1. Section 4.2 “The Quantum Model of the Atom”
Pre-AP Chemistry

3. Chapter 4 Vocabulary
12. Heisenberg uncertainty principle 13. Quantum theory 14. Orbital 15. Quantum number 16. Principal quantum number 17. Angular momentum quantum number 18. Magnetic quantum number 19. Spin quantum number

4. Chapter 4 Notes
E. Quantum Model F. Quantum Numbers G. Atomic Orbitals H. Energy Levels

5. Chapter 4 Preview Lesson Starter Objectives Electrons as Waves
Section 2 The Quantum Model of the Atom
Chapter 4
Preview
Lesson Starter
Objectives
Electrons as Waves
The Heisenberg Uncertainty Principle
The Schrödinger Wave Equation
Atomic Orbitals and Quantum Numbers

6. Chapter 4 Lesson Starter
Section 2 The Quantum Model of the Atom
Chapter 4
Lesson Starter
Write down your address using the format of street name, house/apartment number, and ZIP Code.
These items describe the location of your residence.
How many students have the same ZIP Code? How many live on the same street? How many have the same house number?

7. Lesson Starter, continued
Section 2 The Quantum Model of the Atom
Chapter 4
Lesson Starter, continued
In the same way that no two houses have the same address, no two electrons in an atom have the same set of four quantum numbers.
In this section, you will learn how to use the quantum-number code to describe the properties of electrons in atoms.

8. Section 2 The Quantum Model of the Atom
Chapter 4
Objectives
Discuss Louis de Broglie’s role in the development of the quantum model of the atom.
Compare and contrast the Bohr model and the quantum model of the atom.
Explain how the Heisenberg uncertainty principle and the Schrödinger wave equation led to the idea of atomic orbitals.

9. Chapter 4 Objectives, continued
Section 2 The Quantum Model of the Atom
Chapter 4
Objectives, continued
List the four quantum numbers and describe their significance.
Relate the number of sublevels corresponding to each of an atom’s main energy levels, the number of orbitals per sublevel, and the number of orbitals per main energy level.

10. Section 4.2 Quantum Model
OBJECTIVES:
Discuss Louis de Broglie’s role in the development of the quantum model of the atom

11. Section 4.2 Quantum Model OBJECTIVES:
Compare and contrast the Bohr model and the quantum model of the atom.

12. Wave-Particle Duality
J.J. Thomson won the Nobel prize for describing the electron as a particle.
His son, George Thomson won the Nobel prize for describing the wave-like nature of the electron.
The electron is a particle!
The electron is an energy wave!

13. Ernest Rutherford’s Model
Discovered dense positive piece at the center of the atom- “nucleus”
Electrons would surround and move around it, like planets around the sun
Atom is mostly empty space
It did not explain the chemical properties of the elements – a better description of the electron behavior was needed

14. The Bohr Model of the Atom
I pictured the electrons orbiting the nucleus much like planets orbiting the sun.
However, electrons are found in specific circular paths around the nucleus, and can jump from one level to another.
Niels Bohr

15. Confused? You’ve Got Company!
“No familiar conceptions can be woven around the electron; something unknown is doing we don’t know what.”
Physicist Sir Arthur Eddington
The Nature of the Physical World
1934

16. Louis de Broglie
“Given that light behaves as waves and particles, can particles of matter behave as waves?”
He referred to the wavelike behavior of particles as matter waves.
His reasoning led him to a mathematical expression for the wavelength of a moving particle

17. What is light?  = h/mv (from Louis de Broglie)
Light is a particle - it comes in chunks.
Light is a wave - we can measure its wavelength and it behaves as a wave
If we combine E=mc2 , c=, E = 1/2 mv2 and E = h, then we can get:
 = h/mv (from Louis de Broglie)
called de Broglie’s equation
Calculates the wavelength of a particle.

18. Chapter 4 Electrons as Waves
Section 2 The Quantum Model of the Atom
Chapter 4
Electrons as Waves
French scientist Louis de Broglie suggested that electrons be considered waves confined to the space around an atomic nucleus.
It followed that the electron waves could exist only at specific frequencies.
According to the relationship E = hν, these frequencies corresponded to specific energies—the quantized energies of Bohr’s orbits.

19. Electrons as Waves, continued
Section 2 The Quantum Model of the Atom
Chapter 4
Electrons as Waves, continued
Electrons, like light waves, can be bent, or diffracted.
Diffraction refers to the bending of a wave as it passes by the edge of an object or through a small opening.
Electron beams, like waves, can interfere with each other.
Interference occurs when waves overlap.

20. The Heisenberg Uncertainty Principle
Section 2 The Quantum Model of the Atom
Chapter 4
The Heisenberg Uncertainty Principle
German physicist Werner Heisenberg proposed that any attempt to locate a specific electron with a photon knocks the electron off its course.
The Heisenberg uncertainty principle states that it is impossible to determine simultaneously both the position and velocity of an electron or any other particle.

21. The Schrödinger Wave Equation
Section 2 The Quantum Model of the Atom
Chapter 4
The Schrödinger Wave Equation
In 1926, Austrian physicist Erwin Schrödinger developed an equation that treated electrons in atoms as waves.
Together with the Heisenberg uncertainty principle, the Schrödinger wave equation laid the foundation for modern quantum theory.
Quantum theory describes mathematically the wave properties of electrons and other very small particles.

22. The Schrödinger Wave Equation, continued
Section 2 The Quantum Model of the Atom
Chapter 4
The Schrödinger Wave Equation, continued
Electrons do not travel around the nucleus in neat orbits, as Bohr had postulated.
Instead, they exist in certain regions called orbitals.
An orbital is a three-dimensional region around the nucleus that indicates the probable location of an electron.

23. Chapter 4 Electron Cloud Section 2 The Quantum Model of the Atom
Click below to watch the Visual Concept.
Visual Concept

24. Section 4.2 Quantum Model OBJECTIVES:
Explain how the Heisenberg uncertainty principle and the Schrödinger wave equation led to the idea of atomic orbitals.

25. The physics of the very small
Quantum mechanics explains how very small particles behave
Quantum mechanics is an explanation for subatomic particles and atoms as waves
Classical mechanics describes the motions of bodies much larger than atoms

26. Heisenberg Uncertainty Principle
It is impossible to know exactly the location and velocity of a particle.
The better we know one, the less we know the other.
Measuring changes the properties.
True in quantum mechanics, but not classical mechanics

27. Heisenberg Uncertainty Principle
“One cannot simultaneously determine both the position and momentum of an electron.”
You can find out where the electron is, but not where it is going.
OR…
You can find out where the electron is going, but not where it is!
Werner Heisenberg

28. It is more obvious with the very small objects
To measure where a electron is, we use light.
But the light energy moves the electron
And hitting the electron changes the frequency of the light.

29. After Before Photon wavelength changes Photon Moving Electron
Electron velocity changes

30. The Quantum Model Energy is “quantized” - It comes in chunks.
A quantum 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.
In 1926, Erwin Schrodinger derived an equation that described the energy and position of the electrons in an atom

31. Schrodinger’s Wave Equation
Equation for the probability of a single electron being found along a single axis (x-axis)
Erwin Schrodinger
Erwin Schrodinger
Quantum Leap TV intro

32. The Quantum 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 (like plum pudding!)

33. The Quantum 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.

34. The Quantum Mechanical Model
e- found inside blurry “electron cloud” (area where there’s chance of finding e-)
fan blades
bicycle wheel

35. The Quantum Model
The atom is found inside a blurry “electron cloud”

36. Chapter 4 Notes E. Quantum Model 1. Louis de Broglie
e- exists as waves at specific frequencies
can be bent (diffraction) and interfere with each other (interference)
2. Werner Heisenberg
-Heisenberg Uncertainty Principle
- impossible to determine simultaneously both positon and velocity of an e-

37. Chapter 4 Notes E. Quantum Model 1. Louis de Broglie
2. Werner Heisenberg (Uncertainty Principle)
3. Erwin Schrödinger Wave Equation
developed equation to treat e- as waves
responsible for 3 of the 4 quantum numbers

38. Section 4.2 Quantum Model OBJECTIVES:
List the four quantum numbers and describe their significance.

39. Section 4.2 Quantum Model OBJECTIVES:
Relate the number of sublevels corresponding to each of an atom’s main energy levels, the number of orbitals per sublevel, and the number of orbitals per main energy level.

40. Atomic Orbitals and Quantum Numbers
Section 2 The Quantum Model of the Atom
Chapter 4
Atomic Orbitals and Quantum Numbers
Quantum numbers specify the properties of atomic orbitals and the properties of electrons in orbitals.
The principal quantum number, symbolized by n, indicates the main energy level occupied by the electron.
The angular momentum quantum number, symbolized by l, indicates the shape of the orbital.

41. Atomic Orbitals and Quantum Numbers, continued
Section 2 The Quantum Model of the Atom
Chapter 4
Atomic Orbitals and Quantum Numbers, continued
The magnetic quantum number, symbolized by m, indicates the orientation of an orbital around the nucleus.
The spin quantum number has only two possible values—(+1/2 , −1/2)—which indicate the two fundamental spin states of an electron in an orbital.

42. Quantum Numbers and Orbitals
Section 2 The Quantum Model of the Atom
Chapter 4
Quantum Numbers and Orbitals
Click below to watch the Visual Concept.
Visual Concept

43. Shapes of s, p, and d Orbitals
Section 2 The Quantum Model of the Atom
Chapter 4
Shapes of s, p, and d Orbitals

44. Electrons Accommodated in Energy Levels and Sublevels
Section 2 The Quantum Model of the Atom
Chapter 4
Electrons Accommodated in Energy Levels and Sublevels

45. Electrons Accommodated in Energy Levels and Sublevels
Section 2 The Quantum Model of the Atom
Chapter 4
Electrons Accommodated in Energy Levels and Sublevels

46. Quantum Numbers of the First 30 Atomic Orbitals
Section 2 The Quantum Model of the Atom
Chapter 4
Quantum Numbers of the First 30 Atomic Orbitals

47. Chapter 4 Notes F. 4 Quantum Numbers
Principal Quantum Number (n)- energy level
- distance from nucleus: levels 1-7
2. Angular Momentum Quantum Number (l= 0,1,2,3)
– shape: s,p,d, or f
3. Magnetic Quantum Number (m) – orientation
- x, y, or z axis
4. Spin Quantum Number (- ½, + ½) - spin
- 2 e- with opposite spin in same orbital
* First 3 Quantum numbers came from Schrödinger's equation

50. Chapter 4 Notes
G. Atomic Orbital Shapes 1. s = = 2. p = = 3. d = (4/5) = 4. f = =
spherical
1 orbital = 2 e- (s2)
dumbbell
3 orbitals = 6 e- (p6)
cloverleaf
5 orbitals = 10 e- (d10)
complicated
7 orbitals = 14 e- (f14)

51. Orbital Location on Periodic Table

52. Atomic Orbitals
Principal Quantum Number (n) = the energy level of the electron: 1, 2, 3, etc.
Within each energy level, the complex math of Schrodinger’s equation describes several shapes.
These are called atomic orbitals (coined by scientists in 1932) - regions where there is a high probability of finding an electron.
Sublevels- like theater seats arranged in sections: letters s, p, d, and f

53. Principal Quantum Number
Generally symbolized by “n”, it denotes the shell (energy level) in which the electron is located.
Maximum number of electrons that can fit in an energy level is:
2n2
How many e- in level 2? 3?

54. Notecard: Max e- in principle energy level (n)
Maximum number of electrons that can fit in an energy level is:
2n2

55. Summary 2 6 10 14 # of shapes (orbitals) Maximum electrons
Starts at energy level 2 s 1 1 6 p 3 2 10 d 5 3 7 14 4 f

56. By Energy Level First Energy Level Second Energy Level
Has only s orbital
1s2 (1 orbital)
2 electrons
Second Energy Level
Has s and p orbitals available
2 in s, 6 in p
2s22p6 (4 orbitals)
8 total electrons
s and p orbitals 1:20

57. By Energy Level Third energy level Has s, p, and d orbitals
2 in s, 6 in p, and 10 in d
3s23p63d10
18 total electrons
Fourth energy level
Has s, p, d, and f orbitals
2 in s, 6 in p, 10 in d, and 14 in f
4s24p64d104f14
32 total electrons
d orbitals 3:40

58. 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.

59. Chapter 4 Notes
H. Energy Levels 1 = 1 sublevel = 1s = 2 = 2 sublevels = 2s, 2p = 3 = 3 sublevels = 3s, 3p, 3d = 4 = 4 sublevels = 4s, 4p, 4d, 4f =
2e-
8 e-
18 e-
32 e-

60. Summary of Principal Energy Levels, Sublevels, and Orbitals
Number of sublevels
Type of sublevel
Max # of electrons
Electron configuration
n = 1 1
1s (1 orbital) 2
1s2
n = 2
2s (1 orbital
2p (3 orbitals) 8
2s2
2p6
n = 3 3
3s (1 orbital)
3p (3 orbitals)
3d (5 orbitals) 18
3s2
3p6
3d10
n = 4 4
4s (1 orbital)
4p (3 orbitals)
4d (5 orbitals)
4f (7 orbitals) 32
4s2
4p6
4d10
4f14

61. Sec 4.2 Practice Problems
1. How many sublevels are in the following principal energy levels? List the sublevels. a. n = 1 b. n = 2 c. n = 3 d. n = 4 1
1s2 2
2s2 2p6
3s2 3p6 3d10 3
4s2 4p6 4d10 4f14 4

62. Sec 4.2 Practice Problems
2. How many orbitals are in the following sublevels?
a. 1s sublevel e. 4f sublevel
b. 5s sublevel f. 7s sublevel
c. 3p sublevel g. 6d sublevel
d. 4d sublevel h. fourth principal energy level 1 7 1 1 3 5 5 16

63. Sec 4.2 Assignments
Ch 4 Vocabulary
4.2 Study Guide (1-50) handout

64. End of Section 4.2