The Quantum
Mechanical Atom
CHAPTER 8
Chemistry: The Molecular Nature of Matter, 6th edition
By Jesperson, Brady, & Hyslop
CHAPTER 8: Quantum Mechanical Atom
Learning Objectives
 Light as Waves, Wavelength and Frequency
 The Photoelectric Effect, Light as Particles and the Relationship between
Energy and Frequency
 Atomic Emission and Energy Levels
 The Bohr Model and its Failures
 Electron Diffraction and Electrons as Waves
 Quantum Numbers, Shells, Subshells, and Orbitals
 Electron Configuration, Noble Gas Configuration and Orbital Diagrams
 Aufbau Principle, Hund’s Rule, and Pauli Exclusion Principle, Heisenberg
Uncertainty Principle
 Valence vs Inner Core Electrons
 Nuclear Charge vs Electron Repulsion
 Periodic Trends: Atomic Radius, Ionization Energy, and Electron Affinity
2
Electron
Configurations
Periodic Table & Electron
Configurations
• Divided into regions of 2, 6, 10, and 14 columns
• This equals maximum number of electrons in s, p,
d, and f sublevels
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Molecular Nature of Matter, 6E
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Electron
Configurations
Periodic Table & Electron
Configurations
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Molecular Nature of Matter, 6E
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Electron
Configurations
Shorthand: Electron
Configurations
• [noble gas of previous row] and electrons filled in next row
• Represents core + outer shell electrons
• Use to emphasize that only outer shell electrons react
Ex: Group 2 A elements:
Z
Electron Configuration
Abbrev
Be
4
1s 22s 2
[He] 2s 2
Mg
12
1s 22s 22p 63s 2
[Ne] 3s 2
Ca
20
1s 22s 22p 63s 23p 64s 2
[Ar] 4s 2
Sr
38
1s 22s 22p 63s 23p 63d 104s 24p 65s 2
[Kr] 5s 2
Ba
56
1s 22s 22p 63s 23p 63d 104s 24p 64d 105s 25p 66s 2
[Xe] 6s 2
Ra
88
1s 22s 22p 63s 23p 63d 104s 24p 64d 104f 145s 25p 6
5d 106s 26p 67s 2
[Rn] 7s 2
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Molecular Nature of Matter, 6E
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Electron
Configurations
Shorthand: Orbital Diagrams
 Write out lines for orbital beyond Noble gas
 Higher energy orbital to right
 Fill from left to right
Abbreviated Orbital Diagrams
Ru
[Kr]





4d
S
[Ne]

 
5s

3s
3p
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Molecular Nature of Matter, 6E

6
Electron
Configurations
Valance Shell Electron
Configurations
Valence Electrons =
Electrons in the outer most shell (ie, highest n)
• Here only electrons in outer shell important for bonding
• Only electrons in s and p subshells
• Valence shell = outer shell
= occupied shell with highest n
• Result – use even more abbreviated notation
for electron configurations
• Sn = 5s 25p 2
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Molecular Nature of Matter, 6E
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Electron
Configurations
Element
Cr
Cu
Ag
Au
Exceptions to the Rules:
Electron Configurations
Expected
[Ar] 3d 44s 2
[Ar] 3d 94s 2
[Kr] 4d 95s 2
[Xe] 5d 96s 2
Experimental
[Ar] 3d 54s 1
[Ar] 3d 104s 1
[Kr] 4d 105s 1
[Xe] 5d 106s 1
 Exactly filled and exactly half-filled subshells have extra
stability
 Promote one electron into ns orbital to gain this extra stability
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Molecular Nature of Matter, 6E
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Electron
Cloud
Heisenberg Uncertainty Principle
• Can’t know both exact position and exact speed of
subatomic particle simultaneously
• Such measurements always have certain minimum
uncertainty associated with them
h
Dx Dmv ³
4p
x = particle position
mv = particle momentum
= mass × velocity of particle
h = Planck’s constant = 6.626 × 10–34 J s
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Molecular Nature of Matter, 6E
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Electron
Cloud
Heisenberg Uncertainty Principle
Macroscopic scale
• Errors in measurements much smaller
than measured value
Subatomic scale
• Errors in measurements equal to or
greater than measured value
– If you know position exactly, know
nothing about velocity
– If you know velocity exactly, know
nothing about position
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Molecular Nature of Matter, 6E
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Electron
Cloud
Heisenberg Uncertainty Principle:
Consequences
• Can’t talk about absolute position
• Can only talk about electron probabilities
– Where is e – likely to be?
• ψ = wavefunction
– Amplitude of electron wave
• ψ2 = probability of finding electron at given
location
• Probability of finding an electron in given
region of space equals the square of the
amplitude of wave at that point
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Molecular Nature of Matter, 6E
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Orbitals
Electron Cloud
Electron dot picture = snapshots
– Lots of dots shown by large amplitude of wave
function
• High probability of finding electrons
Electron density
– How much of electrons charge packed into
given volume
• High Probability
– High electron density or Large electron
density
• Low Probability
– Low electron density or Small electron density
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Molecular Nature of Matter, 6E
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Orbitals
1 s Orbital Representations
a. Dot-density diagram
b. Probability of finding electron around given point, ψ2, with
respect to distance from nucleus
c. Radial probability distribution = probability of finding
electron between r and r + x from nucleus
– rmax = Bohr radius
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Molecular Nature of Matter, 6E
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Orbitals
Distribution of Electron Density
• Determined by
• Electron density

Shape
Size
n
Orientation m
– No sharp boundary
– Gradually fades away
• “Shape”
– Imaginary surface enclosing 90% of electron
density of orbital
– Probability of finding electrons is same
everywhere on surface
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Molecular Nature of Matter, 6E
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Orbitals
Effect of n on
the s Orbital
• In any given direction probability
of finding electron same
• All s orbitals are spherically
shaped
• Size increases as n increases
15
Jesperson, Brady, Hyslop. Chemistry: The
Molecular Nature of Matter, 6E
Orbitals
Spherical Nodes
• At higher n, now have spherical nodes
– Spherical regions of zero probability, inside orbital
• Node for electron wave
– Imaginary surface where electron density = 0
– 2s, one spherical node, size larger
– 3s, two spherical nodes, size larger yet
In general:
• Number of spherical nodes
=n–1
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Molecular Nature of Matter, 6E
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Orbitals
p Orbitals
• Possess one nodal plane through nucleus
– Electron density only on two sides of nucleus
– Two lobes of electron density
• All p orbitals have same overall shape
– Size increases as n increases
– For 3p have one spherical node
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Molecular Nature of Matter, 6E
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Orbitals
p Orbitals
• Constant probability surface for 2p orbital
• Simplified p orbital emphasizing
directional nature of orbital
• All 2p orbitals in p sub shell
– One points along each axis
2px
2py
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Molecular Nature of Matter, 6E
2pz
18
Orbitals
d Orbitals
• Four with four lobes of electron density
• One with two lobes and ring of electron density
• Result of two nodal planes though nucleus
• Number of nodal planes through nucleus = 
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Molecular Nature of Matter, 6E
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Orbitals
A.
D.
Ex: Identify Each Orbital
C.
B.
E.
z
y
x
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Molecular Nature of Matter, 6E
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Periodic
Trends
Periodic Properties
To explain chemical & physical properties, must first consider
amount of positive charge felt by outer electrons (valence
electrons)
• Core electrons spend most of their time closer to nucleus
than valence (outer shell) electrons
• Shield or cancel out (screen out, neutralize) some of
positive charge of nucleus
Effective Nuclear
Charge (Zeff)
• Net positive charge outer
electron feels
• Core electrons shield
valence electrons from full
nuclear charge
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Molecular Nature of Matter, 6E
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Periodic
Trends
Shielding
• Electrons in same subshell don't shield each other
– Same average distance from nucleus
– Trying to stay away from each other
– Spend very little time one below another
• Effective nuclear charge determined primarily by
– Difference between charge on nucleus (Z ) and
charge on core (number of inner electrons)
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Molecular Nature of Matter, 6E
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Periodic
Trends
Atomic Size
• Theory suggests sizes of atoms and ions indistinct
• Experiment shows atoms/ions behave as if they
have definite size
– C and H have ~ same distance between nuclei
in large number of compounds
Atomic Radius (r)
• Half of distance between two like atoms
– H—H C—C etc.
– Usually use units of picometer
– 1 pm = 1 × 10–12 m
– Range 37 – 270 pm for atoms
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Molecular Nature of Matter, 6E
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Periodic
Trends
Atomic Size
Increases down Column (group)
– Zeff essentially constant
– n increases, outer electrons farther away from
nucleus and radius increase
Decreases across row (period)
– n constant
– Zeff decreases, outer electrons feel larger Zeff
and radius decreases
Transition Metals and Inner Transition Metals
– Size variations less pronounced as filling core
– n same (outer electrons) across row
– Decrease in Zeff and r more gradually
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Molecular Nature of Matter, 6E
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Periodic
Trends
Atomic & Ionic Radii (in picometers)
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Molecular Nature of Matter, 6E
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Periodic
Trends
Ionic Radii
• Increases down column (group)
• Decreases across row (period)
Anions larger than parent atom
– Same Zeff, more electrons
– Radius expands
Cations smaller than parent atom
– Same Zeff, less electrons,
– Radius contracts
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Molecular Nature of Matter, 6E
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Periodic
Trends
•
•
•
•
Ionization Energy
Energy required to remove electron from gas phase atom
Corresponds to taking electron from n to n = 
First ionization energy M (g)  M +(g) + e–
IE = E
Trends:
• Ionization energy decreases down column (group) as n
increases
• Ionization energy increases across row (period) as Zeff
increases
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Molecular Nature of Matter, 6E
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Periodic
Trends
First Ionization Energies
 Largest first ionization
energies are in upper
right
 Smallest first ionization
energies are in lower
left
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Molecular Nature of Matter, 6E
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Periodic
Trends
Successive Ionization Energies
• Increases slowly as
remove each
successive electron
• See big increase in
ionization energy
– When break into
exactly filled or
half filled subshell
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Molecular Nature of Matter, 6E
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Periodic
Trends
Successive Ionization Energies
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Molecular Nature of Matter, 6E
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Periodic
Trends
Electron Affinity (EA)
• Potential energy change associated with addition
of one electron to gas phase atom or ion in the
ground state
X(g) + e–  X –(g)
• O and F very favorable to add electrons
• Comparing first electron affinities usually negative
(exothermic)
• Larger negative value means more favorable to
add electron
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Molecular Nature of Matter, 6E
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Periodic
Trends
Electron Affinities
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Molecular Nature of Matter, 6E
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Periodic
Trends
Electron Affinity Trends
• Electron affinity becomes less exothermic down
column (group) as n increases
– Electron harder to add as orbital farther from
nucleus and feels less positive charge
• Electron affinity becomes more exothermic across
row (period) as Zeff increases
• Easier to attract electrons as positive charge
increases
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Molecular Nature of Matter, 6E
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Periodic
Trends
Successive Electron Affinities
• Addition of first electron – often exothermic
• Addition of more than one electron requires energy
• Consider addition of electrons to oxygen:
Change:
EA(kJ/mol)
O(g) + e –  O–(g)
–141
O–(g) + e –  O2–(g)
+844
Net: O(g) + 2e –  O2–(g)
+703
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Molecular Nature of Matter, 6E
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Problem
Set C