2. Rules of Electron Location and Orbital Filling Order
Quantum Numbers
Rules of Electron Location and
Orbital Filling Order

3. Quantum Numbers At the conclusion of our time together, you should be able to:
List and define each of the 4 quantum numbers.
Relate these numbers to the state, city, street and home address for the electron.
Give the maximum number of electrons for each level and sublevel.
Draw the basic shape of the 4 sublevels.

4. Principal Quantum Number - n
Symbol = n
Represents the main energy level of the electron and its distance from the nucleus
Equation: 2n2 - shows how many electrons can be in each energy level
(e.g. 3rd energy level: 2(3)2 = 18 total possible e in this energy level)
Your turn: How many electrons in the 4th energy level? 32

5. Principal Quantum Number - n
In an address analogy, this would be the state in which the electron would probably be found. Presently, we can find electrons in 7 states.
Values are 1-7
Ex. = 1s1 (the electron configuration for H)
Principal Quantum number = 1

6. The First of 4 Quantum Numbers for the One Electron of Hydrogen
n (energy level) 1

7. The Second Quantum Number - l
This number describes sublevels, shapes of these sublevels and is the Angular momentum quantum number. The number of sublevels (shapes) in an energy level equals the value of n, the principle quantum number. The first 4 sublevels are named s, p, d, f.
Each sublevel has a unique shape:

8. Shape of the “s” Orbital
s for "Sphere": the simplest shape, or shape of the simplest atoms like hydrogen and helium
Electrons don't interfere with, or block, each other from the pull of the nucleus - ball shape
Each energy level has an "s" orbital at the lowest energy within that level

9. Shapes of the “p” Orbitals
p for "Peanut/Petal": a more complex shape that occurs at energy levels 2 and above

10. Shapes of the “d” Orbitals
d for "Double Peanut/Petal": a complex shape occurring at energy levels 3 and above
The arrangement of these orbitals allows for "s" and "p" orbitals to fit closer to the middle/nucleus

11. Shapes of the “f” Orbitals
f for "Flower": bizarre-shaped orbitals for electrons of very large atoms
electrons filling these orbitals are weakly attached to the atom because they are so far away from the pull of the nucleus

12. The Second Quantum Number - l
In the address analogy, this would be the city in which the electron would probably be found. In the first state there would be 1 city, in the second state there would be 2 cities...
This number is from the formula: 0 to (n-1)

13. The Second Quantum Number - l
The 2nd Quantum Number = 0 to (n-1)
Ex. = 1s1 , s sublevel number is 0 to (1-1) = 0
p sublevel number is, 0 to (2-1) = 1
d sublevel number is, 0 to (3-1) = 2
f sublevel number is, 0 to (4-1) = 3
Therefore:
For s, l = 0
For p, l = 1
For d, l = 2
For f, l = 3

14. The Second of 4 Quantum Numbers for the One Electron of Hydrogen
Ex. = 1s1, 0 to (1-1) = 0
Second Quantum number for Hydrogen = 0
n (energy level) 1
l (angular momentum, sublevel shape)

15. The Third Quantum Number - m
This number describes orientations of the orbitals that each sublevel can have and is the Magnetic quantum number.
s has one orientation,
p has three orientations ,
d has five orientations and
f has 7 orientations.
We’ll see how we got these orientation numbers in just a moment.

16. The Third Quantum Number - m
In the address analogy, this would be the street on which the electron would probably be found.
In the first state there is one city. In this first city there would be one street.
In the second state there are two cities. The first city with its one street and a second city with its 3 streets for a total of 4.
In the 3rd state would have the previous 4 streets plus 5 more streets from the 3rd city for a total of 9.

17. The Third Quantum Number - m
3rd Quantum Number = –l to 0 to +l
We know what the shape looks like from the second Quantum Number, now we know how many orientations of these shapes each sublevel has by plugging the l value into the formula above.

18. The Third Quantum Number - m
Value = –l to 0 to +l, therefore:
s = ___
Or just 1 orientation

19. The Third Quantum Number - m
Values are –l to 0 to +l, therefore:
p = ___ ___ ___
Or 3 orientations

20. The Third Quantum Number - m
Values are –l to 0 to +l, therefore:
d = ___ ___ ___ ___ ___
or 5 orientations

21. The Third Quantum Number - m
Values are –l to 0 to +l, therefore:
f = ___ ___ ___ ___ ___ ___ ___
or 7 orientations

22. The Third Quantum Number - m
Let’s Review the Values for m:
s = ___ p = ___ ___ ___
d = ___ ___ ___ ___ ___
f = ___ ___ ___ ___ ___ ___ ___
Ex. = 1s1 = 0
Third Quantum number from s = 0, or 1 shape

23. The Third of the 4 Quantum Numbers for the One Electron of Hydrogen
n (energy level) 1
l (angular momentum, sublevel shape)
m (magnetic, orientation)

24. The Fourth Quantum Number - s
This number describes the spin of the electrons in an orbital. There can be two electrons in each orbital as long as they are spinning in opposite directions.
In the address analogy, this would be
the house number of the electron.
There can only be 2 houses on each street
Values are +1/2 = clockwise spin
-1/2 = counter clockwise spin

25. The Fourth Quantum Number - s
Ex. = 1s1 , spin is up or +1/2
Fourth Quantum number from 1 = +1/2

26. The Fourth of the 4 Quantum Numbers for the One Electron of Hydrogen
n (energy level) 1
l (angular momentum, sublevel shape)
m (magnetic, orientation)
s (spin, clockwise or counterclockwise)
+1/2

27. Quantum # Summary for Hydrogen
Hydrogen has one electron spinning in a clockwise direction in the first energy level that has one orbital and only one orientation in its s sublevel shape which is spherical.
The 4 quantum numbers for H are:
1, 0, 0, +1/2

28. Quantum Numbers Let’s see if you can:
List and define each of the 4 quantum numbers.
Relate these numbers to the state, city, street and home address for the electron.
Give the maximum number of electrons for each level and sublevel.
Draw the basic shape of the 4 sublevels.

29. How do we know when an electron has moved from an excited state to the ground state? The electron will
Release a photon.
Release a specific amount of energy.
Release a specific color.
Release a quantum of energy.
All of the above are correct.

30. What does the second quantum number (l) describe?
Orbital shape.
Energy level.
Electron spin.
Orbital orientation.

31. Which quantum number has values of +½ or –½?
Orbital shape.
Energy level.
Electron spin.
Orbital orientation.

32. Which of the following is not a possible orbital shape?z f

33. What is currently the highest possible principal quantum number an electron can have?
No limit 5 6 7

34. How many electrons will the 4th energy level hold?
No limit 8 18 32 50

35. The p sublevel would look like a
sphere
petal
double petal
flower
mess

36. Quantum Numbers At the conclusion of our time together, you should be able to:
Continue to relate Quantum Numbers to the state, city, street and home address for the electron.
Give the 4 quantum number for every electron of every atom on the periodic table.

37. Let’s Try Helium
H is 1s1
He has 2 electrons, can we add another electron spinning in the other direction in the first energy level of the s sublevel with its 1 spherical orbital?
Yes, He is 1s2
He has 2 electrons spinning in opposite directions in the s sublevel with its spherical shape with 1 orientation.

38. Remember the Quantum # Summary for Hydrogen
Hydrogen has one electron spinning in a clockwise direction in the first energy level that has one spherical orbital in its s sublevel.
The 4 quantum numbers for H are:
1, 0, 0, +1/2

39. The Pauli Exclusion Principle
No two electrons in an atom can have the same set of four quantum numbers.
Therefore, the second electron that He has must have a different set of 4 Quantum Numbers.
What would they be??

40. The 4 Quantum Numbers of Helium1 l m s
-1/2

41. The 4 Quantum Numbers of Helium
No two electrons in an atom can have the same set of four quantum numbers.
What principle??
Pauli Exclusion Principle
Therefore, the second electron that He has must have a different set of 4 Quantum Numbers.
What would they be??
1, 0, 0, -1/2

42. Let’s Try Lithium He is 1s2
He has 2 electrons, can we add another electron spinning in another direction in the first energy level of the s sublevel with its 1 spherical orbital?
No, the third electron must go to the 2nd energy level which has 2 sublevels, s and p, s with its one spherical orbital and p with its 3 orientations of its petal shaped orbitals.

43. Let’s Try Lithium So the address for all 3 electrons of Li is: 1s2 2s1
This is called the electron configuration for Li and basically says that the first two electrons of Li are in the s sublevel with its one spherical shape with the 3rd electron in the 2 energy level, s sublevel with its bigger spherical shape.
The Quantum #’s of the 3rd electron:

44. The 4 Quantum Numbers for the 3rd Electron of Lithium2 l m s
+1/2

45. Now Beryllium: Add one more electron to Li :
1s2 2s1? Where would it go??
1s2 2s2
The 2s sublevel with its one spherical orbital can hold 2 electrons spinning in opposite directions.
The Quantum #’s of the 4th electron:

46. The 4 Quantum Numbers for the 4th Electron of Beryllium2 l m s
-1/2

47. What About Boron: Add one more electron to Be:
1s2 2s2? Where would it go??
1s2 2s3 ? No
1s2 2s2 2p1
The 2s sublevel with its one spherical orbital is full. We must now start filling the 2p sublevel with its 3 orbitals
The Quantum #’s of the 5th electron:

48. The Electrons of the 2nd Energy Level for Boron
s = ___ p = ___ ___ ___

49. The 4 Quantum Numbers for the 5th Electron of Boron2 l 1 m -1 s
+1/2

50. Let’s Move to Carbon: Add one more electron to B: 1s2 2s2 2p2
The 2p sublevel has 3 orbitals. However, we can’t put another electron in the first orbital of p. Why?
Hund’s Rule: Orbitals of equal energy are each occupied by one electron before any orbital is occupied by a second electron.

51. The Electrons of the 2nd Energy Level for Carbon
s = ___ p = ___ ___ ___

52. The 4 Quantum Numbers for the 6th Electron of Carbon2 l 1 m s
+1/2

53. Nitrogen: Add one more electron to C: 1s2 2s2 2p3
The 3rd electron in the p sublevel must go into the 3rd orbital. Why?
Again Hund’s Rule: Orbitals of equal energy are each occupied by one electron before any orbital is occupied by a second electron.

54. The Electrons of the 2nd Energy Level for Carbon
s = ___ p = ___ ___ ___

55. The 4 Quantum Numbers for the 7th Electron of Nitrogen2 l 1 m s
+1/2

56. Oxygen: Add one more electron to N: 1s2 2s2 2p4
The 4th electron in the p sublevel must begin to double up the electrons of the three p orbitals.

57. The Electrons of the 2nd Energy Level for Carbon
s = ___ p = ___ ___ ___

58. The 4 Quantum Numbers for the 8th Electron of Oxygen2 l 1 m -1 s
-1/2

59. Fluorine: Add one more electron to O: 1s2 2s2 2p5
Where would the 5th electron for the 2p orbitals go?

60. The Electrons of the 2nd Energy Level for Fluorine
s = ___ p = ___ ___ ___

61. The 4 Quantum Numbers for the 9th Electron of Fluorine2 l 1 m s
-1/2

62. Neon: Add one more electron to F: 1s2 2s2 2p6
Where would the 6th electron for the 2p orbitals go?

63. The Electrons of the 2nd Energy Level for Neon
s = ___ p = ___ ___ ___

64. The 4 Quantum Numbers for the 10th Electron of Neon2 l 1 m s
-1/2

65. What About Sodium: Add one more electron to Ne: 1s2 2s2 2p7 No!!
The 2p sublevel with its 3 orbitals is full. We must now go to the 3rd energy level with its 3 sublevels, s, p, and d, and start filling electrons all over again!

66. The Electrons of the 3rd Energy Level for Sodium
s = ___ p = ___ ___ ___
d = ___ ___ ___ ___ ___

67. The 4 Quantum Numbers for the 11th Electron of Sodium3 l m s
+1/2

68. What About Magnesium: Add one more electron to Na: 1s2 2s2 2p6 3s2
Remember, the s sublevel with its one spherical orbital can have one more electron.

69. The Electrons of the 3rd Energy Level for Magnesium
s = ___ p = ___ ___ ___
d = ___ ___ ___ ___ ___

70. The 4 Quantum Numbers for the 12th Electron of Magnesium3 l m s
-1/2

71. Aluminum: Add one more electron to Mg: 1s2 2s2 2p6 3s2 3p1
Remember, the s sublevel with its one spherical orbital can only have 2 electrons. The next electron must start to fill the 3p sublevel with its 3 orbitals.

72. The Electrons of the 3rd Energy Level for Aluminum
s = ___ p = ___ ___ ___
d = ___ ___ ___ ___ ___

73. The 4 Quantum Numbers for the 13th Electron of Aluminum-1 s
+1/2

74. Silicon to Argon: Keep adding one more electron to Al:
1s2 2s2 2p6 3s2 3p2-6
Remember Hund’s rule. We will put one electron in each of the p orbitals and then come back to double up.

75. The Electrons of the 3rd Energy Level for Silicon to Argon
s = ___ p = ___ ___ ___
d = ___ ___ ___ ___ ___

76. The 4 Quantum Numbers for the 18th Electron of Argon3 l 1 m s
-1/2

77. Quantum Numbers Let’s see if you can:
Continue to relate Quantum Numbers to the state, city, street and home address for the electron.
Give the 4 quantum number for every electron of every atom on the periodic table.

78. The 5f sublevel with its orbitals would look like a
sphere
petal
double petal
flower
mess

79. How many orbitals are in the 5f sublevel?
No limit 1 3 5 7

80. How many electrons will the 4f sublevel hold?2 6 10 14 18

81. In the address analogy, the first quantum number is the state and the second quantum number is the city. How many cities are there in the second state? 1 2 3 4 5

82. In the address analogy, the second state can have how many total streets?1 2 3 4 5

83. Quantum Numbers At the conclusion of our time together, you should be able to:
Explain the Aufbau principle and the diagonal rule.
Use Hund’s rule in an orbital filling diagram.
Give the quantum numbers for every electron of every atom on the periodic table.
Draw the electron configuration and orbital notation for every element.

84. Now Potassium:
We should now start to fill the 3d sublevel with its 5 orbitals.
1s2 2s2 2p6 3s2 3p6 3d1
But now we must consider the Aufbau Principle:
An electron will occupy the lowest energy level orbital that can receive it.
Look at the energy needed for 3d vs. 4s:
???

86. The Aufbau Principle
You will need to remember this chart so that you place electrons in the correct order.
An easy way to remember the filling order is to follow the diagonal rule.
Check it out on the next slide:

87. Maybe You’ve Seen This Chart???1 2 3 4 5 6 7 s
s 2p
s 3p 3d
s 4p 4d 4f
s 5p 5d 5f 5g?
s 6p 6d 6f 6g? 6h?
s 7p 7d 7f 7g? 7h? 7i?

88. It Represents the Diagonal Rule
Steps:
Write the energy levels top to bottom.
Write the orbitals in s, p, d, f order. Write the same number of orbitals as the energy level.
Draw diagonal lines from the top right to the bottom left.
To get the correct order, follow the arrows!

89. 1 2 3 4 5 6 7 Diagonal Rule s s 2p s 3p 3d s 4p 4d 4f s 5p 5d 5f 5g?
By this point, we are past the current periodic table so we can stop.
s 3p 3d
s 4p 4d 4f
s 5p 5d 5f 5g?
s 6p 6d 6f 6g? 6h?
s 7p 7d 7f 7g? 7h? 7i?

90. The Aufbau Principle
But there is even an easier way to remember the filling order.
Have you noticed areas in the periodic table where certain sublevels are filling??
Check it out on the next slide:

91. The 4 Blocks of the Periodic Table

92. The Aufbau Principle
So, what block is always filling on the left side of the periodic table??
The s block!!
What period is it??
The 4th!!
Therefore, 4s will begin filling before we fill 3d!!!

93. So is Potassium?
1s2 2s2 2p6 3s2 3p6 3d1
No!!!
1s2 2s2 2p6 3s2 3p6 4s1

94. The Electrons of the 4rd Energy Level for Potassium and Calcium
s = ___ p = ___ ___ ___
d = ___ ___ ___ ___ ___

95. The 4 Quantum Numbers for the 20th Electron of Calciumm s
-1/2

96. The “D” Block Electrons
The next electron for Scandium will now start to fill the “D” block.
Please note that the energy level for the d sublevel is not 4. We have not filled 3d yet.
Therefore, the “D” block will always be one energy level behind the current energy level.

97. Remember the Shape of the “d” Orbitals
d for "Double Peanut/Petal": complex shape occurring at energy levels 3 and above
How many orbitals (orientations) does “d” have? 5

98. So for Scandium to Zinc
Following Hund’s Rule, we will put one electron in each of the 3d orbitals before we begin to double up the electrons in each orbital.
Remember that the “d” block is always one energy level behind.

99. The Electrons of the 3rd Energy Level for Scandium to Zinc
s = ___ p = ___ ___ ___
d = ___ ___ ___ ___ ___

100. The 4 Quantum Numbers for the Circled Electron of Zinc3 l 2 m 1 s
+1/2

101. Gallium to Krypton
So, what block is always filling on the right side of the periodic table??
The p block!!
What period is it??
Back to the 4th!!
Therefore, 4p will begin filling after we fill 3d!!!

103. The Electrons of the 4rd Energy Level for Gallium to Krypton
s = ___ p = ___ ___ ___
d = ___ ___ ___ ___ ___

104. The 4 Quantum Numbers for the Circled Electron of Krypton1 m -1 s
-1/2

105. Rubidium and Strontium
So, what block is always filling on the left side of the periodic table??
The s block!!
What period is it??
5th!!
Remember, the 4th energy level has 4 sublevels, s, p, d, and f. Because of the Aufbau Principle, d and f will fill later.

106. Rubidium and Strontium
Let’s do the electron configuration for these two elements
1s2 2s2 2p6 3s2 3p6 4s2
3d10
4p6
5s1 or
5s2

107. How About Yttrium to Cadmium?
1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2
4d1-10

108. Indium to Xenon?
1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10
5p1-6

109. Cesium and Barium? 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6 6s1-2
Now do the 4 quantum numbers for 55th electron of Barium.

110. The 4 Quantum Numbers for the Circled Electron (55th) of Barium6 l m s
+1/2

111. The “F” Block Elements
Now we come to a confusing part of the periodic table.
Note that element #57, Lanthanum, is in the “d” block but the next element #58, Cerium, drops down to the “f” block.

112. The Periodic Table

113. The “F” Block Elements
Also note that according to the Aufbau Principle, after 6s should fill 4f and then 5d.

115. The “F” Block Elements
Recent discoveries suggest that Lanthanum is not the first element of the 4f block as previously thought, but really is the first element of the 5d block.
From there we will move to the 4f block.

116. Lanthanum? 4f1 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6 6s2 5d1
Then Cerium is
4f1

117. The Rest of the 4f Block #58 Praseodymium to #71 Lutetium
1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6 6s2
5d1
4f1-14

118. The Electrons of the 4f Sublevel
6s = ___ 6p = ___ ___ ___
5d = ___ ___ ___ ___ ___
4f = ___ ___ ___ ___ ___ ___ ___

119. The 4 Quantum Numbers for the Circled Electron (67th) of Lutetium3 m -1 s
-1/2

120. Now Back to the “D” Block Elements
As we follow the numbers on the Periodic Table, you will see that element #72, Hafnium, is back in the “d” block.
Therefore, Hafnium’s configuration would be:
1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6 6s2
5d1 4f14
5d2
Right??
Wrong!!

121. Now Back to the “D” Block Elements
Why? Count the total electrons…
73 not 72
Why? Because 5d2 includes 5d1
I’ve counted 5d1 twice!!
Therefore, I must do this
1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6 6s2
5d1 4f14 5d2

122. The Rest of the “D” Block Elements
Tantalum to Mercury
1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6 6s2
5d1 4f14 5d3-10

123. Now to the 6p Block Elements
Thallium to Radon
1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6 6s2
5d1 4f14 5d10
6p1-6

124. What’s Next 7s1-2 #87 - #88, Francium and Radium
1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6 6s2
5d1 4f14 5d10 6p1-6
7s1-2

125. Now We Run into the Crazy Area
#89, Actinium
1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6 6s2
5d1 4f14 5d10 6p1-6 7s2
6d1
#90 - #103, Thorium to Lawrencium
5d1 4f14 5d10 6p1-6 7s2 6d1
5f1-14

126. Finally, We Finish Up in the D Block
#104 - #112, Rutherfordium to Copernicium
Don’t forget to cross out the 6d1 electron when you come back to the “d” block
1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6 6s2
5d1 4f14 5d10 6p1-6 7s2 6d1 5f14
6d2-10

127. Quantum Numbers Let’s see if you can:
List and define the 4 principles that are part of quantum numbers.
List and define each of the 4 quantum numbers.
Give the quantum number for every electron of every atom on the periodic table.

128. Your Turn
Let’s see if you can do the last 4 orbital filling diagrams and the 4 quantum numbers for the last electron of #112, Copernicium
1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6 6s2
5d1 4f14 5d10 6p1-6 7s2 6d1 5f14 6d10

129. The Electrons of the 4 Configurations for Copernicium
7s = ___ 6p = ___ ___ ___
6d = ___ ___ ___ ___ ___
5f = ___ ___ ___ ___ ___ ___ ___

130. The 4 Quantum Numbers for the Circled Electron (112th) of Copernicium6 l 2 m s
-1/2

131. Heisenberg Uncertainty Principle
It is impossible to determine both the position and the momentum of an electron at the same time.

132. Aufbau Principle
An electron occupies the lowest energy level available.

133. Pauli Exclusion Principle
No two electrons in the same atom can have the same set of four quantum numbers.
In other words, no two electrons can be in the same place at the same time.

134. Hund’s Rule
Orbitals of equal energy are each occupied by ONE electron before any orbital is occupied by a SECOND electron
All electrons in a single occupied orbital must have the same spin.

135. Principal Quantum Number
Symbol = n
Represents the main energy level of the electron
Range = 1- 7
Ex. = 3s2
Principal Quantum number = 3

136. Angular Momentum Quantum Number
Symbol = l (small letter L)
Represents the shape of the orbital (also called sublevel)
Range = 0 – n-1 (whole number)
Shapes:
0 = s (sphere) 1 = p (petal)
2 = d (double petal) 3 = f (flower)
Ex. = 3s2
AM Quantum number = 0

137. Magnetic Quantum Number
Symbol = m
Represents the orientation of the orbital around the nucleus
Each line holds 2 electrons
m = -l to +l; Therefore: s = 0, p = 3, d = 5…
___ = s
___ ___ ___ = p

138. Magnetic Quantum Number (cont.)
___ ___ ___ ___ ___ = d
___ ___ ___ ___ ___ ___ ___ = f
Ex. = 3s2
Magnetic Quantum number = 0

139. Spin Quantum Number 2 Spin States Clockwise spin = +1/2 (upward arrow)
Counterclockwise spin = -1/2 (downward
arrow)
A single orbital can hold two electrons, but they must have opposite spins
Ex. = 3s2
Spin Quantum number = -1/2

140. Congratulations!!!!
You can now do the complete electron configurations, orbital notations and give 4 quantum numbers (addresses) for every electron of every element on the periodic table!!!

141. GRADING SCALE A = upright and taking air B = eyes notable open
C = responding to the environment
D = comatose
F = decomposed
141