1. Chem101
Dr. Ali Jabalameli

2. The Beginnings of Quantum Mechanics
Chemistry101 Spring13
The Beginnings of Quantum Mechanics
Until the beginning of the 20th century it was believed that all physical phenomena were deterministic
Work done at that time by many famous physicists discovered that for sub-atomic particles, the present condition does not determine the future condition
Albert Einstein, Neils Bohr, Louis de Broglie, Max Planck, Werner Heisenberg, P. A. M. Dirac, and Erwin Schrödinger
Quantum mechanics forms the foundation of chemistry – explaining the periodic table and the behavior of the elements in chemical bonding – as well as providing the practical basis for lasers, computers, and countless other applications
Tro: Chemistry: A Molecular Approach, 2/e
Dr. Ali Jabalameli

3. The Behavior of the Very Small
Chemistry101 Spring13
The Behavior of the Very Small
Electrons are incredibly small
a single speck of dust has more electrons than the number of people who have ever lived on earth
Electron behavior determines much of the behavior of atoms
Directly observing electrons in the atom is impossible, the electron is so small that observing it changes its behavior
even shining a light on the electron would affect it
Tro: Chemistry: A Molecular Approach, 2/e
Dr. Ali Jabalameli

4. A Theory that Explains Electron Behavior
Chemistry101 Spring13
A Theory that Explains Electron Behavior
The quantum-mechanical model explains the manner in which electrons exist and behave in atoms
It helps us understand and predict the properties of atoms that are directly related to the behavior of the electrons
why some elements are metals and others are nonmetals
why some elements gain one electron when forming an anion, whereas others gain two
why some elements are very reactive while others are practically inert
and other periodic patterns we see in the properties of the elements
Tro: Chemistry: A Molecular Approach, 2/e
Dr. Ali Jabalameli

5. The Nature of Light: Its Wave Nature
Chemistry101 Spring13
The Nature of Light: Its Wave Nature
Light is a form of electromagnetic radiation
composed of perpendicular oscillating waves, one for the electric field and one for the magnetic field
an electric field is a region where an electrically charged particle experiences a force
a magnetic field is a region where a magnetized particle experiences a force
All electromagnetic waves move through space at the same, constant speed
3.00 x 108 m/s in a vacuum = the speed of light, c
Tro: Chemistry: A Molecular Approach, 2/e
Dr. Ali Jabalameli

6. Electromagnetic Radiation
Chemistry101 Spring13
Electromagnetic Radiation
Tro: Chemistry: A Molecular Approach, 2/e
Dr. Ali Jabalameli

7. Speed of Energy Transmission
Chemistry101 Spring13
Speed of Energy Transmission
Tro: Chemistry: A Molecular Approach, 2/e
Dr. Ali Jabalameli

8. Characterizing Waves The amplitude is the height of the wave
Chemistry101 Spring13
Characterizing Waves
The amplitude is the height of the wave
the distance from node to crest
or node to trough
the amplitude is a measure of how intense the light is – the larger the amplitude, the brighter the light
The wavelength (l) is a measure of the distance covered by the wave
the distance from one crest to the next
or the distance from one trough to the next, or the distance between alternate nodes
Tro: Chemistry: A Molecular Approach, 2/e
Dr. Ali Jabalameli

9. Wave Characteristics Tro: Chemistry: A Molecular Approach, 2/e
Chemistry101 Spring13
Wave Characteristics
Tro: Chemistry: A Molecular Approach, 2/e
Dr. Ali Jabalameli

10. © 2012 Pearson Education, Inc.
Chem101
Waves
To understand the electronic structure of atoms, one must understand the nature of electromagnetic radiation.
The distance between corresponding points on adjacent waves is the wavelength ().
© 2012 Pearson Education, Inc.
Tro: Chemistry: A Molecular Approach, 2/e
Dr. Ali Jabalameli

11. © 2012 Pearson Education, Inc.
Chem101
Waves
The number of waves passing a given point per unit of time is the frequency ().
For waves traveling at the same velocity, the longer the wavelength, the smaller the frequency.
© 2012 Pearson Education, Inc.
Dr. Ali Jabalameli

12. Amplitude & Wavelength
Chemistry101 Spring13
Amplitude & Wavelength
Tro: Chemistry: A Molecular Approach, 2/e
Dr. Ali Jabalameli

13. Chemistry101 Spring13
Characterizing Waves
The frequency (n) is the number of waves that pass a point in a given period of time
the number of waves = number of cycles
units are hertz (Hz) or cycles/s = s−1
1 Hz = 1 s−1
The total energy is proportional to the amplitude of the waves and the frequency
the larger the amplitude, the more force it has
the more frequently the waves strike, the more total force there is
Tro: Chemistry: A Molecular Approach, 2/e
Dr. Ali Jabalameli

14. The Relationship Between Wavelength and Frequency
Chemistry101 Spring13
The Relationship Between Wavelength and Frequency
For waves traveling at the same speed, the shorter the wavelength, the more frequently they pass
This means that the wavelength and frequency of electromagnetic waves are inversely proportional
because the speed of light is constant, if we know wavelength we can find the frequency, and vice versa
Tro: Chemistry: A Molecular Approach, 2/e
Dr. Ali Jabalameli

15. Chemistry101 Spring13
Example 7.1: Calculate the wavelength of red light with a frequency of 4.62 x 1014 s−1
Given:
Find:
n = 4.62 x 1014 s−1
l, (nm)
Conceptual Plan:
Relationships:
l∙n = c, 1 nm = 10−9 m
n (s−1)
l (m)
l (nm)
Solve:
Check:
the unit is correct, the wavelength is appropriate for red light
Tro: Chemistry: A Molecular Approach, 2/e
Dr. Ali Jabalameli

16. Chemistry101 Spring13
Practice – Calculate the wavelength of a radio signal with a frequency of MHz
Tro: Chemistry: A Molecular Approach, 2/e
Dr. Ali Jabalameli

17. Chemistry101 Spring13
Practice – Calculate the wavelength of a radio signal with a frequency of MHz
Given:
Find:
n = MHz
l, (m)
Conceptual Plan:
Relationships:
l∙n = c, 1 MHz = 106 s−1
n (MHz)
n (s−1)
l (m)
Solve:
Check:
the unit is correct, the wavelength is appropriate for radiowaves
Tro: Chemistry: A Molecular Approach, 2/e
Dr. Ali Jabalameli

18. Color The color of light is determined by its wavelength
Chemistry101 Spring13
Color
The color of light is determined by its wavelength
or frequency
White light is a mixture of all the colors of visible light
a spectrum
RedOrangeYellowGreenBlueViolet
When an object absorbs some of the wavelengths of white light and reflects others, it appears colored
the observed color is predominantly the colors reflected
Tro: Chemistry: A Molecular Approach, 2/e
Dr. Ali Jabalameli

19. Electromagnetic Radiation
Chem101
Electromagnetic Radiation
All electromagnetic radiation travels at the same velocity: the speed of light (c),
3.00  108 m/s.
Therefore,
c = 
© 2012 Pearson Education, Inc.
Tro: Chemistry: A Molecular Approach, 2/e
Dr. Ali Jabalameli

20. The Electromagnetic Spectrum
Chemistry101 Spring13
The Electromagnetic Spectrum
Visible light comprises only a small fraction of all the wavelengths of light – called the electromagnetic spectrum
Shorter wavelength (high-frequency) light has higher energy
radiowave light has the lowest energy
gamma ray light has the highest energy
High-energy electromagnetic radiation can potentially damage biological molecules
ionizing radiation
Tro: Chemistry: A Molecular Approach, 2/e
Dr. Ali Jabalameli

21. Types of Electromagnetic Radiation
Chemistry101 Spring13
Types of Electromagnetic Radiation
Electromagnetic waves are classified by their wavelength
Radiowaves = l > 0.01 m
Microwaves = 10−4 < l < 10−2 m
Infrared (IR)
far = 10−5 < l < 10−4 m
middle = 2 x 10−6 < l < 10−5 m
near = 8 x 10−7< l < 2 x 10−6 m
Visible = 4 x 10−7 < l < 8 x 10−7 m
ROYGBIV
Ultraviolet (UV)
near = 2 x 10−7 < l < 4 x 10−7 m
far = 1 x 10−8 < l < 2 x 10−7 m
X-rays = 10−10 < l < 10−8m
Gamma rays = l < 10−10
low frequency and energy
high frequency and energy
Tro: Chemistry: A Molecular Approach, 2/e
Dr. Ali Jabalameli

22. © 2012 Pearson Education, Inc.
Chem101
The Nature of Energy
The wave nature of light does not explain how an object can glow when its temperature increases.
© 2012 Pearson Education, Inc.
Dr. Ali Jabalameli

23. © 2012 Pearson Education, Inc.
The Nature of Energy
Max Planck explained it by assuming that energy comes in packets called quanta.
© 2012 Pearson Education, Inc.

24. © 2012 Pearson Education, Inc.
The Nature of Energy
Chem101
Einstein used this assumption to explain the photoelectric effect.
He concluded that energy is proportional to frequency:
E = h
where h is Planck’s constant,  10−34 J-s.
© 2012 Pearson Education, Inc.
Dr. Ali Jabalameli

25. © 2012 Pearson Education, Inc.
Chem101
The Nature of Energy
Therefore, if one knows the wavelength of light, one can calculate the energy in one photon, or packet, of that light:
c = 
E = h
© 2012 Pearson Education, Inc.
Dr. Ali Jabalameli

26. © 2012 Pearson Education, Inc.
Chem101
The Nature of Energy
Another mystery in the early twentieth century involved the emission spectra observed from energy emitted by atoms and molecules.
© 2012 Pearson Education, Inc.
Dr. Ali Jabalameli

27. © 2012 Pearson Education, Inc.
Chem101
The Nature of Energy
For atoms and molecules, one does not observe a continuous spectrum, as one gets from a white light source.
Only a line spectrum of discrete wavelengths is observed.
© 2012 Pearson Education, Inc.
Dr. Ali Jabalameli

28. © 2012 Pearson Education, Inc.
Chem101
The Nature of Energy
Niels Bohr adopted Planck’s assumption and explained these phenomena in this way:
Electrons in an atom can only occupy certain orbits (corresponding to certain energies).
© 2012 Pearson Education, Inc.
Dr. Ali Jabalameli

29. © 2012 Pearson Education, Inc.
Chem101
The Nature of Energy
Niels Bohr adopted Planck’s assumption and explained these phenomena in this way:
Electrons in permitted orbits have specific, “allowed” energies; these energies will not be radiated from the atom.
© 2012 Pearson Education, Inc.
Dr. Ali Jabalameli

30. © 2012 Pearson Education, Inc.
Chem101
The Nature of Energy
Niels Bohr adopted Planck’s assumption and explained these phenomena in this way:
Energy is only absorbed or emitted in such a way as to move an electron from one “allowed” energy state to another; the energy is defined by
E = h
© 2012 Pearson Education, Inc.
Dr. Ali Jabalameli

31. © 2012 Pearson Education, Inc.
Chem101
The Nature of Energy
The energy absorbed or emitted from the process of electron promotion or demotion can be calculated by the equation:
E = −hcRH
( ) 1
nf2
ni2 -
where RH is the Rydberg constant,  107 m−1, and ni and nf are the initial and final energy levels of the electron.
© 2012 Pearson Education, Inc.
Dr. Ali Jabalameli

32. The Wave Nature of Matter
Chem101
The Wave Nature of Matter
Louis de Broglie posited that if light can have material properties, matter should exhibit wave properties.
He demonstrated that the relationship between mass and wavelength was
 = h mv
© 2012 Pearson Education, Inc.
Dr. Ali Jabalameli

33. The Uncertainty Principle
Chem101
The Uncertainty Principle
Heisenberg showed that the more precisely the momentum of a particle is known, the less precisely is its position is known:
(x) (mv)  h 4
© 2012 Pearson Education, Inc.
Dr. Ali Jabalameli

34. The Uncertainty Principle
Chem101
The Uncertainty Principle
In many cases, our uncertainty of the whereabouts of an electron is greater than the size of the atom itself!
© 2012 Pearson Education, Inc.
Dr. Ali Jabalameli

35. Electron Energy
for an electron with a given energy, the best we can do is describe a region in the atom of high probability of finding it – called an orbital
a probability distribution map of a region where the electron is likely to be found
distance vs. y2

36. © 2012 Pearson Education, Inc.
Chem101
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.
© 2012 Pearson Education, Inc.
Dr. Ali Jabalameli

37. © 2012 Pearson Education, Inc.
Chem101
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.
© 2012 Pearson Education, Inc.
Dr. Ali Jabalameli

38. Schrödinger’s Equation
Chemistry101 Spring13
Schrödinger’s Equation
Schödinger’s Equation allows us to calculate the probability of finding an electron with a particular amount of energy at a particular location in the atom
Solutions to Schödinger’s Equation produce many wave functions, Y
A plot of distance vs. Y2 represents an orbital, a probability distribution map of a region where the electron is likely to be found
Tro: Chemistry: A Molecular Approach, 2/e
Dr. Ali Jabalameli

39. © 2012 Pearson Education, Inc.
Chem101
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.
© 2012 Pearson Education, Inc.
Dr. Ali Jabalameli

40. Wave Function, y
calculations show that the size, shape and orientation in space of an orbital are determined be three integer terms in the wave function
these integers are called quantum numbers
principal quantum number, n
angular momentum quantum number, l
magnetic quantum number, ml

41. Principal Quantum Number (n)
Chem101
Principal Quantum Number (n)
The principal quantum number, n, describes the energy level on which the orbital resides.
The values of n are integers ≥ 1.
© 2012 Pearson Education, Inc.
Dr. Ali Jabalameli

42. Angular Momentum Quantum Number (l)
Chem101
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.
© 2012 Pearson Education, Inc.
Dr. Ali Jabalameli

43. Angular Momentum Quantum Number (l)
Chem101
Angular Momentum Quantum Number (l)
Value of l 1 2 3
Type of orbital s p d f
© 2012 Pearson Education, Inc.
Dr. Ali Jabalameli

44. Magnetic Quantum Number (ml)
Chem101
Magnetic Quantum Number (ml)
The magnetic quantum number describes the three-dimensional orientation of the orbital.
Allowed values of ml are integers ranging from −l to l:
−l ≤ ml ≤ 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.
© 2012 Pearson Education, Inc.
Dr. Ali Jabalameli

45. Magnetic Quantum Number (ml)
Chem101
Magnetic Quantum Number (ml)
Orbitals with the same value of n form a shell.
Different orbital types within a shell are subshells.
© 2012 Pearson Education, Inc.
Dr. Ali Jabalameli

46. The Shapes of Atomic Orbitals
the l quantum number primarily determines the shape of the orbital
each value of l is called by a particular letter that designates the shape of the orbital
s orbitals are spherical
p orbitals are like two balloons tied at the knots
d orbitals are mainly like 4 balloons tied at the knot
f orbitals are mainly like 8 balloons tied at the knot

47. © 2012 Pearson Education, Inc.
Chem101
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.
© 2012 Pearson Education, Inc.
Dr. Ali Jabalameli

48. l = 0, the s orbital each principal energy state has 1 s orbital
lowest energy orbital in a principal energy state
spherical
number of nodes = (n – 1)

49. © 2012 Pearson Education, Inc.
s Orbitals
Chem101
Observing a graph of probabilities of finding an electron versus distance from the nucleus, we see that s orbitals possess n − 1 nodes, or regions where there is 0 probability of finding an electron.
© 2012 Pearson Education, Inc.
Dr. Ali Jabalameli

50. 2s and 3s 2s
n = 2,
l = 0 3s
n = 3,
l = 0

51. © 2012 Pearson Education, Inc.
Chem101
p Orbitals
The value of l for p orbitals is 1.
They have two lobes with a node between them.
© 2012 Pearson Education, Inc.
Dr. Ali Jabalameli

52. l = 1, p orbitals
each principal energy state above n = 1 has 3 p orbitals
ml = -1, 0, +1
each of the 3 orbitals point along a different axis
px, py, pz
2nd lowest energy orbitals in a principal energy state
two-lobed
node at the nucleus

53. p orbitals

54. l = 2, d orbitals
each principal energy state above n = 2 has 5 d orbitals
ml = -2, -1, 0, +1, +2
4 of the 5 orbitals are aligned in a different plane
the fifth is aligned with the z axis, dz squared
dxy, dyz, dxz, dx squared – y squared
3rd lowest energy orbitals in a principal energy state
mainly 4-lobed
one is two-lobed with a toroid
planar nodes
higher principal levels also have spherical nodes

55. © 2012 Pearson Education, Inc.
Chem101
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.
© 2012 Pearson Education, Inc.
Dr. Ali Jabalameli

56. d orbitals

57. l = 3, f orbitals
each principal energy state above n = 3 has 7 d orbitals
ml = -3, -2, -1, 0, +1, +2, +3
4th lowest energy orbitals in a principal energy state
mainly 8-lobed
some 2-lobed with a toroid
planar nodes
higher principal levels also have spherical nodes

58. f orbitals

59. © 2012 Pearson Education, Inc.
Chem101
Energies of Orbitals
For a one-electron hydrogen atom, orbitals on the same energy level have the same energy.
That is, they are degenerate.
© 2012 Pearson Education, Inc.
Dr. Ali Jabalameli

60. © 2012 Pearson Education, Inc.
Chem101
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.
© 2012 Pearson Education, Inc.
Dr. Ali Jabalameli

61. © 2012 Pearson Education, Inc.
Chem101
Spin Quantum Number, ms
In the 1920s, it was discovered that two electrons in the same orbital do not have exactly the same energy.
The “spin” of an electron describes its magnetic field, which affects its energy.
© 2012 Pearson Education, Inc.
Dr. Ali Jabalameli

62. © 2012 Pearson Education, Inc.
Chem101
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.
© 2012 Pearson Education, Inc.
Dr. Ali Jabalameli

63. Pauli Exclusion Principle
Chem101
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.
© 2012 Pearson Education, Inc.
Dr. Ali Jabalameli

64. Electron Configurations
Chem101
Electron Configurations
This term shows the distribution of all electrons in an atom.
Each component consists of
A number denoting the energy level,
4p5
© 2012 Pearson Education, Inc.
Dr. Ali Jabalameli

65. Electron Configurations
Chem101
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
© 2012 Pearson Education, Inc.
Dr. Ali Jabalameli

66. Electron Configurations
Chem101
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
© 2012 Pearson Education, Inc.
Dr. Ali Jabalameli

67. © 2012 Pearson Education, Inc.
Chem101
Orbital Diagrams
Each box in the diagram represents one orbital.
Half-arrows represent the electrons.
The direction of the arrow represents the relative spin of the electron.
© 2012 Pearson Education, Inc.
Dr. Ali Jabalameli

68. © 2012 Pearson Education, Inc.
Chem101
Hund’s Rule
“For degenerate orbitals, the lowest energy is attained when the number of electrons with the same spin is maximized.”
© 2012 Pearson Education, Inc.
Dr. Ali Jabalameli

69. Energy Shells and Subshells

70. © 2012 Pearson Education, Inc.
Chem101
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.
© 2012 Pearson Education, Inc.
Dr. Ali Jabalameli

71. © 2012 Pearson Education, Inc.
Chem101
Some Anomalies
Some irregularities occur when there are enough electrons to half-fill s and d orbitals on a given row.
© 2012 Pearson Education, Inc.
Dr. Ali Jabalameli

72. © 2012 Pearson Education, Inc.
Chem101
Some Anomalies
For instance, the electron configuration for copper is
[Ar] 4s1 3d5
rather than the expected
[Ar] 4s2 3d4.
© 2012 Pearson Education, Inc.
Dr. Ali Jabalameli

73. © 2012 Pearson Education, Inc.
Chem101
Some Anomalies
This occurs because the 4s and 3d orbitals are very close in energy.
These anomalies occur in f-block atoms, as well.
© 2012 Pearson Education, Inc.
Dr. Ali Jabalameli

74. Chemistry101 Spring13
Example: What are the quantum numbers and names (for example, 2s, 2p) of the orbitals in the n = 4 principal level? How many orbitals exist?
Given:
Find:
n = 4
orbital designations, number of orbitals
Conceptual Plan:
Relationships:
l: 0 → (n − 1); ml: −l → +l n l ml
0 → (n − 1)
−l → +l
Solve:
n = 4
 l : 0, 1, 2, 3
n = 4, l = 0 (s)
ml : 0
1 orbital 4s
n = 4, l = 1 (p)
ml : −1,0,+1
3 orbitals 4p
n = 4, l = 2 (d)
ml : −2,−1,0,+1,+2
5 orbitals 4d
n = 4, l = 3 (f)
ml : −3,−2,−1,0,+1,+2,+3
7 orbitals 4f
total of 16 orbitals: = 42 : n2
Tro: Chemistry: A Molecular Approach, 2/e
Dr. Ali Jabalameli