1. Chapter Three Quantum Theory & the Structure of the Atom

2. Objectives/Goals for Today
Discuss logistics of graded assignments
Quiz over Chapter 2
Chapter three notes
Section Section 3.6
Section Section 3.7
Section Section 3.8
Section Section 3.9
Section Section 3.10

3. Section 3.1 Energy & Types of Energy

4. Energy Types of Energy: Kinetic-Energy due to motion
Thermal
Potential-Energy due to position/arrangement
Gravitational
Chemical
Electrostatic
Energy is measured in Joules (J); N*m; kg*m/s2

5. Section 3.2 The Nature of Light

6. A slight history of the atom
Last time in Chemistry…
Atoms had protons, neutrons, & electrons
Protons and neutrons in dense core called nucleus
Electrons orbit nucleus (provide most of volume)
The atom was assumed to look a little bit like a microscopic solar system

7. A Traditional View of the Atom

8. Newton, we have a problem…
Classical descriptions:
Dalton: atoms are hard particles, all atoms of the same element are the same
Energy is continuous
Planetary model of atom
Newtonian laws (macroscopic) were not working for atomic behavior (microscopic)

9. Some Observations… New view of atomic behavior
Blackbody Radiation—Max Planck: heat solids to red or white heat, matter did not emit energy continuously; in whole-number multiples of certain quantities
Matter absorbs or emits energies in packets - quanta

10. Some More Observations:
The Photoelectric Effect—Albert Einstein: used Planck’s theory to observe metals reacting to different colors of light –electrons are ejected from the surface of certain metals exposed to light at a certain minimum frequency
Blue light (n = 6.7 x 1014 Hz) causes Na to emit electrons, red light (n = 4.0 x 1014 Hz) does not
Energy of electrons dependent solely on frequency, not light intensity

11. What’s Going on Inside the Atom?
Scientists began studying the structure and composition of individual atoms.
They used substances’ interactions with light to explain the structure of atoms and develop a model to explain how atoms affected properties of light.
In order to understand interactions, we must understand behavior of light.

12. c = ln (Know these!) Light (m, nm); n (nu) = frequency (1/s, s-1, Hz)
Light is typically described as traveling in waves (similar to water); All electromagnetic (EM) waves (including visible light) are made of two components: electric and magnetic
ALL EM waves travel at the speed of light, c (2.998 x 108)
c = ln (Know these!)
c = speed of light; l (lambda) = wavelength
(m, nm); n (nu) = frequency (1/s, s-1, Hz)

13. Light and the EM Spectrum
EM waves

14. EM Spectrum
Different colors of light correspond to different wavelengths in the visible portion of the EM spectrum. Two wavelengths (l) are shown below. Determine the frequency (n) for each wave.
Blue light Red light
1 nm = 1 x 10-9 m OR 1 x 109 nm = 1 m

15. Double Slit Experiment
From the many experiments about light, light exhibits wave and particle properties
Double Slit Experiment

16. Section 3.3 Quantum Theory

17. From Classical to Quantum Theory
Quantum has come to mean small; originated from Planck’s observation of quantized energy
New set of “rules” had to be used for the subatomic world

18. Wave-Particle Duality
Based on photoelectric effect, light acts as a wave but also exists as a stream of particles called photons
Energy of photons is proportional to frequency, inversely proportional to wavelength
h = x J•s
J = kg • m2 / s2

19. Calculation Practice c = ln;E = hn
1) Which has a higher frequency: light from a red stoplight with a wavelength of 750 nm or a yellow light with a wavelength of 600 nm?
2) What is the wavelength of a radio station’s waves transmitting at a frequency of MHz (megahertz)? (FM radio waves range from 30 – 300 MHz.)
3) Red lights at traffic stops have wavelengths of about 650 nm. What is the frequency (in Hz) of this light?
4) Calculate the energy (in Joules) of a photon with a wavelength of 5.00 x 104 nm (infrared region).
Answers: yellow, m, 4.62 x 1014 Hz, 3.98 x J

20. Beginning of Quantum Theory
Quantum Theory Video

21. Section 3.4 Bohr’s Theory of the Hydrogen Atom

22. The Problem…
As electrons orbit, they radiate energy (due to acceleration)
If electrons radiate energy, they must eventually start spiraling towards nucleus
Electron would eventually hit the nucleus where the proton is and the atom would annihilate itself
This doesn’t happen…whew!

23. The Solution…
Neils Bohr proposed the idea that electrons orbit the nucleus in FIXED orbits

24. Bohr’s Model of the Atom
Electrons travel in discrete, quantized circular orbits; like going up or down stairs.
Each orbit has a specific energy associated with it, labeled as n = 1, 2, etc.
Ground state is the lowest energy level for an atom (n = 1).

25. Electrons Jumping Electrons CANNOT exist in BETWEEN orbits
If an electron is to “jump” orbits (move away from the nucleus), it needs to ABSORB energy in just the right quantity
If an electron is to “drop” orbits (move closer to the nucleus), it will RELEASE energy in the form of electromagnetic radiation
Sometimes visible light, sometimes not

26. Bohr’s Model of the Atom

27. Bohr Model
The Hydrogen Atom

28. Transitions between Energy Levels

29. Visible Light
White light we see consists of all colors in the visible spectrum. Use a prism (or CD) to break them up.
Light given off by atoms doesn’t necessarily corre spond to all visible colors.

30. Emission Spectra Hydrogen  Each element gives off unique spectrum
Tubes
Each element has its own individual emission spectrum. This allowed scientists to identify elements in different minerals.

31. Emission Spectra of Elements
Emission Spectra of Elements
Figure 7.8

32. Section 3.5 Wave Properties of Matter

33. Another Problem… Bohr stated that electrons move in FIXED orbits.
But why???

34. Wavelike Properties of Matter
de Broglie: If light can behave like a wave and a particle, then matter (i.e., electrons) can behave like a wave
If an electron behaves like a standing wave, then it can only have specific wavelengths
Can calculate wavelength for matter if we know its velocity (use v instead of c):
l = h / m v (This is the de Broglie equation.)
h = Planck’s constant, m = mass (electron’s have constant mass: 9.11x10-31 kg), v = velocity (speed)

35. Waves of Electrons

36. Group Quiz #1
1) The energy of a photon is 5.87 x J. What is the frequency of the photon?
2) What is the wavelength of an electron that travels at 34.7 m/s and has a mass of 9.11 x kg?
3) A kg baseball is thrown at a velocity of 42.5 m/s. Calculate the wavelength of the baseball. How does the baseball’s wavelength compare to the electron from the example above?

37. Group Quiz #2
4) Calculate the energy of a photon that has a wavelength of 35.6 nm (in the x-ray region). (Hint: Watch units!!!)

38. Section 3.6 Quantum Mechanics

39. Heisenberg Uncertainty Principle
If electrons have wave-like properties and particle-like, then we can’t know both its position and velocity (momentum) at the same time
In order to determine the position of an electron, we hit it with a photon of light, but this will change its position and velocity.

40. Quantum Mechanical Model
The Bohr model worked well for hydrogen, but failed for elements with more than one proton and one electron.
Quantum Mechanics was developed (by Schrödinger in the 1920’s) to describe the motion of subatomic particles
Did not attempt to describe exact position of particles; used mathematical equations to describe the probability of finding the particles
The probability density (map of likely locations) is the “electron cloud”

41. Atomic Orbitals (NOT ORBITS)
The region of highest probability for finding an electron is an “electron cloud”. This region of high probability is also called an atomic orbital. Each orbital holds at most 2 electrons. 41

42. Section 3.7 Quantum Numbers

43. Quantum Numbers
There are 4 quantum number that help describe the orbitals for electrons
We use these numbers to describe where electrons are most likely to be found for an atom. Can also use the periodic table!!! 43

44. Four Quantum “Numbers”l ml ms

45. The Principal Quantum Number
The Principal Quantum Number, n
describes distance of the electron from the nucleus; called shells
n = 1, 2, 3, etc; larger number is farther from nucleus
n corresponds to a row in the periodic table

46. The Next Quantum Number
The Angular Momentum Quantum Number, l
In the periodic table are different groups of orbitals with different shapes.
These groups of orbitals are called subshells and labeled s (0), p (1), d (2), and f (3).
s subshells are spherical (first two columns)
p subshells are dumb-bell shaped (last six columns)
d subshells are intersecting dumb-bells (transition metals)
f subshells are lanthanides/actinides 46

47. The Last Two Quantum Numbers
The Magnetic Quantum Number, ml
describes the orientation of the orbital with respect to x, y, and z axes
s, p, and d orbitals have different shapes and therefore different orientations
The Spin Quantum Number, ms
describes the spin of an electron in an orbital (shown as up and down arrows in orbital diagrams)

48. Section 3.8 Atomic Orbitals

49. Shapes of Orbitals
s orbitals are spherical; white rings are nodes (regions where an electron won’t be found)
1 s orbital in a subshell 49

50. Shapes of Orbitals
2px orbital
2py orbital
2pz orbital
p orbitals are dumb-bells (2 lobes); node between lobes
3 p orbitals in a subshell 50

51. Shapes of Orbitals
d orbitals: intersecting dumb-bells (4 lobes); nodes between lobes
5 d orbitals in a subshell 51

52. Orbitals
Orbitals of Scandium

53. Shells and Subshells The first shell (row) has 1 subshell (s)
s  only 1 orbital
An s subshell can hold at most 2 electrons
The 2nd shell (row) has 2 subshells (s and p)
p  set of 3 orbitals
A p subshell can hold at most 6 electrons, 2 per orbital
The 3rd shell (row) has 3 subshells (s, p, and d)
d  set of 5 orbitals
A d subshell can hold at most ? electrons
The 4th shell (row) has 4 subshells (s, p, d, and f)
f  set of 7 orbitals
What is the maximum number of electrons allowed in the f subshell? 53

54. Section 3.9 & 3.10 Electron Configurations

55. Electron Configurations
Arrangement of subshells in the Periodic Table 55

56. Things that make you go hmmm….
What is the maximum number of:
electrons allowed in the 2px orbital?
subshells allowed in the 4th shell?
electrons allowed in the 3d subshell?
electrons allowed in the 4d subshell?
electrons allowed in the 3p subshell?
electrons allowed in the 3rd shell?

57. Energies of Orbitals
In hydrogen, all shells are equivalent in energy.

58. Energies of Orbitals
In many-electron models, the energy levels depend on the shell and subshell.

59. Aufbau Principle
Aufbau principle: start with the nucleus and empty orbitals, then “build” up the electron configuration using orbitals of increasing energy. 59

60. Electron Configurations
Arrangement of subshells in the Periodic Table 60

61. Electron Configurations
Arrangement of subshells in the Periodic Table 61

62. Electron Configurations
Arrangement of subshells in the Periodic Table 62

63. Electron Configurations
Arrangement of subshells in the Periodic Table 63

64. Electron Configurations
Arrangement of subshells in the Periodic Table 64

65. Writing Electron Configurations
Write electron configurations for the following atoms. H He Li Be B N O Ne Na Al S Ar K Sc Ti Zn Br

66. Electron Configurations

67. Valence Electrons Electrons in the outermost shell.
1s2 2s2 2p6
1s2 2s2 2p6 3s2 3p5
Identify the number of valence electrons (v. e.) in the following configurations:
1s2 2s2 2p6 3s2
1s2 2s2 2p33s2 1s2 2s2 67

68. Shorthand Notation
Rather than writing out complete electron configurations, we can use the previously filled shell (noble gas) and show the valence electrons (v. e.):
P: 1s2 2s2 2p6 3s2 3p3  [Ne] 3s2 3p3 (5 v. e.)
Write the shorthand notation for: Ca Cl Sr Fe

69. Electron Configuration
Some exceptions to the Aufbau order…
What are the expected electron configurations for Cr and Cu?
Filled and half-filled d subshells seem to be especially stable.
Cr: 1s2 2s2 2p6 3s2 3p6 4s1 3d5
Also true for Mo and W
Cu: 1s2 2s2 2p6 3s2 3p6 4s1 3d10
Also true for Ag and Au 69

70. Hund’s Rule
If two or more orbitals (i.e., a p orbital) with the same energy are available, one electron goes into each orbital until they have to pair up.
Fighting siblings
For example, an atom with 2 p electrons: 1 electron will go into the first (px) orbital, the next electron will go into the second (py) orbital.

71. Pauli Exclusion Principle
Pauli Exclusion Principle: no two electrons can have the same values of all 4 quantum numbers
Describes what happens when electrons share an orbital.
Only two electrons can occupy a single orbital and they must have opposite spin (i.e., the 4th quantum number). The first electron is designated as positive spin (up arrow), the second electron in that orbital has negative spin (down arrow). 71

72. Orbital Diagrams
Orbital diagrams are pictorial representations of electron configurations. 72

73. Group Quiz #3
Write electron configurations for the following elements (long-hand notation).
Indicate the number of v.e. for each element.
potassium
sulfur
carbon
magnesium
lithium