the electron occupies
.
These have the value of
n

1
and are assigned the
values of
= 0, 1, 2, 3, 4, 5, .......(
n

1
)
Like n, these values may also be described as
letters
=
s
(0),
p
(1),
d
(2), f (3),
g
(4),
h
(5),..
This is the shape (volume) that the electrons
occupy 90

95% of the time.
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Quantum Numbers
Magnetic quantum number
–
m
This quantum number indicates specifically which
orbital the electron resides in.
Unlike
,
m
楳湬n 摥d捲楢敤c 湵浢n牳湤慹
桡h攠愠癡汵攠潦e
, 0,
–
⡯爠
±
and 0).
For n = 1,
=
0
,
and m
= 0
this describes the
s
orbital
there is only 1
s
orbital per quantum level (shell)
and
the first shell only has one type of orbital
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Quantum Numbers
Magnetic quantum number
–
m
For n = 2,
㴠=湤‱
景爠渠㴠=†
㴠=Ⱐ,
㴠=
this is an
s
orbital (remember 1
s
per level)
for n = 2
㴠=Ⱐ,
㴠⬱Ⱐ〬0
–
1
this is a
p
orbital, there are 3
p
orbitals
Row 2 (the L shell) is the first shell to have
p
orbitals.
The 3
p
orbitals are described according to the axis
they lie along.
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Quantum Numbers
Magnetic quantum number
–
m
For n = 3,
㴠=Ⱐㄬ湤′
景爠渠㴠=
㴠=Ⱐ,
㴠=
this is an
s
orbital (remember 1
s
per level)
for n = 3
㴠=Ⱐ,
㴠⬱Ⱐ〬0
–
1
this is a
p
orbital, beginning with row 2 there are 3
p
orbitals per shell
for n = 3
㴠=Ⱐ,
㴠⬲Ⱐ⬱Ⱐ〬+
–
1,
–
2
this is a
d
orbital, beginning with row 3, the
possibility of
d
orbitals exists (even though
d
orbitals don’t show up until an element has already
begun to fill shell 4)
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Quantum Numbers
Magnetic quantum number
–
m
For n = 4,
㴠=Ⱐㄬ′ⱡ湤,3
景爠渠㴠=
㴠=Ⱐ,
㴠=
(1 orbital)
this is an
s
orbital (remember 1
s
per level)
for n = 4
㴠=Ⱐ,
㴠⬱Ⱐ〬0
–
1
this is a
p
orbital, 1 group of 3
p
orbitals per shell
beginning with Row 2
for n = 4
㴠=Ⱐ,
㴠⬲Ⱐ⬱Ⱐ〬+
–
1,
–
2
this is a
d
orbital, 1 group of 5
d
orbitals (possible) per
shell beginning with Row 3
for n = 4
㴠=Ⱐ,
㴠⬳Ⱐ⬲Ⱐ⬱Ⱐ〬0
–
1,
–
2,
–
3
these are
f
orbitals, 1 group of 7
f
orbitals (possible) per
shell beginning with Row 4
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Quantum Numbers
Spin Quantum Number

m
s
This is the final quantum number and represents the
spin of the electron.
The spin of an electron is arbitrarily assigned a
value of
±
½.
Each orbital may hold a maximum of 2 electrons,
one with a spin of +
½
, the other with a spin of
–
½
Pauli Exclusion Principle
No two electrons in an atom can have the same
set of 4 quantum numbers.
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Atomic Orbitals
Atomic orbitals are defined as regions of space
where the probability of finding an electron about an
atom is highest.
The orbital levels are described either as:
n = 1, 2, 3, 4, 5…
or by K, L, M, N, …..
FYI
. There is a specific type of nuclear decay in
which the nucleus captures an interior electron as
part of its radioactive decay. This decay is called K

capture after the orbital the electron came from.
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Atomic Orbitals
The innermost orbital of any level is the
s
orbital.
There is
one
s
orbital per level.
㴠=†慮搠m
㴠=
The
s
orbital is spherically symmetrical.
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Atomic Orbitals
Row 2 is the first to have
p
orbitals
㴠=†慮搠m
㴠ㄬ‰Ⱐ
–
1
These orbitals are described as dumbbell or peanut
shaped.
There are 3 mutually perpendicular
p
orbitals
directed along the axes of a Cartesian coordinate.
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Atomic Orbitals
Row 3 is the first to have
d
orbitals allowed
= 2 and m
㴠㈬ ㄬ1〬0
–
1,
–
2
There are 4 clover leaf shaped
d
orbitals
rotated 45
°
off the Cartesian axes
And 1
peanut
shaped orbital with a halo or
donut around it.
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Atomic Orbitals
Row 4 is the first to have
f
orbitals allowed
㴠=†慮搠m
㴠㌬′Ⱐㄬ,〬0
–
1,
–
2,
–
3
These are the most complex shaped orbitals.
Four are described as double cloverleaf or double
dumbbell shaped orbitals.
The remaining three
f
orbitals are dumbbell
shaped each with a pair of halos or donuts
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Atomic Orbitals
Each atom from H through the most recently
discovered is built up sequentially one electron at
a time.
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Atomic Orbitals
The last quantum number deals with the spin of
the electrons.
Electrons spin and since they carry a charge, this
spinning results in a magnetic field.
Experimentally it has been determined that
unpaired electrons have their spin aligned (their
magnetic fields add together).
Each orbital may contain a maximum of 2
electrons.
For electrons to pair, they must have opposite
spins.
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Atomic Orbitals
Compounds which contain unpaired
electrons are paramagnetic.
paramagnetic
–
attracted to a magnet
Compounds in which all electrons are
paired are diamagnetic.
diamagnetic
–
repelled by a magnet
There is one more type of magnetism
associated with compounds,
ferromagnetism.
ferromagnetic
–
compounds of Fe, Co, or Ni,
which may be permanently magnetized
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Atomic Orbitals
The maximum number of orbitals per n level is may
be calculated by n
2
The maximum number of electrons that may exist
per n level is 2n
2
Energy Level
# of Orbitals
Max. # of e
–
n
n
2
2n
2
1
1
2
2
4
8
3
9
18
4
16
32
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Quantum Mechanics
and Atomic Line Spectra
2
2
1
1
λ
1
n
m
R
1
2
nm
10
097
.
1
constant
Rydberg
R
shell
inner
to
is
transition
the
shell
m
shell
outer
from
is
transition
the
shell
n
Lyman series
–
ultraviolet
Balmer series
–
visible
Paschen series

infrared
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Electronic Configurations
Aufbau Principle
The electron that distinguishes an
element from the previous element
enters the lowest energy atomic orbital
available.
Hund’s Rule
Electrons will occupy all orbitals singly
before pairing can begin.
The spins of these electrons will be aligned.
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Electronic Configurations
According to the Aufbau Principle, electrons enter
the lowest energy atomic orbital available.
The first hitch in this orderly progression occurs at
the end of row 3 of the periodic table.
4
s
is lower in energy than 3
d
which is followed by 4
p
This is repeated again at the end of row 4
5
s
is lower in energy than 4
d
which is followed by 5
p
This is repeated again and develops a new twist at
the lanthanides.
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Electronic Configurations
The reason for this anomaly is
Hund’s Rule.
Electron Orbital Stability
Completely filled orbitals are very stable.
Completely empty orbitals are very stable.
Half

filled orbitals, while not as stable as filled or
empty orbitals, are much more stable than
partially filled orbitals.
Reactions occur to obtain orbital stability.
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Electronic Configurations
Consider the two possibilities available to an
electron entering after 3
p.
4
3
s
d
partially filled orbital
unstable
4
3
s
d
half filled orbital
stable
Now add the second electron to these two possibilities.
4
3
s
d
partially filled orbitals
unstable
4
3
s
d
filled orbital
very
stable
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Electronic Configurations
The easiest way to see this is to use the
periodic table.
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Electronic Configurations
An alternate method to view the periodic table is:
1
2
3
4
5
6
7
3
d
4
d
5
d
6
d
4
f
5
f
d

transition elements
f

transition elements
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Electronic Configurations
Just as each element differs from its
predecessor by the addition of one proton,
each element differs from the preceding
element by the addition of 1 electron to its
orbital configuration.
Atomic orbitals are built up by this step

wise addition of electrons.
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Electronic Configurations
1
st
Row Elements
ion
Configurat
Electronic
1
s
1
1
1
H
s
2
2
1
He
s
Remember, the atomic number is equal to the number
of electrons found in the neutral atom.
Each positive charge means 1 less electron than this
number.
Each negative charge means 1 more electron than the
number of protons present.
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Electronic Configurations
2
nd
Row
Elements
ion
Configurat
Electronic
2
2
1
p
s
s
1
2
3
2
1
Li
s
s
2
2
4
2
1
Be
s
s
1
2
2
5
2
2
1
B
p
s
s
2
2
2
6
2
2
1
C
p
s
s
3
2
2
7
2
2
1
N
p
s
s
4
2
2
8
2
2
1
O
p
s
s
5
2
2
9
2
2
1
F
p
s
s
6
2
2
10
2
2
1
Ne
p
s
s
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Electronic Configurations
3
rd
Row Elements
ion
Configurat
Electronic
3
3
p
s
1
11
3
Ne
Ne
Na
s
2
12
3
Ne
Ne
Mg
s
1
2
13
3
3
Ne
Ne
Al
p
s
2
2
14
3
3
Ne
Ne
Si
p
s
3
2
15
3
3
Ne
Ne
P
p
s
4
2
16
3
3
Ne
Ne
S
p
s
5
2
17
3
3
Ne
Ne
Cl
p
s
6
2
18
3
3
Ne
Ne
Ar
p
s
49
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Dr. Beverly A. Clement
Copyright, 2002
49
Blinn College, Bryan Campus
Dr. Beverly A. Clement
Copyright, 2007
Electronic
Configurations
4
th
Row
Elements
ion
Configurat
Electronic
4
4
3
p
s
d
Two half filled orbitals are more stable than a filled and
partially filled orbital.
This is seen throughout the elements.
1
19
4
Ar
Ar
K
s
2
20
4
Ar
Ar
Ca
s
1
2
21
3
4
Ar
Ar
Sc
d
s
2
2
22
3
4
Ar
Ar
Ti
d
s
3
2
23
3
4
Ar
Ar
V
d
s
5
1
24
3
4
Ar
Ar
Cr
d
s
50
Blinn College, Bryan Campus
Dr. Beverly A. Clement
Copyright, 2002
50
Blinn College, Bryan Campus
Dr. Beverly A. Clement
Copyright, 2007
Electronic Configurations
4
th
Row Elements
5
2
25
3
4
Ar
Ar
Mn
d
s
6
2
26
3
4
Ar
Ar
Fe
d
s
7
2
27
3
4
Ar
Ar
Co
d
s
8
2
28
3
4
Ar
Ar
Ni
d
s
10
1
29
3
4
Ar
Ar
Cu
d
s
10
2
30
3
4
Ar
Ar
Zn
d
s
ion
Configurat
Electronic
4
4
3
p
s
d
51
Blinn College, Bryan Campus
Dr. Beverly A. Clement
Copyright, 2002
51
Blinn College, Bryan Campus
Dr. Beverly A. Clement
Copyright, 2007
Electronic Configurations
4
th
Row Elements
ion
Configurat
Electronic
4
4
3
p
s
d
1
10
2
31
4
3
4
Ar
Ar
Ga
p
d
s
2
10
2
32
4
3
4
Ar
Ar
Ge
p
d
s
3
10
2
33
4
3
4
Ar
Ar
As
p
d
s
4
10
2
34
4
3
4
Ar
Ar
Se
p
d
s
5
10
2
35
4
3
4
Ar
Ar
Br
p
d
s
6
10
2
36
4
3
4
Ar
Ar
Kr
p
d
s
52
Blinn College, Bryan Campus
Dr. Beverly A. Clement
Copyright, 2002
52
Blinn College, Bryan Campus
Dr. Beverly A. Clement
Copyright, 2007
Electronic Configurations
What about the direction of the arrows
indicating the spin on the electron?
It doesn’t what direction of spin you choose to use
first for an atom as long as you are consistent.
If the first arrow is shown pointed down, each of the
electrons must enter empty orbitals with a downward
pointing electron.
(or vice versa)
53
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Dr. Beverly A. Clement
Copyright, 2002
53
Blinn College, Bryan Campus
Dr. Beverly A. Clement
Copyright, 2007
Atomic Radii
(A Group Elements Only)
Atomic radii describes the size of atoms.
This increases as you go from the right to the left.
(opposite what you would think since more e
–
are
added.)
This increases from top to bottom.
(as expected
–
more shells are being added)
radii increases
54
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Dr. Beverly A. Clement
Copyright, 2002
54
Blinn College, Bryan Campus
Dr. Beverly A. Clement
Copyright, 2007
Atomic Radii
All radii are in angstroms,
Å
.
55
Blinn College, Bryan Campus
Dr. Beverly A. Clement
Copyright, 2002
55
Blinn College, Bryan Campus
Dr. Beverly A. Clement
Copyright, 2007
Atomic Radii
The decreasing radii across a period is due to the
shielding or screening effect of the inner electrons
[He] or [Ne], etc.
Consequently the outer electrons feel a stronger
effective nuclear charge than expected.
Li [He] shields effective charge is +1
Be [He] shields effective charge is +2
F [He] shields effective charge is +7
Na [Ne] shields effective charge is +1
56
Blinn College, Bryan Campus
Dr. Beverly A. Clement
Copyright, 2002
56
Blinn College, Bryan Campus
Dr. Beverly A. Clement
Copyright, 2007
End of Chapter 5
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