1. The Quantum Mechanical Atom
CHAPTER 8
Chemistry: The Molecular Nature of Matter, 6th edition
By Jesperson, Brady, & Hyslop

2. 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

3. 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
Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6E

4. Electron Configurations
Periodic Table & Electron Configurations
Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6E

5. 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
Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6E

6. Abbreviated Orbital Diagrams
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 5s S
[Ne]
   
3s p
Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6E

7. Electrons in the outer most shell (ie, highest n)
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
Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6E

8. Electron Configurations
Exceptions to the Rules:
Electron Configurations
Element
Expected
Experimental Cr Cu Ag Au
[Ar] 3d 44s 2
[Ar] 3d 94s 2
[Kr] 4d 95s 2
[Xe] 5d 96s 2
[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
Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6E

9. Heisenberg Uncertainty Principle
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
x = particle position
mv = particle momentum = mass × velocity of particle
h = Planck’s constant = × 10–34 J s
Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6E

10. Heisenberg Uncertainty Principle
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
Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6E

11. Heisenberg Uncertainty Principle: Consequences
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
Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6E

12. Electron dot picture = snapshots
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
Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6E

13. 1 s Orbital Representations
Orbitals
1 s Orbital Representations
Dot-density diagram
Probability of finding electron around given point, ψ2, with respect to distance from nucleus
Radial probability distribution = probability of finding electron between r and r + x from nucleus
rmax = Bohr radius
Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6E

14. Shape  Size n Orientation m Orbitals
Distribution of Electron Density
Determined by
Electron density
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
Shape 
Size n
Orientation m
Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6E

15. In any given direction probability of finding electron same
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
Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6E

16. At higher n, now have spherical nodes
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
Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6E

17. Possess one nodal plane through nucleus
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
Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6E

18. 2px 2py 2pz 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
2pz
Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6E

19. Four with four lobes of electron density
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 = 
Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6E

20. A. B. C. D. E. Orbitals Ex: Identify Each Orbital
Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6E

21. Effective Nuclear Charge (Zeff)
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
Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6E

22. Electrons in same subshell don't shield each other
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)
Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6E

23. Theory suggests sizes of atoms and ions indistinct
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
Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6E

24. Increases down Column (group) Zeff essentially constant
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
Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6E

25. Atomic & Ionic Radii (in picometers)
Periodic Trends
Atomic & Ionic Radii (in picometers)
Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6E

26. Increases down column (group) Decreases across row (period)
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
Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6E

27. Energy required to remove electron from gas phase atom
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
Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6E

28. First Ionization Energies
Periodic Trends
First Ionization Energies
Largest first ionization energies are in upper right
Smallest first ionization energies are in lower left
Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6E

29. Successive Ionization Energies
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
Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6E

30. Successive Ionization Energies
Periodic Trends
Successive Ionization Energies
Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6E

31. Electron Affinity (EA)
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
Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6E

32. Periodic Trends Electron Affinities
Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6E

33. Electron Affinity Trends
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
Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6E

34. Change: EA(kJ/mol) O(g) + e –  O–(g) –141 O–(g) + e –  O2–(g) +844
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
Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6E

35. Problem
Set C