1. Chapter 6
Wavelength

2. Light
The study of light led to the development of the quantum mechanical model.
Light is a kind of electromagnetic radiation.
In Wave Model, Light is considered to consist of electromagnetic waves that travel in a speed of x 108 m/s
Electromagnetic radiation includes many kinds of waves
All move at 3.00 x 108 m/s ( c)

3. ER
Electromagnetic Radiation – forms of energy that exhibits wavelight behavior as it travels thru space
Examples of Electromagnetic Radiation:
Radio Wvaes
Microwaves
Infrared
Visible Light
Ultraviolet
X-Rays
Gamma Rays
ER has measurable wave properties of wavelength and frequency

7. Parts of a wave
Crest
Wavelength
Amplitude
Orgin
Trough

8. Parts of Wave Orgin - the base line of the energy.
Crest - high point on a wave
Trough - Low point on a wave
Amplitude - distance from origin to crest
Wavelength - distance from crest to crest
Wavelength - is abbreviated l Greek letter lambda.

9. Frequency
The number of waves that pass a given point per second.
Units are cycles/sec or hertz (hz)
Abbreviated n the Greek letter nu
c = ln

10. Frequency and wavelength
Are inversely related
As one goes up the other goes down.
Different frequencies of light is different colors of light.
There is a wide variety of frequencies
The whole range is called a spectrum

11. c = ln c= speed of light l= Wavelength
Frequency and Wavelength are mathematically related, they are inversely related
The relationship is shown by the following equation:
c = ln
c= speed of light
l= Wavelength

12. Long Wavelength =
Low Energy
Low Frequency
Short Wavelength
High Energy
High Frequency

13. Low energy
High energy
Radiowaves
Microwaves
Infrared .
Ultra-violet
X-Rays
GammaRays
Low Frequency
High Frequency
Long Wavelength
Short Wavelength
Visible Light

14. Calculating Light
What is the wavelength if light with a frequency of 5.89 x 105 Hz?
What is the frequency of blue light with a wavelength of 484 nm?

15. H.W. Questions List 5 examples of E.R.
What is the speed of all forms of E.R. in a vacuum
Relate Frequency and Wavelength
The speed of light is 3.00 x 108 m/s and the frequency is x 1012 Hz. Calculate the Wavelength of E.R.
Determine the frequency of light w/ a wavelength of x 10-7 cm.

16. How color tells us about atoms
Atomic Spectrum
How color tells us about atoms

17. Spectrum
Spectrum- Range of wavelengths of E.R., wavelengths of visible light are separated when a beam of white light passes thru a prism
Example of Spectrum
Rainbow (also a phenomenon)
Each droplet of water acts as a prism to produce a spectrum
Each color blends into the next color.

18. Colors of the Spectrum Colors of the Spectrum:
Red (Longest Wavelength & Lowest Frequency)
Orange
Yellow
Green
Blue
Indigo
Violet (Shortest Wavelength & Highest Frequency)
These colors are known as the visible part of the spectrum

19. Prism
White light is made up of all the colors of the visible spectrum.
Passing it through a prism separates it.

20. Diffraction
When light passes through, or reflects off, a series of thinly spaced line, it creates a rainbow effect
because the waves interfere with each other.

21. A wave moves toward a slit.

22. Comes out as a curve

23. with two holes

24. Two Curves
with two holes

25. Two Curves
with two holes
Interfere with each other

26. Two Curves
with two holes
Interfere with each other
crests add up

27. Several waves

28. Several waves
Several Curves

29. Several waves
Several waves
Several Curves
Interference Pattern

30. Spectroscopic analysis of the visible spectrum…
…produces all of the colors in a continuous spectrum

31. If the light is not white
By heating a gas with electricity we can get it to give off colors.
Passing this light through a prism does something different.
More on that Later

32. Quantum Concept
Laws of Physics state no limits on how much or how little energy can be gained or lost.
Classic physics assumed atoms and molecules could emit any arbitrary amount of radiant energy.
Does not explain the Emission Spectrum of Atoms

33. Max Plank Tried to explain why the body changed colors as it heated.
He could only explain the change if assumed energy of the body changes in small discrete units (brick by brick).
Plank showed mathematically that the amount of radiant energy, absorbed or emitted by a body is proportional to the frequency of radiation

34. Plank’s Quantum Concept
Plank went against classic physics
Stated: atoms and molecules could emit energy only is discrete quantities, like small packages or bundles
Quantum- smallest quantity of energy that can be emitted in the form of E.R.
The energy of a single quantum is given by E = hν

35. Planck’s Quantum Theory Cont.
According to theory, energy is always emitted in multiples of hν.
Example: 2hv, 3hv, ect…..
Never in 1.67hv and so on
Could not explain why energies are fixed but explained the emission of solids over the entire range or wavelengths.

36. Energy and frequency E = h x n E is the energy of the photon
n is the frequency
h is Planck’s constant
h = x Joules sec.
joule is the metric unit of Energy

37. Examples
What is the wavelength of blue light with a frequency of 8.3 x 1015 hz?
What is the frequency of red light with a wavelength of 4.2 x 10-5 m?
What is the energy of a photon of each of the above?

38. Solving for photons Calculate the energy of:
A) photon with a wavelength 5.00 x 104 nm (infrared region)
B) photon with a wavelength of 5.00 x 102 nm (X ray region)

39. Einstein and Photoelectric Effect
5 years later Einstein used Planck’s theory to derive the Photoelectric Effect
Photoelectric Effect- a phenomenon in which electrons are ejected from the surface of certain metals exposed to light of at least a certain minimum frequency
Threshold Frequency

40. Photoelectric Effect
Number of electrons ejected was proportional to the intensity (brightness) of the light, but the energies of the electrons were not.
Below the threshold frequency no electrons were ejected no matter how intense the light.
Could not be explained by the wave theory of light.

41. Photoelectric cont. Einstein proposed:
That a beam of light is really a stream of particles.
Particles of light are now called Photons.
Used Planck’s equation to determine:
Electrons are held in a metal surface by attractive forces, and removing them from the metal requires light of a sufficiently high frequency ( which corresponds to sufficiently high energy) to break them free.

42. Shining a beam of light onto a metal surface can be though as shooting a beam of particles/photons at the metal atoms.
Frequency of photons = binding energy, then light will have just enough energy to knock them free
What if the frequency is higher?

43. Photoelectric cont.
If frequency is stronger they will acquire some K.E. and be knocked loose.
KE = hv – BE
Shows more energetic the photon, greater the K.E. of the ejected electron.

44. Figure: 06-07a, b
Title:
The photoelectric effect.
Caption:
When photons of sufficiently high energy strike a metal surface, electrons are emitted from the metal, as in (a). The photoelectric effect is the basis of the photocell shown in (b). The emitted electrons are drawn toward the positive terminal. As a result, current flows in the circuit. Photocells are used in photographic light meters as well as in numerous other electronic devices.

45. The electron is a particle! The electron is an energy wave!
Wave-Particle Duality
JJ 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!

46. Light is a Particle Energy is quantized. Light is energy
Light must be quantized
These smallest pieces of light are called photons.
Energy and frequency are directly related.

47. Energy Change
The size of an emitted or absorbed Quantum depends on the size of the energy change.
Ex.
Small energy change involves emission or absorption of low frequency radiation.
Large energy change involves emission or absorption of high frequency radiation.

48. The Math in Chapter 12
Only 2 equations
c = ln
E = hn
Plug and chug.

49. An explanation of Atomic Spectra

50. Atomic Spectrum Each element gives off its own characteristic colors.
Can be used to identify the atom.
How we know what stars are made of.

51. Atomic Emission Spectrum
Atomic Emission Spectrum- it passes light emitted by an element thru a prism
Atoms first absorb energy and then lose energy as they emit light
Each line in the emission spectrum corresponds to one exact frequency of light being given off or emitted by an atom.
The light emitted by an electron moving from a higher to lower energy level has a frequency directly proportional to the energy change of the electron
Therefore each line corresponds to one exact amount of energy being emitted.
Emission Spectrum of each element is unique to that element.
The emission spectrum is obtained by an instrument called Emission Spectrograph

52. These are called discontinuous spectra
Or line spectra
unique to each element.
These are emission spectra
The light is emitted given off.

53. Figure: 06-11b
Title:
Atomic emission.
Caption:
Different gases emit light of different characteristic colors upon excitation by an electrical discharge. Neon is in this tube.

54. Figure: 06-11a
Title:
Atomic emission.
Caption:
Different gases emit light of different characteristic colors upon excitation by an electrical discharge. Hydrogen is in this tube.

55. Where the electron starts
When we write electron configurations we are writing the lowest energy.
The energy level and electron starts from is called its ground state.
If the energy levels are quantized, it takes Quantum Energy (E = hn) to raise an electron from ground state to excited state.
Same amount of energy is emitted as a photon when the electron drops from the excited state to the ground state.
Only electrons in transition from higher to lower energy levels lose energy and emit light.

56. Electron transitions involve jumps of definite amounts of energy.
This produces bands of light with definite wavelenghts

57. Emission Spectrum of Hydrogen
Transition Wavelength l (nm)
n = ¥ to n = n = 7 to n = n = 6 to n = n = 5 to n =
n = 4 to n = n = 3 to n =

59. Changing the energy
Let’s look at a hydrogen atom

60. Changing the energy
Heat or electricity or light can move the electron up energy levels

61. Changing the energy
As the electron falls back to ground state it gives the energy back as light

62. Changing the energy May fall down in steps
Each with a different energy

63. { { {

64. Ultraviolet Visible Infrared
Further they fall, more energy, higher frequency.
This is simplified
the orbitals also have different energies inside energy levels
All the electrons can move around.

65. We are worried about the change
When the electron moves from one energy level to another.
DE = Efinal - Einitial
DE = x J Z2 (1/ nf2 - 1/ ni2)
Rydberg’s constant and it allowed the calculation of the wavelengths of all the spectral lines of hydrogen.

66. Calculating Energy Problems
What is the energy of the photon emitted when the electron in a hydrogen atom drops from the energy level n=5 to following:
A) n=2
B) n=3

67. More Energy Problems
How much energy must a hydrogen atom absorb to raise its electron from the energy level n=1 to the following:
A) n=2
B) n=4

68. Positive or Negative
When raising an electron the amount of energy is always positive. Why?
When an electron drops the amount of energy is always negative. Why?

69. Calculating Wavelength of Photon
First determine ∆E
Then plug into:
λ= c h / ∆E
What is the wavelength (in nm) of a photon emitted during a transition from ni = 6 to nf = 4

70. What is light Light is a particle - it comes in chunks.
Light is a wave- we can measure its wave length and it behaves as a wave
If we combine E=mc2 , c=ln, E = 1/2 mv2 and E = hn
We can get l = h/mv
The wavelength of a particle.

71. Matter is a Wave Does not apply to large objects
Things bigger that an atom
A baseball has a wavelength of about m when moving 30 m/s
An electron at the same speed has a wavelength of 10-3 cm
Big enough to measure.

72. Calculating Wavelength of a Particle
1) Calculate the wavelength of a particle in:
A) The fastest serve in tennis is about 140 miles per hour, or 63 m/s. Calculate the wavelength associated with a x kg tennis ball traveling at this speed. What color would be produced?

73. B) Calculate the wavelength associated with an electron (9
B) Calculate the wavelength associated with an electron ( x kg) moving at 63 m/s
Which color would be produced?

74. 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

75. The physics of the very small
Quantum mechanics explains how the very small behaves.
Classic physics is what you get when you add up the effects of millions of packages.
Quantum mechanics is based on probability because

76. More obvious with the very small
To measure where a electron is, we use light.
But the light moves the electron
And hitting the electron changes the frequency of the light.

77. After Before Photon changes wavelength Photon
Electron Changes velocity
Moving Electron

78. “One cannot simultaneously determine both the position and momentum of an electron.”

79. Heisenberg Uncertainty Principle
It is impossible to know exactly the position and velocity (momentum) of a particle.
The better we know one, the less we know the other.
The act of measuring changes the properties.
More precisely the velocity is measured, less precise is the position (vice versa).