1. Chapter 5

2. Quantum Theory and Electron Configurations

3. Quantum-Mechanical Model of the Atom
Since the Bohr model had a very limited use, a new and very different model of the atom exists
The Quantum Mechanical Model (1926) contains:
Quantum energy levels
Dual wave/particle nature of electrons
Electron clouds
In the new model, don’t know exactly where electrons are - only know probabilities of where they could be

4. Heisenberg Uncertainty Principle
Heisenberg Uncertainty Principle = impossible to know both the velocity (or momentum) and position of an electron at the same time

5. The Quantum Mechanical Model
Chapter 5

6. Quantum Mechanical Model
Einstein (1905)
Light consists of quanta, called photons
Photoelectric Effect – Sunlight striking a sheet of metal will knock off the outermost electrons and move, causing an electric current
de Broglie (1924) = Photons both particles and waves
Davisson (1927) = Electrons both particles and waves

7. Quantum-Mechanical Model of the Atom
Orbital = region around nucleus where an electron with a given energy level will probably (90%) be found
Four kinds of orbitals
s - spherical in shape, lowest orbital for every energy level
p - dumbbell shaped, second orbital
d - complex “flower” shape, third orbital
f - very complex shape, highest orbital

8. s-orbitals All s-orbitals are spherical.
As n increases, the s-orbitals get larger.

9. p- orbitals Three p-orbitals: px, py, and pz
Lie along the x-, y- and z- axes of a Cartesian system.
Dumbbell shaped, gets larger as n increases

10. d and f - orbitals
There are five d and seven f-orbitals.

12. Quantum Mechanical Model
Principle Energy Levels (n)
Labeled from 1-7
First energy level is n=1
Contains sublevels (s, p, d and f)
Each energy level contains the number of sublevels equal to it’s value for n
If n=3, there are three sublevels

13. Quantum Mechanical Model
In each sublevel there are atomic orbitals
Atomic orbitals – describe a space where an electron is likely to be found
Type of subshell
Shape of orbitals
Number of orbitals
Orbital ‘names’ s
Spherical 1 p
Dumbbell 3
px, py, pz d
Cloverleaf (and one donut) 5 f
Multi-lobed 7

14. Quantum Mechanical Model
Each orbital can contain two electrons.
Since negative-negative repel, these electrons occupy the orbital with opposite spins.

15. Quantum Mechanical Model
The total number of orbitals of an energy level is n2.
For the third principle energy level, n=3, which means there are 9 orbitals
These orbitals are 3s, 3px, 3py, 3pz and the 5 d orbitals
Remember, we no longer think of orbitals as concentric circles, but we can say that n=4 extends farther from the nucleus than n=1.

16. Valence Electrons
Only those electrons in the highest principle energy level

17. Electron Configuration and Orbital Notation
Aufbau Principle – electrons fill lower energy orbitals first, “bottom-up”
n=1 fills before n=3
Will an electron fill the 1s or the 2s orbital first?
Energy
2px
2py
2pz 2s 1s

18. Electron Configuration &Orbital Notation
Hund’s Rule – electrons enter same energy orbitals so that each orbital has one electron before doubling up
Each of the first electrons to enter the equal energy orbitals must have the same spin
If we have 7 electrons, how will they fill in the below orbitals?
Energy
2px
2py
2pz 2s 1s

19. Electron Configuration and Orbital Notation
Pauli Exclusion Principle – an orbital can contain no more than 2 electrons. Electrons in the same orbital must have different spins.
If we have 8 electrons, how will they be arranged?
Energy
2px
2py
2pz 2s 1s

23. Apartment Analogy Atom is the building Floors are energy levels
Rooms are orbitals
Only two people per room

24. Orbital Diagrams Draw each orbital as a box.
Each electron is represented using an arrow.
Up arrows – clockwise spin
Down arrows – counter-clockwise spin
Determine the total number of electrons involved.
Start with the lowest energy level (1s) and start filling in the boxes according the rules we just learned.

25. Transition Metal Exceptions
Can move from the highest filled s orbital to create a fully filled, or half filled d or f
TRANSITION METAL EXCEPTIONS

26. Total # of electrons in an Energy Level
n=1 2 x 12 + = 2
n=2 2 x 22 + = 8
n=3 2 x 32 + = 18
n=4
n=5
n=6
n=7
Chapter 5

27. Orbitals and Energy Levels
Principal
Sublevels
Orbitals
Energy Level
n = 1 1s 1s
(one)
n = 2 2s 2p , 2s
(one) + 2p
(three)
n = 3 3s , 3p , 3d 3s
(one) + 3p
(three) + 3d
(five)
n = 4 4s , 4p , 4d , 4f 4s
(one) + 4p
(three) + 4d
(five) + 4f
(seven)
Chapter 5

28. Summary # of shapes Max electrons Starts at energy level s p d f
Chapter 5

29. Orbitals and Energy Levels4p 4d 4f
n = 4
and so on.... 3s 3p 3d
n = 3
Increasing energy 2s 2p
n = 2 1s
n = 1

30. Orbital Diagrams
Orbital diagrams are used to show placement of electrons in orbitals.
Need to follow three rules (Aufbau, Pauli, Hund’s) to complete diagrams Li Be B C N Ne Na

31. Orbital Diagram 2s 1s 3s 4s 2p 3p 4p 3d
Energy

32. Electron Configuration
Let’s determine the electron configuration for Phosphorus
Need to account for 15 electrons
Chapter 5

33. Increasing energy 7p 6d 5f 7s 6p 5d 6s 4f 5p 4d 5s 4p 3d 4s 3p 3s 2p
Chapter 5

34. Increasing energy 7p 6d 5f 7s 6p 5d 6s 4f 5p 4d 5s 4p 3d 4s 3p 3s 2p
The first to electrons go into the 1s orbital
Notice the opposite spins
only 13 more
Chapter 5

35. Increasing energy 7p 6d 5f 7s 6p 5d 6s 4f 5p 4d 5s 4p 3d 4s 3p 3s 2p
The next electrons go into the 2s orbital
only 11 more
Chapter 5

36. Increasing energy 7p 6d 5f 7s 6p 5d 6s 4f 5p 4d 5s 4p 3d 4s 3p
The next electrons go into the 2p orbital
only 5 more
Chapter 5

37. Increasing energy 7p 6d 5f 7s 6p 5d 6s 4f 5p 4d 5s 4p 3d 4s 3p
The next electrons go into the 3s orbital
only 3 more
Chapter 5

38. Increasing energy 7p 6d 5f 7s 6p 5d 6s 4f 5p 4d 5s 4p 3d 4s
The last three electrons go into the 3p orbitals.
They each go into separate shapes
3 unpaired electrons
1s22s22p63s23p3
Chapter 5

39. Writing Electron Configuration
Determine the total number of electrons.
Write the principle energy level number as a coefficient, the letter for the subshell, and an exponent to represent the number of electrons in the subshell.
He: 1s2

40. The Kernel (Noble Gas) Notation
Determine the total number of electrons
Find the previous noble gas and put its symbol in brackets
Write the configuration from that noble gas forward as usual

41. Writing electron configurations
Examples
O 1s2 2s2 2p4
Ti 1s2 2s2 2p6 3s2 3p6 3d2 4s2
Br 1s2 2s2 2p6 3s2 3p6 3d10 4s2 4p5
Core format
O [He] 2s2 2p4
Ti [Ar] 3d2 4s2
Br [Ar] 3d10 4s2 4p5
Chapter 5

43. Quantum Numbers
Each electron can be described by four numbers unique to that electron (like a fingerprint)
“n” – the principal quantum # describes the principal energy level, n=1, 2, 3…,7
“l” – describes the shape of subshell
s subshell = 0
p subshell = 1
d subshell = 2
f subshell = 3
“m” –describes the orientation , m = -l….0….+l
“s” – describes the spin, s=1/2 or -1/2

45. Quantum Numbers
Example: Look at carbon’s orbital diagram which contains 6 electrons. What are the quantum #s for the last electron to be filled?
Example: Look at Vanadium’s Kernel notation. Do the orbital diagram for only the valence electrons. What are the quantum #’s for the second to last electron to be filled?