Waves & Electromagnetic Spectrum

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

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

Waves Wave – a periodic oscillation that transmits energy through space Wavelength () - length of one complete wave; measured in meters (m) 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 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 www.nisd.net/communicationsarts/pages/chem

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). http://www.softwarereality.com/soapbox/images/DogEars.jpg 12 cycles/second = 12 hertz 36 cycles/second = 36 hertz O’Connor, Davis, MacNab, McClellan, CHEMISTRY Experiments and Principles 1982, page 166

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

Relationship between frequency, wavelength and energy: There is an inverse relationship between wavelength and frequency. There is a direct relationship between energy and frequency. Therefore: As wavelength increases, both the frequency and energy of the wave decrease. As wavelength decreases, both the frequency and energy of the wave increases.

The Electromagnetic Spectrum Copyright © 2007 Pearson Benjamin Cummings. All rights reserved.

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 10-33 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

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.

Warm-Up What are the units for frequency? Which color of light is associated with the highest amount of energy? Which color of light has the longest wavelength? What are the units of wavelength? What does the amplitude of the wave measure?

What is a photon? Photon: A quantum of light A discrete bundle (packet) of electromagnetic energy that interacts with matter similarly to particles

The Speed of Light Electromagnetic waves travel at a constant speed through a vacuum (space). They will slow down if traveling through a different medium. (substance) c = speed of light symbol 3.0 X 108 m/s (300,000,000 m/s) 186,282 miles/sec or 671,000,000 mph Please note: speed of sound is only 343.2 m/s or 768 mph!

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 www.nisd.net/communicationsarts/pages/chem

Examples of Calculations 1. Calculate the frequency of a wave traveling at 3.0 x108 m/s with a wavelength of 1.96 x 10-6 m.

Examples of Calculations 2. Calculate the wavelength of the yellow light emitted by a sodium lamp if the frequency of the radiation is 5.09X1014 Hz.

Calculating Energy of a Wave The energy of a photon is directly proportional to its frequency. E = h E: energy (J, joules) h: Planck’s constant (6.626  10-34 J·s) : frequency (Hz or s-1) Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

Examples of Calculations 1. What is the energy of a photon of radiation with a frequency of 7.85 X 1013 s-1?

Examples of Calculations 2. The microwaves emitted by a cell phone have a wavelength of 2.35 X10-2 m. What is the energy associated with this wavelength of radiation?