Download Ch 3 Lecture Notes

10/31/2016
CHAPTER 3
Atomic Structure:
Explaining the Properties of Elements
We are going to learn about the electronic structure of the atom,
and will be able to explain many things, including atomic
orbitals, oxidation numbers, and periodic trends.
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Chapter Outline
3.1 Waves of Light
3.2 Atomic Spectra
3.3 Particles of Light: Quantum Theory
3.4 The Hydrogen Spectrum and the Bohr Model
3.5 Electrons as Waves
3.6 Quantum Numbers
3.7 The Sizes and Shapes of Atomic Orbitals
3.8 The Periodic Table and Filling Orbitals
3.9 Electron Configurations of Ions
3.10 The Sizes of Atoms and Ions
3.11 Ionization Energies
3.12 Electron Affinities
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The Electromagnetic Spectrum
Continuous range of radiant energy,
(also called electromagnetic radiation).
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Electromagnetic Radiation
Mutually propagating electric and magnetic fields, at right
angles to each other, traveling at the speed of light c
a) Electric
b) Magnetic
Speed of light (c) in vacuum = 2.998 x 108 m/s
Properties of Waves - in the examples below,
both waves are traveling at the same velocity
Long wavelength = low frequency
Short wavelength = high frequency
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·  u
 = wavelength,  = frequency, u = velocity
Units: wavelength = meters (m)
frequency = cycles per second or Hertz (s-1)
wavelength (m) x frequency (s-1) = velocity (m/s)
Example:
A FM radio station in Portland has a
carrier wave frequency of 105.1
MHz. What is the wavelength?
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Chapter Outline
3.1 Waves of Light
3.2 Atomic Spectra
3.3 Particles of Light: Quantum Theory
3.4 The Hydrogen Spectrum and the Bohr Model
3.5 Electrons as Waves
3.6 Quantum Numbers
3.7 The Sizes and Shapes of Atomic Orbitals
3.8 The Periodic Table and Filling Orbitals
3.9 Electron Configurations of Ions
3.10 The Sizes of Atoms and Ions
3.11 Ionization Energies
3.12 Electron Affinities
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Atomic Spectra
a) Absorption: Fraunhofer lines (dark spectra)
b) Emission: e.g Na (bright line spectra)
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Atomic Absorption Spectra: Dark Lines
Spectrometer - a device that separates out the different wavelengths of
light. A “white” light sources produces a “continuous” spectrum; atomic
sources produces a "discrete" spectrum.
a) Hydrogen
b) Helium
c) Neon
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Atomic Emission (Line) Spectra
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Chemistry in Action: Element from the Sun
In 1868, Pierre Janssen detected a new emission line in the solar
emission spectrum that did not match known emission lines
The mystery element was named --
Chapter Outline
3.1 Waves of Light
3.2 Atomic Spectra
3.3 Particles of Light: Quantum Theory
3.4 The Hydrogen Spectrum and the Bohr Model
3.5 Electrons as Waves
3.6 Quantum Numbers
3.7 The Sizes and Shapes of Atomic Orbitals
3.8 The Periodic Table and Filling Orbitals
3.9 Electron Configurations of Ions
3.10 The Sizes of Atoms and Ions
3.11 Ionization Energies
3.12 Electron Affinities
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4
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Blackbody Radiation
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Photoelectric Effect
• phenomenon of light striking a metal surface and
producing an electric current (flow of electrons).
• If radiation below threshold energy, no electrons
released.
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Blackbody Radiation and the
Photoelectric Effect
Explained by a new theory:
Quantum Theory
• Radiant energy is “quantized”
– Having values restricted to whole-number
multiples of a specific base value.
• Quantum = smallest discrete quantity of
energy.
• Photon = a quantum of electromagnetic
radiation
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Quantized States
Quantized states:
discrete energy
levels.
Continuum states:
smooth transition
between levels.
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The energy of the photon is given by Planck’s Equation.
E = h
h = 6.626 × 10−34 J∙s
(Planck’s constant)
Sample Exercise 7.2
What is the energy of a photon of red light
that has a wavelength of 656 nm? The value
of Planck’s constant (h) is 6.626 × 10-34 J . s,
and the speed of light is 3.00 × 108 m/s.
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Chapter Outline
3.1 Waves of Light
3.2 Atomic Spectra
3.3 Particles of Light: Quantum Theory
3.4 The Hydrogen Spectrum and the Bohr Model
3.5 Electrons as Waves
3.6 Quantum Numbers
3.7 The Sizes and Shapes of Atomic Orbitals
3.8 The Periodic Table and Filling Orbitals
3.9 Electron Configurations of Ions
3.10 The Sizes of Atoms and Ions
3.11 Ionization Energies
3.12 Electron Affinities
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1
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The Hydrogen Spectrum and the
Rydberg Equation

 1
1
1 
= 1.097 10  2 nm 1  2  2 
n

λ
 i nf 
Exercise 7.4: using the Rydberg Equation
What is the wavelength of the line in the emission
spectrum of Hydrogen corresponding from ni = 7 to nf = 2?

 1
1
1 
= 1.097 102 nm1  2  2 
n n 
λ
f 
 i
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Using the Rydberg Equation for Absorption
What is the wavelength of the line in the absorption
spectrum of Hydrogen corresponding from ni = 2 to nf = 4?

 1
1
1 
= 1.097 102 nm1  2  2 
n n 
λ
f 
 i
The Bohr Model of Hydrogen
Neils Bohr used Planck and Einstein’s ideas of photons and quantization
of energy to explain the atomic spectra of hydrogen
photon of
light (h)
n=4
n=3
n=2
+
h
h
n=1
n=2
n=3
n=1
absorption
emission
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Electronic States
• Energy Level:
• An allowed state that an electron can occupy in
an atom.
• Ground State:
• Lowest energy level available to an electron in
an atom.
• Excited State:
• Any energy state above the ground state.
“Solar system” model of the atom where each “orbit”
has a fixed, QUANTIZED energy given by -
E orbit
2.178 x 10-18 Joules

n2
where n = “principle quantum number” = 1, 2, 3….
This energy is exothermic because it is potential
energy lost by an unbound electron as it is attracted
towards the positive charge of the nucleus.
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E = h
E = h
The Rydberg Equation can be derived from Bohr’s theory Ephoton = DE = Ef - Ei
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Example DE Calculation
Calculate the energy of a photon absorbed when an electron is
promoted from ni = 2 to nf = 5.
Sample Exercise 3.5
How much energy is required to ionize a ground-state hydrogen
atom? Put another way, what is the ionization energy of
hydrogen?
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Strengths and Weaknesses of the
Bohr Model
• Strengths:
• Accurately predicts energy needed to remove an
electron from an atom (ionization).
• Allowed scientists to begin using quantum theory to
explain matter at atomic level.
• Limitations:
• Applies only to one-electron atoms/ions; does not
account for spectra of multielectron atoms.
• Movement of electrons in atoms is less clearly defined
than Bohr allowed.
Chapter Outline
3.1 Waves of Light
3.2 Atomic Spectra
3.3 Particles of Light: Quantum Theory
3.4 The Hydrogen Spectrum and the Bohr Model
3.5 Electrons as Waves
3.6 Quantum Numbers
3.7 The Sizes and Shapes of Atomic Orbitals
3.8 The Periodic Table and Filling Orbitals
3.9 Electron Configurations of Ions
3.10 The Sizes of Atoms and Ions
3.11 Ionization Energies
3.12 Electron Affinities
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Light behaves both as a wave and a particle Classical physics - light as a wave:
c =  = 2.998 x 108 m/s
Quantum Physics Planck and Einstein:
photons (particles) of light, E = h
Several blind men were asked to describe an elephant. Each tried to determine
what the elephant was like by touching it. The first blind man said the elephant
was like a tree trunk; he had felt the elephant's massive leg. The second blind
man disagreed, saying that the elephant was like a rope, having grasped the
elephant's tail. The third blind man had felt the elephant's ear, and likened the
elephant to a palm leaf, while the fourth, holding the beast's trunk, contended
that the elephant was more like a snake. Of course each blind man was giving a
good description of that one aspect of the elephant that he was observing, but
none was entirely correct. In much the same way, we use the wave and particle
analogies to describe different manifestations of the phenomenon that we call
radiant energy, because as yet we have no single qualitative analogy that will
explain all of our observations.
http://www.wordinfo.info/words/images/blindmen-elephant.gif
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Standing Waves
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Not only does light behave like a particle
sometimes, but particles like the electron
behave like waves! WAVE-PARTICLE
DUALITY
Combined these two equations:
E = mc2 and E = h, therefore -
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The DeBroglie wavelength explains why only certain
orbits are "allowed" -
a) stable
b) not stable
Sample Exercise 3.6 (Modified): calculating the
wavelength of a particle in motion.
(a)Calculate the deBroglie wavelength of a 142 g baseball thrown at
44 m/s (98 mi/hr)
(b)Compare to the wavelength of a hydrogen atom (9.11 x 10-31 kg)
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Using the wavelike properties of the electron.
Close-up of a milkweed bug
Atomic arrangement of a Bi-SrCa-Cu-O superconductor
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Chapter Outline
3.1 Waves of Light
3.2 Atomic Spectra
3.3 Particles of Light: Quantum Theory
3.4 The Hydrogen Spectrum and the Bohr Model
3.5 Electrons as Waves
3.6 Quantum Numbers NOTE: will do Section 3.7 first
3.7 The Sizes and Shapes of Atomic Orbitals
3.8 The Periodic Table and Filling Orbitals
3.9 Electron Configurations of Ions
3.10 The Sizes of Atoms and Ions
3.11 Ionization Energies
3.12 Electron Affinities
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E. Schrödinger (1927)
The electron as a Standing Wave
 mathematical treatment results in a “wave
function”, 
  = the complete description of electron
position and energy
 electrons are found within 3-D “shells”, not 2-D
Bohr orbits
 shells contain atomic “orbitals” (s, p, d, f)
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E. Schrödinger (1927)
The electron as a Standing Wave
Each orbital can hold up to 2 electrons
The probability of finding the electron = 2
Probabilities are required because of
“Heisenberg’s Uncertainty Principle”
We can never SIMULTANEOUSLY know with absolute
precision both the exact position (x), and momentum
(p = mass·velocity or mv), of the electron.
Dx·D(mv)  h/4
Uncertainty in Uncertainty in
position momentum
If one uncertainty gets very small, then the other becomes
corresponding larger. If we try to pinpoint the electron momentum,
it's position becomes "fuzzy". So we assign a probability to where the
electron is found = atomic orbital.
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If an electron is moving at 1.0 X 108 m/s with an uncertainty in
velocity of 0.10 %, then what is the uncertainty in position?
Dx•D(mv)  h/4
and rearranging
Dx  h/[4D(mv)]
or since the mass is constant
Dx  h/[4mDv]
Dx 
(6.63 x 10-34 Js)
4(9.11 x 10-31 kg)(.001 x 1 x 108 m/s)
Dx  6 x 10-10 m or 600 pm
Probability Electron
Density for 1s Orbital
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Electron “Cloud” Representation
Electron “Orbital” Representation
90%
probablity
surface
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Comparison of “s” Orbitals
One “s”
orbital in
each shell.
nodes
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The Three 2p Orbitals
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The Five 3d Orbitals
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The Seven “f” Orbitals
3s
+
2s
n=1
n=2
n=3
1s
Orbitals are found in 3-D shells
instead of 2-D Bohr orbits. The Bohr
radius for n=1, 2, 3 etc was correct,
however.
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Do not appear until the 2nd shell and higher
3px
3py
3pz
+
n=1
n=2
n=3
2px
2py
2pz
Do not appear until the 3rd shell and higher
+
n=1
n=2
n=3
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“The Shell Game”
(n = 1)
+
n=1
n=2
n=3
In the first shell there is
only an s "subshell"
“The Shell Game”
n=2
+
In the second shell
there is an s "subshell"
and a p "subshell"
n=1
n=2
n=3
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“The Shell Game”
n=3
+
n=1
n=2
n=3
In the third shell
there are s, p, and d
"subshells"
“The Shell Game”
n=4
“f” Orbitals don’t appear
until the 4th shell
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Chapter Outline
3.1 Waves of Light
3.2 Atomic Spectra
3.3 Particles of Light: Quantum Theory
3.4 The Hydrogen Spectrum and the Bohr Model
3.5 Electrons as Waves
3.6 Quantum Numbers
3.7 The Sizes and Shapes of Atomic Orbitals
3.8 The Periodic Table and Filling Orbitals
3.9 Electron Configurations of Ions
3.10 The Sizes of Atoms and Ions
3.11 Ionization Energies
3.12 Electron Affinities
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Completely describe the position and energy of the electron
(part of the wave function )
1. Principle quantum number (n):
n = 1, 2, 3……
gives principle energy level or
"shell"
En  
constants
n2
(just like Bohr's theory)
http://www.calstatela.edu/faculty/acolvil/mineral/atom_structure2.jpg
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2. angular momentum quantum number (l) :
l = 0, 1, 2, 3……n-1
describes the type of orbital or shape
l=0
l=1
l=2
l=3
s-orbital
p-orbital
d-orbital
f-orbital
Equal to the number of
"angular nodes"
3. magnetic quantum number (ml):
ml = - l to + l in steps of 1 (including 0)
indicates spatial orientation
If l = 0, then ml = 0 (only one kind of s-orbital)
ifl= 1, then ml = -1, 0, +1 (three kinds of p-orbitals)
if l = 2, then ml = -2, -1, 0, +1, +2 (five kinds of d-orbitals)
if l = 3, then ml = -3, -2, -1, 0, +1, +2, +3 (seven kinds of f-orbitals)
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Electron Spin
• Not all spectra features explained by wave
equations:
– Appearance of “doublets” in atoms with a single
electron in outermost shell.
• Electron Spin
– Up / down.
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4. spin quantum number (ms):
ms = 1/2 or -1/2
Electrons “spin” on their axis, producing a magnetic field
ms = +1/2
spin “up”
ms = -1/2
spin “down”
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orbital = s
p
d
f
l=0
1
2
3
ml = 0
n=1
2
3
4
5
6
-1 0 +1
-2 -1 0 +1 +2
-3 -2 -1 0 +1 +2 +3
max electrons/subshell = 2(2l + 1)
max electrons/shell = 2n2
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Sample Exercise 3.9:
Identifying Valid Sets of Quantum Numbers
Which of these five combinations of quantum numbers are valid?
n
l
ml
ms
(a)
1
0
-1
+1/2
(b)
3
2
-2
+1/2
(c)
2
2
0
0
(d)
2
0
0
-1/2
(e)
-3
-2
-1
-1/2
Chapter Outline
3.1 Waves of Light
3.2 Atomic Spectra
3.3 Particles of Light: Quantum Theory
3.4 The Hydrogen Spectrum and the Bohr Model
3.5 Electrons as Waves
3.6 Quantum Numbers
3.7 The Sizes and Shapes of Atomic Orbitals
3.8 The Periodic Table and Filling Orbitals
3.9 Electron Configurations of Ions
3.10 The Sizes of Atoms and Ions
3.11 Ionization Energies
3.12 Electron Affinities
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Electron Configurations: In what order do electrons
occupy available orbitals?
Orbital Energy Levels for Hydrogen Atoms
E
3s
3p
2s
2p
3d
1s
Energy of orbitals in multi-electron atoms
Energy depends on n + l
3+2=5
4+0=4
3+1=4
3+0=3
2+1=3
2+0=2
1+0=1
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Probability of finding the electron →
1s
"Penetration"
s>p>d>f
2s
3s
4s
2p
3p
4p
3d
4f
for the same shell (e.g.
n=4) the s-electron
penetrates closer to
the nucleus and feels a
stronger nuclear pull or
charge.
4d
distance from nucleus →
http://www.pha.jhu.edu/~rt19/hydro/img73.gif
Aufbau Principle - the lowest energy orbitals fill up first
Filling order of orbitals in multi-electron atoms
1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s
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Shorthand description of orbital occupancy
1. No more than 2 electrons maximum per orbital
2. Electrons occupy orbitals in such a way to minimize the
total energy of the atom = “Aufbau Principle”
(use filling order diagram)
3. No 2 electrons can have the same 4 quantum numbers
= “Pauli Exclusion Principle” (pair electron spins)
ms = -1/2
spin
“down”
ms = +1/2
spin “up”
•No two electrons in an atom can have the same set of four
quantum numbers (n, l, ml, ms)
•electrons must "pair up" before entering the same orbital




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4. When filling a subshell, electrons occupy empty
orbitals first before pairing up = “Hund’s Rule”



Px
Py
Pz
NOT


Px
Py
Pz
“orbital box diagram”
Electron Shells and Orbitals
• Orbitals that have the exact
same energy level are called
degenerate.
• Core electrons are those in the
filled, inner shells in an atom
and are not involved in chemical
reactions.



Px
Py
Pz
+
• Valence electrons are those in
the outermost shell of an atom
and have the most influence on
the atom’s chemical behavior.
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H:
He:
Li:
Be:
B:
C:
N:
O:
F:
Ne:
 


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Transition metals are characterized by having incompletely
filled d-subshells (or form cations as such).
Electron Configurations from the Periodic Table
n-1
n-2
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Chapter Outline
3.1 Waves of Light
3.2 Atomic Spectra
3.3 Particles of Light: Quantum Theory
3.4 The Hydrogen Spectrum and the Bohr Model
3.5 Electrons as Waves
3.6 Quantum Numbers
3.7 The Sizes and Shapes of Atomic Orbitals
3.8 The Periodic Table and Filling Orbitals
3.9 Electron Configurations of Ions
3.10 The Sizes of Atoms and Ions
3.11 Ionization Energies
3.12 Electron Affinities
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Electron Configurations: Ions
• Formation of Ions:
– Gain/loss of valence electrons to achieve stable
electron configuration (filled shell = “octet rule”).
– Cations:
– Anions:
– Isoelectronic:
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Cations of Transition Metals
Fe
Cu
Sn
Pb
Sample Exercise 3.11:
Determining Isoelectronic Species in Main Group Ions
a) Determine the electron configuration of each of
the following ions: Mg2+, Cl-, Ca2+, and O2b) Which ions are isoelectronic with Ne?
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Chapter Outline
3.1 Waves of Light
3.2 Atomic Spectra
3.3 Particles of Light: Quantum Theory
3.4 The Hydrogen Spectrum and the Bohr Model
3.5 Electrons as Waves
3.6 Quantum Numbers
3.7 The Sizes and Shapes of Atomic Orbitals
3.8 The Periodic Table and Filling Orbitals
3.9 Electron Configurations of Ions
3.10 The Sizes of Atoms and Ions
3.11 Ionization Energies
3.12 Electron Affinities
89
Periodic Trends – trends in atomic and ionic radii,
ionization energies, and electron affinities
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Effective nuclear charge (Zeff) – Inner shell electrons
“SHIELD” the outer shell electrons from the nucleus
Zeff = Z - s
(s = shielding constant)
Zeff  Z – number of inner or core electrons
Across a period -
Z
Core Zeff
Radius (nm)
Na
11
10
1
186
Mg
12
10
2
160
Al
13
10
3
143
Si
14
10
4
132
Effective nuclear charge (Zeff) – Inner shell electrons
“SHIELD” the outer shell electrons from the nucleus
Down a family -
Z
Core Zeff
Radius (nm)
Na
11
10
1
186
K
19
18
1
227
Rb
37
36
1
247
Cs
55
54
1
265
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Trends in Effective Nuclear Charge (Zeff)
and the Shielding Effect
increasing Shielding
increasing Zeff
Atomic, Metallic, Ionic Radii
For diatomic
molecules, equal to
covalent radius
(one-half the
distance between
nuclei).
For metals, equal to
metallic radius (onehalf the distance
between nuclei in
metal lattice).
For ions, ionic radius
equals one-half the
distance between
ions in ionic crystal
lattice.
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Trends in Atomic Size for the
“Representative (Main Group) Elements”
Increasing Atomic Size
Decreasing Atomic Size
Radius of Ions
Cation is always smaller than atom from
which it is formed.
Anion is always larger than atom from
which it is formed.
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Radii of Atoms and Ions
must compare cations to cations and anions to anions
Increasing Ionic Radius
Decreasing Ionic Radius
Sample Exercise 3.13:
Ordering Atoms and Ions by Size
Arrange each by size from largest to smallest:
(a) O, P, S
(b) Na+, Na, K
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Chapter Outline
3.1 Waves of Light
3.2 Atomic Spectra
3.3 Particles of Light: Quantum Theory
3.4 The Hydrogen Spectrum and the Bohr Model
3.5 Electrons as Waves
3.6 Quantum Numbers
3.7 The Sizes and Shapes of Atomic Orbitals
3.8 The Periodic Table and Filling Orbitals
3.9 Electron Configurations of Ions
3.10 The Sizes of Atoms and Ions
3.11 Ionization Energies
3.12 Electron Affinities
99
Ionization energy is the minimum energy (kJ/mol)
required to remove an electron from a gaseous
atom in its ground state.
I1 + X (g)
X+(g) + e-
I1 first ionization energy
I2 + X (g)
X2+(g) + e-
I2 second ionization energy
I3 + X (g)
X3+g) + e-
I3 third ionization energy
I1 < I2 < I3 < …..
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General Trend in First Ionization Energies
Decreasing First Ionization Energy
Increasing First Ionization Energy
Ionization Energies
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http://2012books.lardbucket.org/books/principles-of-general-chemistry-v1.0/s11-03-energetics-of-ion-formation.html
Successive Ionization Energies (kJ/mol)
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Trends in the 1st Ionization Energy for the 2nd Row
Li
520 kJ/mol 1s22s1  1s2
Be
899
1s22s2  1s22s1
B
801
1s22s22p1  1s22s2
C
1086
1s22s22p2  1s22s22p1
N
1402
1s22s22p3  1s22s22p2
O
1314
1s22s22p4  1s22s22p3
F
1681
1s22s22p5  1s22s22p4
Ne
2081
1s22s22p6  1s22s22p5
Sample Exercise 3.14:
Recognizing Trends in Ionization Energies
Arrange Ar, Mg, and P in order of increasing IE
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Chapter Outline
3.1 Waves of Light
3.2 Atomic Spectra
3.3 Particles of Light: Quantum Theory
3.4 The Hydrogen Spectrum and the Bohr Model
3.5 Electrons as Waves
3.6 Quantum Numbers
3.7 The Sizes and Shapes of Atomic Orbitals
3.8 The Periodic Table and Filling Orbitals
3.9 Electron Configurations of Ions
3.10 The Sizes of Atoms and Ions
3.11 Ionization Energies
3.12 Electron Affinities
10
7
Electron affinity is the energy release that occurs
when an electron is accepted by an atom in the gaseous
state to form an anion.
X (g) + e- → X-(g)
Energy released = E.A. (kJ/mol)
F (g) + e- → F-(g)
EA = -328 kJ/mol
O (g) + e- → O-(g)
EA = -141 kJ/mol
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Periodic Trends in Electron Affinity
http://2012books.lardbucket.org/books/principles-of-general-chemistry-v1.0/s11-03-energetics-of-ion-formation.html
55
10/31/2016
56