Chapter 11
Modern Atomic Theory
Chapter 11
Table of Contents
Rutherford’s Atom
Electromagnetic Radiation
Emission of Energy by Atoms
The Energy Levels of Hydrogen
The Bohr Model of the Atom
The Wave Mechanical Model of the Atom
The Hydrogen Orbitals
The Wave Mechanical Model: Further Development
Electron Arrangements in the First Eighteen Atoms
on the Periodic Table
11.10 Electron Configurations and the Periodic Table
11.11 Atomic Properties and the Periodic Table
11.1
11.2
11.3
11.4
11.5
11.6
11.7
11.8
11.9
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Section 11.1
Rutherford’s Atom
Nuclear Model of the Atom
• The atom has a small dense nucleus which
 is positively charged.
 contains protons (+1 charge).
 contains neutrons (no charge).
• The remainder of the atom
 is mostly empty space.
 contains electrons (–1 charge).
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Section 11.1
Rutherford’s Atom
• The nuclear charge (n+) is balanced by the presence of
n electrons moving in some way around the nucleus.
• What are the electrons doing?
• How are the electrons arranged and how do they move?
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Section 11.2
Electromagnetic Radiation
• One of the ways that energy travels through space.
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Section 11.2
Electromagnetic Radiation
Characteristics
• Wavelength ( ) – distance between two peaks or

troughs in a wave.
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Section 11.2
Electromagnetic Radiation
Characteristics
• Frequency ( ) – number
of waves (cycles) per
second that pass a given
point in space
• Speed (c) – speed of light
(2.9979×108 m/s)
c = 
E  h
E 
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hc

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Section 11.2
Electromagnetic Radiation
Dual Nature of Light
• Wave
• Photon – packet of
energy
E 
hc

hc

E  mc2
;
 mc ;
2
h

 mc
1
1
 m or  

m
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E = mc2 or mv2
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Section 11.2
Electromagnetic Radiation
Different Wavelengths Carry Different Amounts of Energy
E 
hc

or E 
1

λ1 > λ2 or E1 < E2
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Section 11.2
Electromagnetic Radiation
Light’s Relationship to Matter
• Atoms can acquire extra energy, but
they must eventually release it
• When atoms emit energy, it always is
released in the form of light
• However, atoms don’t emit all colors,
only very specific wavelengths
– in fact, the spectrum of wavelengths
can be used to identify the element
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Section 11.2
Electromagnetic Radiation
Emission Spectrum
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Section 11.3
11.2
Emission of Energy
Electromagnetic
Radiation
by Atoms
Emission Spectra
Light’s Relationship to Matter
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Section 11.3
Emission of Energy by Atoms
• Atoms can give off light.
 They first must receive energy and become excited.
 The energy is released in the form of a photon.
 The energy of the photon corresponds exactly to the
energy change experienced by the emitting atom.
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Section 11.4
The Energy Levels of Hydrogen
• Atomic states
 Excited state – atom with excess energy
 Ground state – atom in the lowest possible state
• When an H atom absorbs energy from an outside
source it enters an excited state.
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Section 11.4
The Energy Levels of Hydrogen
Energy Level Diagram
• Energy in the photon corresponds to the energy used by
the atom to get to the excited state.
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Section 11.4
The Energy Levels of Hydrogen
• Only certain types of photons are produced when
H atoms release energy. Why?
Hydrogen atom contains only 1 proton and 1 electron!
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Section 11.4
The Energy Levels of Hydrogen
Quantized Energy Levels
• Since only certain energy changes occur the H atom
must contain discrete energy levels.
Hydrogen atom absorbs and hence emits fixed amount of energy
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Section 11.4
The Energy Levels of Hydrogen
Quantized Energy Levels
• The energy levels of all atoms are quantized.
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Section 11.4
The Energy Levels of Hydrogen
Concept Check
Why is it significant that the color emitted from
the hydrogen emission spectrum is not white?
How does the emission spectrum support the
idea of quantized energy levels?
E = hν or hc/λ
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Section 11.4
The Energy Levels of Hydrogen
Concept Check
When an electron is excited in an atom or ion
a) only specific quantities of energy are released in
order for the electron to return to its ground state.
b) white light is never observed when the electron
returns to its ground state.
c) the electron is only excited to certain energy
levels.
d) All of the above statements are true when an
electron is excited.
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Section 11.5
The Bohr Model of the Atom
• Quantized energy levels
• Electron moves in a circular orbit.
• Electron jumps between levels by absorbing or emitting
a photon of a particular wavelength.
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Section 11.5
The Bohr Model of the Atom
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Section 11.5
The Bohr Model of the Atom
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Section 11.5
The Bohr Model of the Atom
• the mathematics of the Bohr Model very accurately
predicts the spectrum of hydrogen
• however its mathematics fails when applied to multielectron atoms
– it cannot account for electron-electron interactions
• a better theory was needed
• Bohr’s model of the atom
was incorrect.
 Electrons do not move in
a circular orbit.
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Section 11.6
11.5
The Wave
Bohr Model
Mechanical
of the Model
Atom of the Atom
• Erwin Schrödinger applied the
mathematics of probability and the
ideas of quantitization to the
physics equations that describe
waves – resulting in an equation
that predicts the probability of
finding an electron with a
particular amount of energy at a
particular location in the atom
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Section 11.6
11.5
The Wave
Bohr Model
Mechanical
of the Model
Atom of the Atom
• the result is a map of regions in the atom
that have a particular probability for
finding the electron
• an orbital is a region where we have a very
high probability of finding the electron
when it has a particular amount of energy
– generally set at > 90 or 95%
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Section 11.6
11.5
The Wave
Bohr Model
Mechanical
of the Model
Atom of the Atom
Orbits vs. Orbitals
Pathways vs. Probability
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Section 11.6
The Wave Mechanical Model of the Atom
Orbitals
• Nothing like orbits
• Probability of finding the electron within a certain space
• This model gives no information about when the electron
occupies a certain point in space or how it moves.
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Section 11.7
The Hydrogen Orbitals
Orbitals
• Orbitals do not have sharp boundaries.
• Chemists arbitrarily define an orbital’s size as the sphere
that contains 90% of the total electron probability.
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Section 11.7
The Hydrogen Orbitals
• in Schrödinger’s Wave Equation,
there are 3 integers, called quantum
numbers, that quantize the energy
• the principal quantum number, n,
specifies the main energy level for
the orbital
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Section 11.7
The Hydrogen Orbitals
Hydrogen Energy Levels
• Hydrogen has discrete
energy levels.
 Called principal energy
levels
 Labeled with whole
numbers
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Section 11.7
The Hydrogen Orbitals
• each principal energy shell has one or more subshells
– the number of subshells = the principal quantum
number
• the quantum number that designates the subshell is
often given a letter
– s, p, d, f
• each kind of sublevel has orbitals with a particular
shape
– the shape represents the probability map
• 90% probability of finding electron in that region
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Section 11.7
The Hydrogen Orbitals
Shells & Subshells
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Section 11.7
The Hydrogen Orbitals
Hydrogen Energy Levels
• Each principal energy level is divided into sublevels.
 Labeled with numbers and letters
 Indicate the shape of the orbital
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Section 11.7
The Hydrogen Orbitals
Hydrogen Energy Levels
• The s and p types of sublevel
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Section 11.7
The Hydrogen Orbitals
Hydrogen Energy Levels
Probability maps & orbital Shape - d Orbitals
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Section 11.7
The Hydrogen Orbitals
Orbital Labels
1. The number tells the principal energy level.
2. The letter tells the shape.
 The letter s means a spherical orbital.
 The letter p means a two–lobed orbital. The
x, y, or z subscript on a p orbital label tells
along which of the coordinate axes the two
lobes lie.
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Section 11.7
The Hydrogen Orbitals
Hydrogen Orbitals
• Why does an H atom have so many orbitals and
only 1 electron?
• An orbital is a potential space for an electron.
 Atoms can have many potential orbitals.
 as in the Bohr Model, atoms gain or lose energy as
the electron leaps between orbitals in different energy
shells and subshells
 the ground state of the electron is the lowest energy
orbital it can occupy
 higher energy orbitals are excited states
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Section 11.8
The Wave Mechanical Model: Further Development
Atoms Beyond Hydrogen
• The Bohr model was discarded because it does not
apply to all atoms.
• Atoms beyond hydrogen have an equal number of
protons and electrons.
 Need one more property to determine how the
electrons are arranged
 Spin – electron spins like a top
Both the Bohr and Quantum Mechanical models predict the
spectrum of hydrogen very accurately
Only the Quantum Mechanical model predicts the spectra of
multielectron atoms
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Section 11.8
The Wave Mechanical Model: Further Development
Atoms Beyond Hydrogen
• Pauli Exclusion Principle – an atomic orbital can
hold a maximum of 2 electrons and those 2
electrons must have opposite spins.
• we often represent an orbital as a square and the electrons
in that orbital as arrows
– the direction of the arrow represents the spin of the
electron
unoccupied
orbital with
orbital with
orbital
1 electron
2 electrons
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Section 11.8
The Wave Mechanical Model: Further Development
Principal Components of the Wave Mechanical Model of the Atom
1. Atoms have a series of energy levels called
principal energy levels (n = 1, 2, 3, etc.).
2. The energy of the level increases as the value
of n increases.
3. Each principal energy level contains one or
more types of orbitals, called sublevels.
4. The number of sublevels present in a given
principal energy level equals n.
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Section 11.8
The Wave Mechanical Model: Further Development
Principal Components of the Wave Mechanical Model of the Atom
5. The n value is always used to label the orbitals
of a given principal level and is followed by a
letter that indicates the type (shape) of the
orbital (1s, 3p, etc.).
6. An orbital can be empty or it can contain one or
two electrons, but never more than two. If two
electrons occupy the same orbital, they must
have opposite spins.
unoccupied
orbital
orbital with
1 electron
orbital with
2 electrons
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Section 11.8
The Wave Mechanical Model: Further Development
Principal Components of the Wave Mechanical Model of the Atom
7. The shape of an orbital does not indicate the
details of electron movement. It indicates the
probability distribution for an electron residing in
that orbital.
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Section 11.8
The Wave Mechanical Model: Further Development
Concept Check
Which of the following statements best describes the
movement of electrons in a p orbital?
a) The electron movement cannot be exactly
determined.
b) The electrons move within the two lobes of the p
orbital, but never beyond the outside surface of
the orbital.
c) The electrons are concentrated at the center
(node) of the two lobes.
d) The electrons move along the outer surface of the p
orbital, similar to a “figure 8” type of movement.
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Section 11.8
The Wave Mechanical Model: Further Development
Schrödinger
Bohr
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Section 11.8
The Wave Mechanical Model: Further Development
7s
6s
Energy
5s
4s
6d
6p
5p
5d
5f
4f
4d
4p
3d
3p
3s
2p
2s
1s
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Section 11.8
The Wave Mechanical Model: Further Development
Order of Subshell Filling
in Ground State Electron Configurations
start by drawing a diagram
putting each energy shell on
a row and listing the subshells,
(s, p, d, f), for that shell in
order of energy, (left-to-right)
1s
next, draw arrows through
the diagonals, looping back
to the next diagonal
each time
2s
2p
3s
3p
3d
4s
4p
4d
4f
5s
5p
5d
5f
6s
6p
6d
7s
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Section 11.9
Electron Arrangements in the First Eighteen Atoms on the Periodic Table
H Atom
• Electron configuration – electron arrangement
1s1
• Orbital diagram – orbital is a box grouped by
sublevel containing arrow(s) to represent
electrons
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Section 11.9
Electron Arrangements in the First Eighteen Atoms on the Periodic Table
Li Atom
• Electron configuration
1s2 2s1
• Orbital diagram
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Section 11.9
Electron Arrangements in the First Eighteen Atoms on the Periodic Table
O Atom
• The lowest energy configuration for an atom is the one
having the maximum number of unpaired electrons in a
particular set of degenerate (same energy) orbitals.
Oxygen:
1s
2s
2p
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Figure 4.130a
Section 11.9
Electron Arrangements in the First Eighteen Atoms on the Periodic Table
1s2, 2s2 2p5
1s2, 2s2 2p6; 2s2 3p5
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Section 11.9
Electron Arrangements in the First Eighteen Atoms on the Periodic Table
• The electron configurations in the sublevel last occupied
for the first eighteen elements.
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Figure 4.130b
Section 11.9
Electron Arrangements in the First Eighteen Atoms on the Periodic Table
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Section 11.9
Electron Arrangements in the First Eighteen Atoms on the Periodic Table
Classifying Electrons
• Core electrons – inner electrons
• Valence electrons – electrons in the outermost (highest)
principal energy level of an atom
 1s22s22p6 (valence electrons = 8)
 The elements in the same group on the periodic table
have the same valence electron configuration.
 Elements with the same valence electron
arrangement show very similar chemical behavior.
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Section 11.9
Electron Arrangements in the First Eighteen Atoms on the Periodic Table
Concept Check
How many unpaired electrons does the element
cobalt (Co) have in its lowest energy state?
a)
b)
c)
d)
0
2
3
7
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Section 11.9
Electron Arrangements in the First Eighteen Atoms on the Periodic Table
Concept Check
Can an electron in a phosphorus atom ever be in a 3d
orbital? Choose the best answer.
a) Yes. An electron can be excited into a 3d orbital.
b) Yes. A ground-state electron in phosphorus is
located in a 3d orbital.
c) No. Only transition metal atoms can have
electrons located in the d orbitals.
d) No. This would not correspond to phosphorus’
electron arrangement in its ground state.
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Section 11.10
Electron Configurations and the Periodic Table
• Look at electron configurations for K through Kr.
1
2
3
4
4s2
3d10
4p6
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Section 11.10
Electron Configurations and the Periodic Table
Orbital Filling and the Periodic Table
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Section 11.10
Electron Configurations and the Periodic Table
Orbital Filling
1. In a principal energy level that has d orbitals,
the s orbital from the next level fills before the d
orbitals in the current level.
2. After lanthanum, which has the electron
configuration [Xe]6s25d1, a group of fourteen
elements called the lanthanide series, or the
lanthanides, occurs. This series of elements
corresponds to the filling of the seven 4f
orbitals.
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Section 11.10
Electron Configurations and the Periodic Table
Orbital Filling
3. After actinum, which has the configuration
[Rn]7s26d1, a group of fourteen elements called
the actinide series, or actinides, occurs. This
series corresponds to the filling of the seven 5f
orbitals.
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Section 11.10
Electron Configurations and the Periodic Table
Orbital Filling
4. Except for helium, the group numbers indicate
the sum of electrons in the ns and np orbitals in
the highest principal energy level that contains
electrons (where n is the number that indicates
a particular principal energy level). These
electrons are the valence electrons.
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Section 11.10
Electron Configurations and the Periodic Table
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Section 11.10
Electron Configurations and the Periodic Table
Exercise
Determine the expected electron
configurations for each of the following.
a) S
1s22s22p63s23p4 or [Ne]3s23p4
b) Ba
[Xe]6s2
c) Eu
Electron configurations
abbreviated using noble gas core
[Xe]6s24f7
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Section 11.11
Atomic Properties and the Periodic Table
Metals and Nonmetals
• Metals tend to lose electrons to form positive ions.
• Nonmetals tend to gain electrons to form negative ions.
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Section 11.11
Atomic Properties and the Periodic Table
Ionization Energy
• Energy required to remove an electron from a
gaseous atom or ion.
 X(g) → X+(g) + e–
Mg → Mg+ + e–
Mg+ → Mg2+ + e–
Mg2+ → Mg3+ + e–
I1 = 735 kJ/mol
I2 = 1445 kJ/mol
I3 = 7730 kJ/mol
(1st IE)
(2nd IE)
*(3rd IE)
*Core electrons are bound much more tightly
than valence electrons.
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Section 11.11
Atomic Properties and the Periodic Table
Ionization Energy
• In general, as we go across a period from left to
right, the first ionization energy increases.
• Why?
 Electrons added in the same principal
quantum level do not completely shield the
increasing nuclear charge caused by the
added protons.
 Electrons in the same principal quantum level
are generally more strongly bound from left to
right on the periodic table.
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Section 11.11
Atomic Properties and the Periodic Table
Ionization Energy
Coulomb's inverse-square law
F1  F2
Force 
2
r
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Figure 4.130b
Section 11.11
Atomic Properties and the Periodic Table
F1  F2
Force 
2
r
Nuclear charge increase but distance stays the same
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Section 11.11
Atomic Properties and the Periodic Table
Ionization Energy
• In general, as we go down a group from
top to bottom, the first ionization energy
decreases.
• Why?
 The electrons being removed are, on
average, farther from the nucleus.
Coulomb's inverse-square law
F1  F
Force 
2
r
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Section 11.11
Atomic Properties and the Periodic Table
Ionization Energy
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Section 11.11
Atomic Properties and the Periodic Table
Noble
Gases
nonmetals have higher ionization
potentials than metals
VIIA
VA
IA
VIA
IVA
IIA
IIIA
nonmetals
metals
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11.3
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Section 11.11
Atomic Properties and the Periodic Table
Concept Check
Which atom would require more energy to
remove an electron? Why?
Na
Cl
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Section 11.11
Atomic Properties and the Periodic Table
Concept Check
Which atom would require more energy to
remove an electron? Why?
Li
Cs
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Section 11.11
Atomic Properties and the Periodic Table
Atomic Size
• In general as we go across a period from left to
right, the atomic radius decreases.
 Effective nuclear charge increases, therefore
the valence electrons are drawn closer to the
nucleus, decreasing the size of the atom.
• In general atomic radius increases in going
down a group.
 Orbital sizes increase in successive principal
quantum levels.
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Section 11.11
Atomic Properties and the Periodic Table
Relative Atomic Sizes for Selected Atoms
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Section 11.11
Atomic Properties and the Periodic Table
Trends in Atomic Radii
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Section 11.11
Atomic Properties and the Periodic Table
Concept Check
Which should be the larger atom? Why?
Na
Cl
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Section 11.11
Atomic Properties and the Periodic Table
Concept Check
Which should be the larger atom? Why?
Li
Cs
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Section 11.11
Atomic Properties and the Periodic Table
Concept Check
Which is larger?
• The hydrogen 1s orbital
• The lithium 1s orbital
Which is lower in energy?
•The hydrogen 1s orbital
•The lithium 1s orbital
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Section 11.11
Atomic Properties and the Periodic Table
Exercise
Arrange the elements oxygen, fluorine, and
sulfur according to increasing:
 Ionization energy
S, O, F

Atomic size
F, O, S
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Section 11.11
Chapter
11 Properties
Homeworkand the Periodic Table
Atomic
Homework
• Reading assignment
– Pages 322 through 352
• Homework Problems
– Questions and problems 5, 7, 13, 15, 17, 19, 23, 27,
31, 33, 35, 39, 41, 43, 47, 51, 53, 54, 55, 61, 63, 65,
67, 71, 75, 81.
• Due on
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