1. Thermodynamics & the Atom
ElectroMagnetic Radiation & The Bohr Model
Quantum Mechanics
Electron Configurations
Atomic/Ionic Radii, Ionization energy, & Electron Affinity
∆Energy of Ionic Bonds
∆Energy of Covalent Bonds
Lewis Structures, Shapes & Polarity
Bonding Theories
∆Energy of Nuclear Changes

2. Atomic Model
Similarities and differences in atomic and electron structure of the elements can be used to explain the patterns of physical and chemical properties that occur in the periodic table.
Let’s consider the
electron structure
of an atom……...
but first we must study EM radiation!

3. Traveling waves
Much of what has been learned about atomic structure has come from observing the interaction of visible light and matter.
An understanding of waves and electromagnetic radiation would be helpful at this point.

4. Waves Some definitions
Wavelength, l (lambda) - The distance for a wave to go through a complete cycle.
Amplitude,  (chi) - Half of the vertical distance from the top to the bottom of a wave.
Frequency, n (nu) - The number of cycles that pass a point each second.

5. Waves + + + - - - - y axis wavelength amplitude x axis nodes
frequency 3.5 waves/s
speed, m/s = wavelength x frequency

6. Wavelength vs. Frequency
y axis
Frequency = 3.5 s-1
Frequency = 7.0 s-1
x axis
As wavelength decreases, the frequency increases.
As wavelength decreases, the energy of the radiation increases.
Therefore, energy increases with frequency.

7. Electromagnetic (EM) radiation
A form of energy that consists of perpendicular electrical and magnetic fields that change, at the same time and in phase, with time.
The SI unit of frequency is the hertz, Hz
1 Hz = 1 s-1
Wavelength and frequency are related
ln = c
c is the speed of light, x108 m/s

8. Electromagnetic radiation
Gamma rays
X- rays
Ultraviolet
Visible
Infrared
Microwave
Television
Radio
Wavelength , m
Frequency, s-1

9. Electromagnetic Radiation
All electromagnetic radiation travels at the same velocity: the speed of light (c),
3.00  108 m/s.
c = 
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10. Wave Interference y axis x axis
When two waves occur in sync with each other, constructive interference occurs causing the amplitude to increase.

11. Wave Interference y axis x axis
When two waves occur out of sync with each other, destructive interference occurs causing the amplitude to decrease.

12. The Nature of Energy
In the early 1900’s two phenomena were observed that could not be explained by the wave nature of light.
Hot Body Radiation: The wave nature of light does not explain how an object can glow when its temperature increases.
Photoelectric Effect
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13. The Nature of Energy
Max Planck explained the observed phenomena well by assuming that energy comes in packets called quanta. E = h
where h is Planck’s constant,  10−34 J-s, and  is frequency in Hz.
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14. The Nature of Energy Quantized vs. Continuous
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15. Particle properties
Although EMR has definite wave properties, it also exhibits particle properties.
Photoelectric effect.
First observed by Hertz and then later explained by Einstein.
When light falls on Group IA metals, electrons are emitted (photoelectrons).
As the light gets brighter, more electrons are emitted.
The energy of the emitted electrons depends on the frequency of the light.

16. Photoelectric effect
The cathode has a surface that emits photons, such as a metal or CdS crystals.
When light hits the cathode
electrons are ejected.
They are collected at the
anode and can be
measured.
cathode
anode

17. Photoelectric effect Photon energy, E = h n
Studies of this effect led to the discovery that light existed as small particles of electromagnetic radiation called photons.
The energy of a photon is directly proportional to the frequency.
Photon energy, E = h n
h - Planck’s constant, x J . S / photon
Therefore, the energy must be inversely proportional to the wavelength.
Photon energy = h c l

18. Photon energy example
Determine the energy, in kJ/mol of a photon of blue-green light with a wavelength of 486nm.
energy of a photon = =
= x J / photon
h c l
(6.626 x J.s)(2.998 x 108 m.s-1)
(4.86 x 10-7 m)

19. Photon energy example
We now need to determine the energy for a mole of photons (6.02 x 1023)
Energy for a mole of photons.
= (4.09 x J / photon) (6.02 x 1023 photons/mol)
= J/mol
Finally, convert to kJ
= ( J/mol )
= 244 kJ / mol
1 kJ
103 J

20. (You must be able to use these relationships!)
The Nature of Energy
The DUAL NATURE of LIGHT (particle and wave)
Therefore, knowing the wavelength of light, we can calculate the energy in one photon, or packet, of that light:
c = 
E = h
(You must be able to use these relationships!)
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21. The Nature of Energy
Another mystery in the early twentieth century involved the emission spectra observed from energy emitted by atoms and molecules.
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22. The Nature of Energy
White light produces a continuous spectrum, but atoms and molecules do
Only a line spectrum of discrete wavelengths is observed.
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23. The Nature of Energy
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24. Bohr model of the atom
Bohr proposed a model of how electrons moved around the nucleus.
He wanted to explain why electrons did not fall in to the nucleus.
He also wanted to account for spectral lines being observed.
He proposed that the energy of the electron was quantized - only occurred as specific energy levels.

25. Bohr model of the atom The Bohr model is a ‘planetary’ type model.
The nucleus is at the center of the model.
Electrons can only exist at specific energy levels (orbit).
Each energy level was assigned a principal quantum number, n.
Each principal quantum
represents a new ‘orbit’ or layer.

26. Bohr model of the atom
Bohr derived an equation that determined the energy of each allowed orbit for the electron in the hydrogen atom.
n is the principle quantum number
When electrons gain energy, they jump to a higher energy level which is farther from the nucleus.
Energy is released when the electrons drops down to a lower energy level closer to the nucleus.

27. Bohr model of the atom n=5 -52 kJ n=4 -82 kJ n=3 -146 kJ n=2 -328 kJ

28. Bohr model of the atom Account for the observed spectral lines.
Bohr was able to use his model of hydrogen to:
Account for the observed spectral lines.
Calculate the radius for hydrogen atoms.
His model did not account for:
Atoms other than hydrogen.
Why energy was quantized.
His concept of electrons moving in fixed orbits was later abandoned.

29. Need a New or Revised Atomic Model
What will it be?
The Quantum Mechanical Model
a.k.a Wave Model, Electron Cloud Model
But, first we need to know about a couple of developments….
Wave Nature of the Electron
Heisenberg Uncertainty Principle

30. Wave theory of the electron
1924 De Broglie suggested electrons have wave properties to account for their energy being quantized.
The electron was fixed in the space around the nucleus.
Represented the electron as a standing wave.
As a standing wave, each electron’s path must equal a whole number times the wave’s fundamental frequency.

31. The electron wave
1927 American physicists, Davisson and Germer, demonstrate that an electron beam exhibits wave interference properties.
bands of
constructive
interference
cathode
tube - +
power
source
reflecting
crystal

32. De Broglie waves (Matter Waves)
De Broglie proposed that all particles have a wavelength as related by:
l = wavelength, meters
h = Planck’s constant
m = mass, kg
v = velocity, m/s
l = h mv

33. De Broglie waves
Using de Broglie’s equation, we can calculate the wavelength of an electron.
6.6 x kg m2 s-1
(9.1 x kg)(2.2 x 106 m s-1)
l =
= 3.3 x m
The speed of an electron had already been reported by Bohr as 2.2 x 106 m s-1.

34. Heisenberg uncertainty principle
According to Heisenberg, it is impossible to know both the position and the speed of an object precisely.
He developed the following relationship:
∆x ∆(mv)
As the mass of an object gets smaller, the product of the uncertainty of its position (∆x) and speed (∆v) increase. h
4 π m
>

35. Quantum Mechanics
Erwin Schrödinger developed a mathematical treatment into which both the wave and particle nature of matter could be incorporated.
This is known as quantum mechanics.
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36. Quantum Mechanics
The wave equation is designated with a lowercase Greek psi ().
The square of the wave equation, 2, gives a probability density map of where an electron has a certain statistical likelihood of being at any given instant in time.
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37. Quantum Numbers
Solving the wave equation gives a set of wave functions, or orbitals, and their corresponding energies.
Each orbital describes a spatial distribution of electron density.
An orbital is described by a set of three quantum numbers.
Each electron is completely described by four quantum numbers.
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38. Principal Quantum Number (n)
The principal quantum number, n, describes the energy level or shell on which the orbital resides.
The values of n are integers ≥ 1.
n = 1, 2, 3, …. 
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39. Angular Momentum Quantum Number (l)
This quantum number defines the shape of the orbital.
Allowed values of l are integers ranging from 0 to n − 1.
We use letter designations to communicate the different values of l and, therefore, the shapes and types of orbitals.
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40. Angular Momentum Quantum Number (l)
Value of l 1 2 3
Type of orbital s p d f
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41. Magnetic Quantum Number (ml)
The magnetic quantum number describes the three-dimensional orientation of the orbital.
Allowed values of ml range from −l through 0 to positive l:
−l ≤ ml ≤ l
−l , … 0, …, +l
Therefore, on any given energy level, there can be up to 1 s orbital, 3 p orbitals, 5 d orbitals, 7 f orbitals, and so forth.
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42. Magnetic Quantum Number (ml)
Orbitals with the same value of n form a shell.
Different orbital types within a shell are subshells.
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43. s Orbitals The value of l for s orbitals is 0.
They are spherical in shape.
The radius of the sphere increases with the value of n.
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44. The s orbital 2s 1s 1s 2s The s orbital is a sphere.
The 1s orbital has a maximum probability region at a radius of 1 Å from the nucleus.
The 2s orbital has a maximum probability region at a radius of ~ 3 Å from the nucleus. 1s
Probability 2s 2s 1s
Distance from nucleus, r (Å)
The s orbital is a sphere.
Every level has one s orbital.

45. The s orbital
The s orbital is a sphere. Every level has one s orbital, which increases in size as n increases.

46. p Orbitals The value of l for p orbitals is 1.
They have two lobes with a node between them.
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47. p orbitals
There are three p orbitals: px, py and pz

48. p orbitals
There are three p orbitals: px, py and pz

49. d Orbitals The value of l for a d orbital is 2.
Four of the five d orbitals have 4 lobes; the other resembles a p orbital with a doughnut around the center.
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50. Representative d orbitals
There are five d orbitals
(4 have the four-leaf clover shape)

51. Combined orbitals - n = 1, 2 & 3
1s, 2s, 2p, 3s, 3p and 3d sublevels

52. Representative f orbitals
There are seven f orbitals
(4 have the eight-lobe shape)

53. Quantum number values subshell # of n  m label orbitals 1 0 0 1s 1
, 0, 1 2p 3
s 1
, 0, 1 3p 3
2 -2, -1, 0, 1, 2 3d 5
s 1
, 0, 1 4p 3
2 -2, -1, 0, 1, 2 4d 5
, -2, -1, 0, 1, 2, 3 4f 7

54. Spin Quantum Number, ms
In the 1920s, it was discovered that the interaction of elements with magnets depended on the spin of the electrons in the atom.
The “spin” of an electron describes its magnetic field.
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55. Spin Quantum Number, ms
This led to a fourth quantum number, the spin quantum number, ms.
The spin quantum number has only 2 allowed values: +1/2 and −1/2.
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56. Pauli Exclusion Principle
No two electrons in the same atom can have exactly the same energy.
Therefore, no two electrons in the same atom can have identical sets of quantum numbers. The first three can be the same but the spins must be opposite.
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57. Energies of Orbitals
For a one-electron hydrogen atom, orbitals on the same energy level have the same energy.
That is, they are degenerate.
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58. Electron configuration
For the hydrogen atom, the principal quantum number determines the energy of the orbital.

59. Electron configuration
Things get a bit more complex where more than one electron is involved.
Effective nuclear charge(kernel charge)
Inner electrons act to shield outer ones from the positive charge of the nucleus.
Some orbitals penetrate to the nucleus more than others: s > p > d > f

60. Energies of Orbitals
As the number of electrons increases, though, so does the repulsion between them.
Therefore, in many-electron atoms, orbitals on the same energy level are no longer degenerate, but subshells are.
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61. Aufbau(building) approach
We can use this approach to ‘build’ atoms and describe their electron configurations.
For any element, you know the number of electrons in the neutral atom equals the atomic number. For an ion, the number of electrons equals the number of protons minus the charge.
Start filling orbitals, from lowest to highest energy.
If two or more orbitals exist at the same energy sublevel, do not pair the electrons until you first have one electron per orbital.

62. Major trends in electron filling 1s2 2s2 2p6 3s2 3p6 3d10
Blue sublevels
not occupied…
Not enough e-
4s2
4p6
4d10
4f14
5s2
5p6
5d10
5f14
5g18
6s2
6p6
6d10
6f14
6g18
6h22
7s2
7p6
7d10
7f14
7g18
7h22
7i26

63. Classification by sublevelsp H He d Li Be B C N O F Ne Na Mg Al Si P S Cl Ar K Ca Sc Hf Zr Ti V Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr Rb Sr Y Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te I Xe Cs Ba Lu Ta W Re Os Ir Pt Au Hg Tl Pb Bi Po At Rn Fr Ra Lr La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb f Ac Th Pa U Np Pu Am Cm Bk Cf Es Fm Md No

64. Electron Configurations
This term shows the distribution of all electrons in an atom.
Each component consists of
A number denoting the energy level,
4p5
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65. Electron Configurations
This term shows the distribution of all electrons in an atom
Each component consists of
A number denoting the energy level,
A letter denoting the type of orbital,
4p5
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66. Electron Configurations
This term shows the distribution of all electrons in an atom.
Each component consists of
A number denoting the energy level,
A letter denoting the type of orbital,
A superscript denoting the number of electrons in those orbitals.
4p5
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67. Writing electron configurations
Examples
O 1s 2 2s 2 2p 4
Ti 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 2
Br 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 4p 5
Core format
O [He] 2s 2 2p 4
Ti [Ar] 4s 2 3d 2
Br [Ar] 4s 2 3d 10 4p 5

68. Hund’s Rule
When putting electrons into orbitals with the same energy, place one electron in each orbital before pairing them up. The lone electrons will have the same direction of spin.
The existence of
unpaired electrons
can be tested for
since each acts like
a tiny electromagnet.

69. Hund’s Rule
“For degenerate orbitals, the lowest energy is attained when the number of electrons with the same spin is maximized.”
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70. Hund’s Rule
Paramagnetic - attracted to magnetic field. Indicates the presence of unpaired electrons.
Diamagnetic - unaffected by a magnetic field. Indicates that all electrons are paired.

71. Aufbau examples 2p 2p 2p 2s 2s 2s
energy 1s 1s 1s
C O F

72. Writing electron configurations
Electron configurations can be written for atoms or ions.
Start with the ground-state configuration for the atom.
For positively-charged cations, remove a number of the outermost electrons equal to the charge.
For negatively-charged anions, add a number of outermost electrons equal to the charge.

73. Writing electron configurations
Example - Cl-
First, write the electron configuration for chlorine:
Cl 17 e-
1s 2 2s 2 2p 6 3s 2 3p 5 or [Ne] 3s 2 3p 5
Because the charge is 1-, add one electron.
Cl- 1s 2 2s 2 2p 6 3s 2 3p 6
or [Ne] 3s 2 3p 6 or [Ar]

74. Writing electron configurations
Example - Ba2+
First, write the electron configuration for barium.
Ba 56 e-
1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6 6s2
or [Xe] 6s2
Because the charge is 2+, remove two electrons.
Ba2+
1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6
or [Xe] or [Kr] 5s2 4d10 5p6

75. Orbital Notation
A simple method used to show only the electrons in the highest main energy level. The d and f sublevels are not shown unless they are partially filled.
Indicates which orbitals are occupied and whether or not electrons are paired with other electrons in the orbitals.

76. O Orbital Notation For O, 1s2 2s2 2p4 , the orbital notation is 2s 2p
Notice that the electrons do not pair up in orbitals of the same energy sublevel until each of the orbitals is occupied by a single electron, all spinning the same direction. (Hund’s Rule)

77. Orbital Notation
For V, 1s2 2s2 2p6 3s2 3p6 4s2 3d3 , the orbital notation is
4s 3d V
Notice that there must be five d orbitals shown, even though two of the orbitals are empty.

78. Lewis Electron-Dot Diagrams
Basic rules
Draw the atomic symbol.
Treat each side as an orbital that can hold up to two electrons.
Count the electrons in the valence shell.
Start filling the boxes, as you would the orbitals. px X py s pz

79. O Lewis symbols px py s pz
Note: The position of the pairs of electrons is not important. px O py s
Oxygen has 6 electrons
in its valence - VIA.
Start putting them in
the boxes. pz

80. Li Be B C N O F Ne Lewis symbols
Lewis symbols of second period elements
Li Be B C
N O F Ne

81. Periodic Table We fill orbitals in increasing order of energy.
Different blocks on the periodic table (shaded in different colors in this chart) correspond to different types of orbitals.
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82. Some Anomalies
Some irregularities occur when there are enough electrons to half-fill s and d orbitals on a given row.
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83. Some Anomalies For instance, the electron configuration for copper is
[Ar] 4s1 3d5
rather than the expected
[Ar] 4s2 3d4.
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84. Some Anomalies
This occurs because the 4s and 3d orbitals are very close in energy.
These anomalies occur in f-block atoms, as well.
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85. Quantum model of the atom
Schrödinger developed an equation to describe the behavior and energies of electrons in atoms.
His equation is used to plot the position of the electron relative to the nucleus as a function of time.
While the equation is too complicated to write here, we can still use the results.
Each electron can be described in terms of its quantum numbers.

86. Quantum numbers Principal quantum number, n
Tells the size of an orbital and largely determines its energy.
n = 1, 2, 3, ……
Orbital (azimuthal) quantum number, l
The number of subshells that a principal level contains. It tells the shape of the orbitals.
l = 0 to n - 1

87. Quantum numbers Magnetic quantum number, m
Describes the orientation that the orbital has in space, relative to an x, y, z plot.
m = -  to +  (all integers, including zero)
For example, if  = 1, then m would have values of -1, 0, and +1.
Knowing all three numbers provide us with a picture of all of the orbitals.