1. Electrons in Atoms

2. Dalton’s Atomic Theory
John Dalton ( ) had four theories
All elements are composed of submicroscopic indivisible particles called atoms
Atoms of the same element are identical. The atoms of anyone element are different from those of any other element
Atoms of different elements can physically mix together or can chemically combine w/ one another in simple whole-number ratios to form compounds
Chemical reactions occur when atoms are separated, joined, or rearranged. However, atoms of one element are never changed into atoms of another elements as a result of a chemical reaction

3. Thomson’s Atomic Model
Thomson though electrons were like plums embedded in a positively charged “pudding”, so his model was called the “plum pudding” model

4. Thomson’s Theory
Thomson stated: The atom had negatively charged electrons stuck into a lump of positively charged protons.
Thomson never explained
Number of protons and neutrons
The arrangement of the particles in the atom
The ease with which atoms are stripped of electrons to form ions

5. Rutherford Model Rutherford used the Gold Foil Experiment
Rutherford proposed the following:
Thomson model was incorrect
Most of the mass of the atom and all of its positive charge reside in a very small, extremely dense region, which he called the nucleus
Most of the total volume of the atom is empty space in which electrons move around the nucleus

6. Rutherford’s Model
Discovered dense positive piece at the center of the atom
Nucleus
Electrons moved around
Mostly empty space

7. Bohr Model
Bohr changed the Rutherford model and explained how the electrons travel.
Bohr explained the following in his model:
Electrons travel in definite orbits around the nucleus
Electrons are arranged in concentric circular paths or orbitals around the nucleus
Electrons don’t fall into the nucleus because electrons in particular path have fixed energy and don’t lose energy
His model was patterned after the motion of the planets around the sun. It is often called the Planetary model.

8. Bohr Model Cont.
                              

9. Bohr’s Model
Nucleus
Electron
Orbit
Energy Levels

10. Quantum Theory
Bohr explained how electrons were moving via Quantum Theory
Key Terms:
Energy Levels- Regions around the nucleus where the electron is likely moving
Quantum- Amount of energy required to move an electron from one energy level to the next
Quantum Leap- Abrupt Change

11. } Bohr’s Model Fifth Fourth Increasing energy Third Second First
Further away from the nucleus means more energy.
There is no “in between” energy
Energy Levels
Fifth
Fourth
Third
Increasing energy
Second
First
Nucleus

12. Bohr’s Model cont. Energy levels are not equally spaced.
Energy levels more closely spaced further from the nucleus
Higher energy level occupied by an electron, the more energetic that electron is.
Amount of energy gained or lost by an electron is not always the same amount.

13. Bohr Model Cont. The Bohr Model did not account for:
Emission spectra of atoms containing more than one electron.
So comes along the next model:

14. The Quantum Mechanical Model
Energy is quantized. It comes in chunks.
A quanta is the amount of energy needed to move from one energy level to another.
Since the energy of an atom is never “in between” there must be a quantum leap in energy.
Schrodinger derived an equation that described the energy and position of the electrons in an atom

15. The Quantum Mechanical Model
Things that are very small behave differently from things big enough to see.
The quantum mechanical model is a mathematical solution
It is not like anything you can see.

16. Wave Functions
Erwin Schrödinger: We can describe the electron mathematically, using quantum mechanics (wave mechanics).
Schrödinger developed a wave equation to describe the hydrogen atom.
An acceptable solution to Schrödinger’s wave equation is called a wave function.
A wave function represents an energy state of the atom.

17. Schrödinger’s Equation
The wave function is a F(x, y, z)
Actually F(r,θ,φ)
Solutions to the equation are called orbitals.
These are not Bohr orbits.
Each solution is tied to a certain energy
These are the energy levels
Animation

18. Schrödinger’s Equation

19. The Quantum Mechanical Model
Has energy levels for electrons.
Orbits are not circular.
It can only tell us the probability of finding an electron a certain distance from the nucleus.

20. The Quantum Mechanical Model
The atom is found inside a blurry “electron cloud”
A area where there is a chance of finding an electron.
Draw a line at 90 %

21. The Uncertainty Principle
Werner Heisenberg: We can’t know exactly where a moving particle is AND exactly how fast it is moving at the same time.
The photon that will enter the microscope, so that we might “see” the electron …
… has enough momentum to deflect the electron.
The act of measurement has interfered with the electron’s motion.

22. The Uncertainty Principle
A wave function doesn’t tell us where the electron is. The uncertainty principle tells us that we can’t know where the electron is.
However, the square of a wave function gives the probability of finding an electron at a given location in an atom.
Analogy: We can’t tell where a single leaf from a tree will fall. But (by viewing all the leaves under the tree) we can describe where a leaf is most likely to fall.

23. Atomic Orbitals
There are the region of space which there is a high probability of finding an electron
Within each energy level the complex math of Schrodinger’s equation describes several shapes.
These are called atomic orbitals
Quantum Numbers- numbers that specify the properties of atomic orbitals and their electrons

24. Quantum Numbers There are 4 types of Quantum Numbers
Principal – distance from the nucleus
Angular Momentum- Orbital Shape
Magnetic- Orbital position with respect to the X, Y, & Z axes.
Spin- Has only two values (+1/2 or –1/2) and is needed to specify 1 of 2 positional orientations of an electron

25. Principal Quantum Number
Symbolized by the letter N, indicates the main energy levels surrounding the nucleus
There are 7 principal quantum numbers
A.K.A. – Shells
Value of N is a whole number ex. 1,2,3 ect..
Main Energy Level – N=1; closest to the nucleus or ground state
Ground State- state of the lowest energy of the atom.
As N increases, the distance from the nucleus increases and the energy increases

26. Angular Momentum Quantum Number
Indicates the shape of the orbital.
Within each main energy level beyond the first, orbitals with different shapes occupy different regions
A.K.A. – Sublevels or Subshells
The number of sublevels = Value of the Principal Quantum Number

27. Magnetic Quantum Number
Indicates the orientation of a orbital about the nucleus
There are 4 types of orbital orientation
S Orbital
P Orbital
D Orbital
F Orbital

28. Spin Quantum Number
Has only two possible values: +1/2 or –1/2. These values indicate two possible states of an electron in an orbital
Spin Quantum # is significant because each single orbital can hold no more than two electrons, which must have opposite spin.

29. S orbitals 1 s orbital for every energy level Spherical shaped
Each s orbital can hold 2 electrons
Called the 1s, 2s, 3s, etc.. orbitals.

30. P orbitals Start at the second energy level 3 different directions
3 different shapes
Each can hold 2 electrons

31. P Orbitals

32. D orbitals Start at the third energy level 5 different shapes
Each can hold 2 electrons

33. F orbitals Start at the fourth energy level
Have seven different shapes
2 electrons per shape

34. F orbitals

35. Summary # of shapes Max electrons Starts at energy level s 1 2 1 p 3 6d 5 10 3 7 14 4 f

36. By Energy Level First Energy Level only s orbital only 2 electrons 1s2
Second Energy Level
s and p orbitals are available
2 in s, 6 in p
2s22p6
8 total electrons

37. By Energy Level Third energy level s, p, and d orbitals
2 in s, 6 in p, and 10 in d
3s23p63d10
18 total electrons
Fourth energy level
s,p,d, and f orbitals
2 in s, 6 in p, 10 in d, ahd 14 in f
4s24p64d104f14
32 total electrons

38. By Energy Level
Any more than the fourth and not all the orbitals will fill up.
You simply run out of electrons
The orbitals do not fill up in a neat order.
The energy levels overlap
Lowest energy fill first.

39. Question for You How many principal quantum numbers are there?
What is the maximum number of electrons that can fill the 3rd energy level?
How many orbitals are in the sublevel F?
What is the total number of orbitals for the 3rd main energy level?

40. Electron Configuration
The way electrons are arranged in atoms
There are three rules which help dictate how electrons are arranged in the atoms.
Aufbau Principle- electrons occupy the orbitals of the lowest energy first
Hund’s Rule- Orbitals of equal energy are each occupied by one electron before any one orbital is occupied by a second electron. All electrons in a single occupied orbital must have the same spin.

41. Electron Configuration cont.
Pauli Exclusion Principle- No two electrons may occupy any given orbital without having opposite spin. No two electrons in the same atom can have the same set of four quantum numbers.
Let’s determine electron configuration.
Let’s start with Phosphorus.
Need to account for all 15 electrons

42. Electron Configurations
Distribution of all electrons in an atom
Consist of
Number denoting the energy level

43. Electron Configurations
Distribution of all electrons in an atom
Consist of
Number denoting the energy level
Letter denoting the type of orbital

44. Electron Configurations
Distribution of all electrons in an atom.
Consist of
Number denoting the energy level.
Letter denoting the type of orbital.
Superscript denoting the number of electrons in those orbitals.

45. Electron Configurations
An electron configuration describes the distribution of electrons among the various orbitals in the atom.
Electron configuration is represented in two ways.
The spdf notation uses numbers to designate a principal shell and letters (s, p, d, f) to identify a subshell; a superscript indicates the number of electrons in a designated subshell.

47. Orbital Diagrams Each box represents one orbital.
Half-arrows represent the electrons.
The direction of the arrow represents the spin of the electron.

48. Hund’s Rule
“For degenerate orbitals, the lowest energy is attained when the number of electrons with the same spin is maximized.”

49. Exceptions to Electron Configuration

50. Orbitals fill in order Lowest energy to higher energy.
Adding electrons can change the energy of the orbital.
Half filled orbitals have a lower energy.
Makes them more stable.
Changes the filling order

51. Write these electron configurations
Titanium - 22 electrons
1s22s22p63s23p64s23d2
Vanadium - 23 electrons 1s22s22p63s23p64s23d3
Chromium - 24 electrons
1s22s22p63s23p64s23d4 is expected
But this is wrong!!

52. Chromium is actually 1s22s22p63s23p64s13d5 Why?
This gives us two half filled orbitals.
Slightly lower in energy.
The same principal applies to copper.

53. Copper’s electron configuration
Copper has 29 electrons so we expect
1s22s22p63s23p64s23d9
But the actual configuration is
1s22s22p63s23p64s13d10
This gives one filled orbital and one half filled orbital.
Remember these exceptions

54. Shortcuts for Electron Configuration
There are two short handed methods of writing the electron configuration.
The 1st method is called the outer-level configuration. That tells you the outer-most configuration for that element.
The 2nd method is called the Noble Gas Notation. This tells you the complete notation using Noble Gases.
Let’s start with outer-level notation!!!

55. Exceptions to the Aufbau Principle
Half-filled d subshell plus half-filled s subshell has slightly lower in energy than s2 d4.
Filled d subshell plus half-filled s subshell has slightly lower in energy than s2 d9.
More exceptions occur farther down the periodic table. They aren’t always predictable, because energy levels get closer together.

56. H 1 Li 3 Na 11 K 19 Rb 37 Cs 55 Fr 87
1s1
1s22s1
1s22s22p63s1
1s22s22p63s23p64s1
1s22s22p63s23p64s23d104p65s1
1s22s22p63s23p64s23d104p65s24d10 5p66s1
1s22s22p63s23p64s23d104p65s24d105p66s24f145d106p67s1

57. 1s2
1s22s22p6
1s22s22p63s23p6
1s22s22p63s23p64s23d104p6
1s22s22p63s23p64s23d104p65s24d105p6
1s22s22p63s23p64s23d104p65s24d10 5p66s24f145d106p6 He 2 Ne 10 Ar 18 Kr 36 Xe 54 Rn 86

59. S- block s1 s2 Alkali metals all end in s1
Alkaline earth metals all end in s2
really have to include He but it fits better later.
He has the properties of the noble gases.

60. The P-block p1 p2 p3 p4 p6 p5

61. Transition Metals -d block

62. F - block f1 f5 f2 f3 f4 f6 f7 f8 f9 f10 f11 f12 f14 f13
inner transition elements f1 f5 f2 f3 f4 f6 f7 f8 f9
f10
f11
f12
f14
f13

63. Each row (or period) is the energy level for s and p orbitals.1 2 3 4 5 6 7
Each row (or period) is the energy level for s and p orbitals.

64. D orbitals fill up after previous energy level so first d is 3d even though it’s in row 4.1 2 3 4 5 6 7 3d

65. 1 2 3 4 5 6 7 4f 5f
f orbitals start filling at 4f

66. Summary Outer-Level Configuration

67. Writing Electron configurations the easy way
Yes there is a shorthand

68. Electron Configurations repeat
The shape of the periodic table is a representation of this repetition.
When we get to the end of the column the outermost energy level is full.
This is the basis for our shorthand.

69. The Shorthand Write the symbol of the noble gas before the element.
Then the rest of the electrons.
Aluminum - full configuration.
1s22s22p63s23p1
Ne is 1s22s22p6
so Al is [Ne] 3s23p1

70. More examples Ge = 1s22s22p63s23p64s23d104p2 Ge = [Ar] 4s23d104p2
Hf=1s22s22p63s23p64s23d104p65s2 4d105p66s24f145d2
Hf=[Xe]6s24f145d2

71. The Shorthand Again Sn- 50 electrons The noble gas before it is Kr
Takes care of 36
Next 5s2
Then 4d10
Finally 5p2
[ Kr ]
5s2
4d10
5p2

72. 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.

73. The Wave-like Electron
The electron propagates through space as an energy wave. To understand the atom, one must understand the behavior of electromagnetic waves.
Louis deBroglie

74. The Quantum Mechanical Model
A totally new approach
De Broglie said matter could be like a wave.
De Broglie said they were like standing waves.
The vibrations of a stringed instrument

76. What’s possible?
You can only have a standing wave if you have complete waves.
There are only certain allowed waves.
In the atom there are certain allowed waves called electrons.
1925 Erwin Schroedinger described the wave function of the electron
Much math, but what is important are the solutions

77. Schrödinger’s Equation
The wave function is a F(x, y, z)
Actually F(r,θ,φ)
Solutions to the equation are called orbitals.
These are not Bohr orbits.
Each solution is tied to a certain energy
These are the energy levels
Animation

78. What does the wave Function mean?
nothing.
it is not possible to visually map it.
The square of the function is the probability of finding an electron near a particular spot.
best way to visualize it is by mapping the places where the electron is likely to be found.

79. Probability
Distance from nucleus

80. Sum of all Probabilities
Distance from nucleus

81. Defining the size The nodal surface.
The size that encloses 90% to the total electron probability.
NOT at a certain distance, but a most likely distance.
For the first solution it is a a sphere.

82. Quantum Mechanics
Erwin Schrödinger developed a mathematical treatment into which both the wave and particle nature of matter could be incorporated.
It is known as quantum mechanics.
© 2009, Prentice-Hall, Inc.

83. Quantum Mechanics
The wave equation is designated with a lower case 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.
© 2009, Prentice-Hall, Inc.

84. 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.
© 2009, Prentice-Hall, Inc.

85. Quantum Numbers There are many solutions to Schrödinger’s equation
Each solution can be described with quantum numbers that describe some aspect of the solution.
Principal quantum number (n) size and energy of an orbital
Has integer values >0

86. s Orbitals
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.
© 2009, Prentice-Hall, Inc.

87. p Orbitals The value of l for p orbitals is 1.
They have two lobes with a node between them.
© 2009, Prentice-Hall, Inc.

88. 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.
© 2009, Prentice-Hall, Inc.

89. Quantum numbers Angular momentum quantum number l shape of the orbital
integer values from 0 to n-1
l = 0 is called s
l = 1 is called p
l =2 is called d
l =3 is called f
l =4 is called g

90. 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, etc.
© 2009, Prentice-Hall, Inc.

91. Magnetic Quantum Number (ml)
Orbitals with the same value of n form a shell.
Different orbital types within a shell are subshells.
© 2009, Prentice-Hall, Inc.

92. 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.
© 2009, Prentice-Hall, Inc.

93. 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.
© 2009, Prentice-Hall, Inc.