1. Frequency and Wavelength
Objectives:
To explain the wave nature of light.
To state the relationship of wavelength, frequency, and energy of light.

2. Waves on the Ocean

3. Waves on the Ocean
Zumdahl, Zumdahl, DeCoste, World of Chemistry 2002, page 324

4. Wavelength of a Wave l
Zumdahl, Zumdahl, DeCoste, World of Chemistry 2002, page 324

5. Wavelength of a Wave l
Zumdahl, Zumdahl, DeCoste, World of Chemistry 2002, page 324

6. Visible Spectrum of Light
Waves 1/33,000” long
Waves 1/70,000” long
Red
Orange
Yellow
Green
Blue
Indigo
Violet
PRISM
Slit
Ray of
White Light
All light is bent passing through a prism; violet is bent most and red least. A beam of sunlight produces a continuous band of rainbow colors showing that light is a mixture of colors.

8. Visible Spectrum of Light
All light is bent passing through a prism; violet is bent most and red least. A beam of sunlight produces a continuous band of rainbow colors showing that light is a mixture of colors.

9. Unplucked string 1 half-wavelengths 2 half-wavelengths
de Broglie also investigated why only certain orbits were allowed in Bohr’s model of the hydrogen atom.
• de Broglie hypothesized that the electron behaves like a standing wave, a wave that does not travel in space.
• Standing waves are used in music: the lowest-energy standing wave is the fundamental vibration, and higher-energy vibrations are overtones and have successively more nodes, points where the amplitude of the wave is zero.
• de Broglie stated that Bohr’s allowed orbits could be understood if the electron behaved like a standing circular wave. The standing wave could exist only if the circumference of the circle was an integral multiple of the wavelength causing constructive interference. Otherwise, the wave would be out of phase with itself on successive orbits and would cancel out, causing destructive interference.
2 half-wavelengths
3 half-wavelengths

10. n = 4 orbit
n = 6 orbit
Only certain wavelengths will `fit' into an orbit. If the wavelength is longer or shorter, then the ends do not connect. Thus, deBroglie explains the Bohr atom in that on certain orbits can exist to match the natural wavelength of the electron. If an electron is in some sense a wave, then in order to fit into an orbit around a nucleus, the size of the orbit must correspond to a whole number of wavelengths.

11. Waves Wavelength () - length of one complete wave
Frequency () - # of waves that pass a point during a certain time period
hertz (Hz) = 1/s
Amplitude (A) - distance from the origin to the trough or crest f
Wave — a periodic oscillation that transmits energy through space
Characteristic properties of waves
1. Waves are periodic.
– They repeat regularly in both space and time.
2. Wavelength
– Distance between two corresponding points in a wave
– Symbolized by 
– Described by any appropriate unit of distance
3. Frequency of a wave
– Number of oscillations that pass a particular point in a given period of time
– Represented by the symbol 
– Units are oscillations per second or 1/s = s-1, which is called the hertz (Hz)
4. Amplitude, or vertical height, of a wave
– Defined as half the peak-to-trough height
– As the amplitude of a wave with a given frequency increases, so does its energy
– Two waves can have the same amplitude but different wavelengths
5. Speed
– Distance traveled by a wave per unit of time
– Represented by the symbol 
– Measured in meters per second (m/s)
– Speed of a wave is equal to the product of its wavelength and frequency
(wavelength) (frequency) = speed
 = 
(meters) (waves) = meters
(waves) (second) second
Courtesy Christy Johannesson

12.  A A  Waves crest greater amplitude origin (intensity) trough
greater frequency
(color)
Courtesy Christy Johannesson

13. The Electromagnetic Spectrum
HIGH
ENERGY
Decreasing wavelength
LOW
ENERGY
Increasing frequency
Increasing photon energy
AM radio
Short wave
radio
Television channels FM
Radar
Microwave
Radio Waves V i s b l e L g h t
Gamma Rays UV
Rays
“The Electromagnetic Spectrum”
Description: This slide depicts the electromagnetic spectrum from gamma rays through radio waves.
Basic Concepts
·         All forms of electromagnetic radiation are not identical
·         All forms of electromagnetic radiation travel at the same speed in a vacuum (the speed of light, c = 3.00 x 108 m/sec).
·         Wavelength and frequency are inversely proportional for a wave traveling at a constant speed.
·         Energy and frequency are directly proportional for electromagnetic waves traveling at the speed of light.
Teaching Suggestions
Use this transparency to review the relationship of visible light to other types of radiation. Explain that all of the rays and waves shown are types of electromagnetic radiation. Point out that they differ essentially from each other only in energy level, wavelength, and frequency. Try the analogy of an ocean wave to help students understand electromagnetic waves. Question 6 can be used to assess the students understanding of wave velocity, wavelength, and frequency.
Questions:
List the ways in which visible light is different from the other types of radiation shown in the diagram.
List the ways in which all of the types of radiation shown in the diagram are similar.
You are told that sound waves cannot travel in a vacuum. Are sound waves a types of electromagnetic radiation? Explain your logic.
Radio waves can go around an obstruction if the obstruction is smaller than the radio wave’s wavelength. What would you expect to happen if visible light were beamed at a thin wire 2 x 10-5 centimeter thick? Explain your answer.
For electromagnetic waves traveling at the speed of light, the wavelength is inversely proportional to frequency, as expressed by the equation c = fl, where c = speed of light in vacuum (3.00 x 108 meters/second), f = frequency, and l= wavelength. Using this equation, calculate the frequency of a 3-meter radio wave traveling at the speed of light. Compare your answer with the diagram.
Suppose that at a particular beach the ocean waves are traveling at a speed of 2 meters/second. If you know that the distance between waves is 10 meters, can you calculate how often they hit the shore? Explain your answer.
For electromagnetic waves traveling at the speed of light, the energy of a single photon is expressed by the equation E = hf, where E = energy, f = frequency, and h = Planck’s constant, 6.6 x joules/hertz.
Which has more energy, a photon of visible light or a photon of radar, if both traveling at the speed of light?
Do you think you can calculate the energy of an ocean wave using this energy equation? Explain your answer.
infrared
X- Rays
R O Y G B I V
Red Orange Yellow Green Blue Indigo Violet

14. Frequency 1 second Frequency 4 cycles/second = 4 hertz
The energy of light is closely related to its color. High energy light appears purple, low energy light appears red, and intermediate energies of light have intermediate colors such as blue, green, yellow, and orange.
Higher frequency waves have more energy and are of a shorter wavelength.
In visible light, red light has the longest wavelength (lowest frequency) and blue/violet light has the shortest wavelength (highest frequency).
12 cycles/second = 12 hertz
36 cycles/second = 36 hertz
O’Connor, Davis, MacNab, McClellan, CHEMISTRY Experiments and Principles 1982, page 166

15. AM & FM Waves Carrier frequency Sound pattern
Amplitude Modulated carrier
Frequency Modulated carrier

16. AM & FM Waves Carrier frequency Sound pattern
AM - FM Radio
Amplitude Modulated carrier
Frequency Modulated carrier

17. Copyright © 2007 Pearson Benjamin Cummings. All rights reserved.

18. Electromagnetic Spectrum
Visible spectrum
HIGH
ENERGY
Violet
Blue
Green
Yellow
Orange
Red
LOW
ENERGY
400 nm
500 nm
600 nm
700 nm
White
Light
g rays
X-rays
Ultraviolet
Infrared
Microwave
Radio waves
Water waves transmit energy through space by the periodic oscillation of matter.
• Energy that is transmitted, or radiated, through space in the form of periodic oscillations of an electric and a magnetic field is called electromagnetic radiation.
Electromagnetic radiation
– Consists of two perpendicular waves, one electric and one magnetic, propagates at the speed of light, abbreviated c, and has a value of x 108 m/s
– Is radiant energy that includes radio waves, microwaves, visible light, X -rays, and gamma rays
– Various kinds of electromagnetic radiation all have the same speed (c) but differ in wavelength and frequency
– Frequency of electromagnetic radiation is inversely proportional to the wavelength
c =  or  = c/
– Energy of electromagnetic radiation is directly proportional to its frequency (E  ) and inversely proportional to its wavelength (E  1/)
Radar TV FM
Short
Wave
Long
Wave
10-2nm
10-1nm
100nm
101nm
102nm
103nm
10-3cm
10-2cm
10-1cm
100cm
101cm
1cm
101m
102m
103m
104m
Wavelength, l
1019Hz
1018Hz
1017Hz
1016Hz
1015Hz
1014Hz
1013Hz
1012Hz
1011Hz
1010Hz
109Hz
100 MHz
10 MHz
1 MHz
100 KHz
Frequency, n
Electromagnetic spectrum
Davis, Frey, Sarquis, Sarquis, Modern Chemistry 2006, page 98

19. Common wavelength units for electromagnetic radiation
Unit Symbol Wavelength, (m) Type of Radiation
Picometer pm Gamma ray
Ångstrom Å X-ray
Nanometer nm X-ray
Micrometer mm Infrared
Millimeter mm Infrared
Centimeter cm Microwave
Meter m Radio
Copyright © 2007 Pearson Benjamin Cummings. All rights reserved.

20. Waves Low frequency High frequency long wavelength l
Amplitude
Low
frequency
short wavelength l
Amplitude
High
frequency

21. Waves Low frequency High frequency long wavelength l
Amplitude
Low
frequency
60 photons
162 photons
low energy
short wavelength l
Amplitude
Einstein‘s photons of light were individual packets of energy that had many characteristics of particles.
• Einstein’s hypothesis that energy is concentrated in localized bundles was in sharp contrast to the classical notion that energy is spread out uniformly in a wave.
High
frequency
high energy

22. Red and Blue Light Photons
- particle of light that carries a quantum of energy
Zumdahl, Zumdahl, DeCoste, World of Chemistry 2002, page 325

23. Electromagnetic Radiation
Light as a wave
Einstein‘s photons of light were individual packets of energy that had many characteristics of particles.
• Einstein’s hypothesis that energy is concentrated in localized bundles was in sharp contrast to the classical notion that energy is spread out uniformly in a wave.
Light as a stream of energy
(packets of photons)
Zumdahl, Zumdahl, DeCoste, World of Chemistry 2002, page 325

24. Wavelength and Frequency
“nu” “lambda”
c = n l f
c = speed of light (3 x 108 m/s)
= frequency (s-1)
l = wavelength (m)
E = h n
E = energy (Joules or J)
h = Planck’s constant (6.6 x10-34 J/s)
= frequency (s-1)

25. Electromagnetic Spectrum
Frequency & wavelength are inversely proportional
c = 
c: speed of light (3.00  108 m/s)
: wavelength (m, nm, etc.)
: frequency (Hz)
Courtesy Christy Johannesson

26. Electromagnetic Spectrum
EX: Find the frequency of a photon with a wavelength of 434 nm.
GIVEN:
f = ?
 = 434 nm
= 4.34  10-7 m
c = 3.00  108 m/s
WORK:
1 m
1 x 109 nm
f = 3.00  108 m/s
4.34  10-7 m
f = 6.91  1014 Hz
Courtesy Christy Johannesson

27. Quantum Theory Max Planck (1900)
Observed - emission of light from hot objects
Concluded - energy is emitted in small, specific amounts (quanta)
Quantum - minimum amount of energy change
Max Planck
In 1900, Max Planck explained the “ultraviolet catastrophe” by assuming that the energy of electromagnetic waves is quantized rather than continuous—energy could be gained or lost only in integral multiples of some smallest unit of energy, a quantum.
• Classical physics had assumed that energy increased or decreased in a smooth, continuous manner.
• Planck postulated that the energy of a particular quantum of radiant energy could be described by the equation E = h, where h is the Planck’s constant and is equal to x joule•second (J•s).
• As the frequency of electromagnetic radiation increases, the magnitude of the associated quantum of radiant energy increases.
Courtesy Christy Johannesson

28. Bohr Model of Hydrogen Nucleus Possible electron orbits e e
Zumdahl, Zumdahl, DeCoste, World of Chemistry 2002, page 331

29. Continuous vs. Quantized Energy
A B
continuous quantized
Zumdahl, Zumdahl, DeCoste, World of Chemistry 2002, page 330

30. Continuous vs. Quantized
A B
Zumdahl, Zumdahl, DeCoste, World of Chemistry 2002, page 330

31. Quantum Theory vs. Planck (1900) Classical Theory Quantum Theory
Courtesy Christy Johannesson

32. Quantum Theory Albert Einstein (1905) Observed - photoelectric effect
Planck’s quantization hypothesis was used to explain a second phenomenon that conflicted with classical physics.
• When certain metals are exposed to light, electrons are ejected from their surface.
– Classical physics predicted that the number of electrons emitted and their kinetic energy should depend only on the intensity of light, not on its frequency.
– However, each metal was found to have a characteristic threshold frequency of light — below that frequency, no electrons are emitted regardless of the light’s intensity, above the threshold frequency, the number of electrons emitted was found to be proportional to the intensity of light and their kinetic energy proportional to its frequency, a phenomenon called the photoelectric effect.
“The free, unhampered exchange of ideas and scientific conclusions is necessary for the sound development of science, as it is in all spheres of cultural life. ...
We must not conceal from ourselves that no improvement in the present depressing situation is possible without a severe struggle; for the handful of those who are really
determined to do something is minute in comparison with the mass of the lukewarm and the misguided. ... Humanity is going to need a substantially new way of thinking if it is to survive!" (Albert Einstein)
Courtesy Christy Johannesson

33. Wavelength and Frequency
“nu” “lambda”
c = n l f
c = speed of light (3 x 108 m/s)
= frequency (s-1)
l = wavelength (m)
E = h n
E = energy (Joules or J)
h = Planck’s constant (6.6 x10-34 J/s)
= frequency (s-1)