wavelength x frequency = velocity, environmental science homework help

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Table 1 liststhenames of thedifferentforms of electromagneticradiationandtheirassociatedfrequencies. Thewavelengthandenergy of radiowaveshavebeencalculatedforyou. Determinethewavelengthsandenergies of theremainingforms, as follows:

Foranywave—be it an oceanwave, a soundwave, or an electromagneticwave—thefollowingrelationshipholdstrue:

wavelength x frequency = velocity.

Electromagneticwavesalltravel at thespeed of light. Thus:

wavelength (m) x frequency (Hz) = 3.00 x 108 m/s.

To calculate wavelength, divide the speed of light by frequency.Recordyouranswers in Column 3. Theunitfortheresultingwavelengthwill be themeter (m).

Becausethewavelengths of electromagneticwavesaresosmall, theyareoftenexpressed in nanometers, ratherthanmeters. TocompleteColumn 4, multiply the wavelengths in Column 3 by 1 x 109.

Theenergies of electromagneticwaves can be calculatedbymultiplyingtheirfrequenciesby a constant, h, known as Planck'sconstant. That is,

energy = h x frequency.

Tocalculateenergy, multiply the frequency by 6.626 x 10-34 J·s.Recordyouranswers in Column 5. Theunitfortheresultingenergywill be thejoule.

Noticethatvisiblelightmakesup a verysmallportion of theelectromagneticspectrum. Table 2 listsall of thecolors of visiblelightandtheirassociatedfrequencies. Repeatsteps 1-3 tocompleteTable 2. Thefirstrow has beencompletedforyou.

ElectromagneticSpectrum

NowthatyouhavecompletedTables 1 and 2, you can create a labeleddiagram of theelectromagneticspectrum. TheElectromagneticSpectrum (thediagram at theend of thisworksheet) indicatesthefrequenciesassociatedwithdifferenttypes of waves. Complete thediagram as follows:

LabeleachblockundertheFrequencyheadingwiththewavetype (radio, visible, etc.).
Intherectanglerepresentingallthefrequencies of visiblelight, coloreachblocktheappropriatecolor.
Labeleachline in theblocksundertheWavelengthandEnergyheadingswiththevaluesyoucalculated in Tables 1 and 2.
IntheblocksundertheVelocityheadings, indicatethevelocity of electromagneticwaves. Write thisinformationvertically, since allelectromagneticwaveshavethesamevelocity.
Nexttoeach of theFrequencycolumns, draw a redarrowthatindicatesthedirection in whichfrequencyincreases.
Nexttoeach of theWavelengthcolumns, draw a bluearrowthatindicatesthedirection in whichwavelengthincreases.
Nexttoeach of theEnergycolumns, draw a greenarrowthatindicatesthedirection in whichenergyincreases.

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Name(s): Class: Date: Electromagnetic Waves Light is but one kind of wave found in the electromagnetic spectrum. The electromagnetic spectrum consists of all the different forms of radiation that result from vibrating electric and magnetic fields (which are at right angles to one another). Although each form of radiation is caused by these vibrations, varied forms of radiation occur due to different frequencies, wavelengths, and energies. In this lesson, you are going to learn what kinds of waves are found in the electromagnetic spectrum and how they differ. Procedure Table 1 lists the names of the different forms of electromagnetic radiation and their associated frequencies. The wavelength and energy of radio waves have been calculated for you. Determine the wavelengths and energies of the remaining forms, as follows: 1. For any wave—be it an ocean wave, a sound wave, or an electromagnetic wave—the following relationship holds true: 2. wavelength x frequency = velocity. 3. Electromagnetic waves all travel at the speed of light. Thus: 4. wavelength (m) x frequency (Hz) = 3.00 x 108 m/s. 5. To calculate wavelength, divide the speed of light by frequency. Record your answers in Column 3. The unit for the resulting wavelength will be the meter (m). 6. Because the wavelengths of electromagnetic waves are so small, they are often expressed in nanometers, rather than meters. To complete Column 4, multiply the wavelengths in Column 3 by 1 x 109. 7. 8. The energies of electromagnetic waves can be calculated by multiplying their frequencies by a constant, h, known as Planck's constant. That is, 9. energy = h x frequency. 10. To calculate energy, multiply the frequency by 6.626 x 10-34 J·s. Record your answers in Column 5. The unit for the resulting energy will be the joule. 11. Notice that visible light makes up a very small portion of the electromagnetic spectrum. Table 2 lists all of the colors of visible light and their associated frequencies. Repeat steps 1-3 to complete Table 2. The first row has been completed for you. Electromagnetic Spectrum Now that you have completed Tables 1 and 2, you can create a labeled diagram of the electromagnetic spectrum. The Electromagnetic Spectrum (the diagram at the end of this worksheet) indicates the frequencies associated with different types of waves. Complete the diagram as follows: Label each block under the Frequency heading with the wave type (radio, visible, etc.). In the rectangle representing all the frequencies of visible light, color each block the appropriate color. Label each line in the blocks under the Wavelength and Energy headings with the values you calculated in Tables 1 and 2. In the blocks under the Velocity headings, indicate the velocity of electromagnetic waves. Write this information vertically, since all electromagnetic waves have the same velocity. Next to each of the Frequency columns, draw a red arrow that indicates the direction in which frequency increases. Next to each of the Wavelength columns, draw a blue arrow that indicates the direction in which wavelength increases. Next to each of the Energy columns, draw a green arrow that indicates the direction in which energy increases. • • • • • • • Analysis Use the completed tables and diagram to answer the following questions. 12. Identify the type of wave in the electromagnetic spectrum that has the 13. a. highest frequency b. c. highest wavelength d. e. highest energy f. g. highest velocity h. lowest frequency i. j. k. lowest wavelength l. m. lowest energy n. 14. What color has the longest wavelength? the shortest wavelength? 15. 16. High frequency waves have (long, short) wavelengths and are (high, low) in energy. (Circle the correct answers.) 17. 18. Electromagnetic waves with long wavelengths have (high, low) frequencies and are (high, low) in energy. (Circle the correct answers.) 19. 20. High energy waves have (high, low) frequencies and (long, short) wavelengths. (Circle the correct answers.) 21. 22. Sunlight contains both infrared and ultraviolet waves. Examine the electromagnetic spectrum you created. Which type of waves would be more damaging (i.e., more likely to promote cancer) and why? 23. 24. Through this activity, you learned about the relationships among wavelength, frequency, and energy: 25. wavelength x frequency = speed of light (3.00 x 108 m/s) • • energy = h x frequency (h = 6.626 x 10-34 J·s) • • Use these two relationships to solve the following problems. Show your work and indicate the appropriate units for your answers. o. What is the wavelength of a radar signal that operates at a frequency of 1.095 x 10 10 Hz? p. q. Calculate the frequency of a microwave that has a wavelength of 0.0150 m. r. s. High-energy gamma rays are emitted by the sun. How much energy do such gamma rays possess, if they have a frequency of 1 x 1025 Hz? Table 1: Characteristics of Electromagnetic Radiation Type of Wave Radio Microwave Infrared Visible Ultraviolet X Rays Gamma Rays Frequencies (Hz) < 3 x 109 3 x 109 - 3 x 1012 3 x 1012 - 4.3 x 1014 4.3 x 1014 - 7.5 x 1014 7.5 x 1014 - 3 x 1017 3 x 1017 - 3 x 1019 > 3 x 1019 Wavelengths (m) > 0.1 Wavelengths (nm) > 1 x 108 Energies (J) < 2.0 x 10-24 Wavelengths (m) 6.98 x 10-7 - 6.25 x 10-7 Wavelengths (nm) 698 - 625 Energies (J) 2.8 x 10-19 - 3.2 x 10-19 Table 2: Characteristics of Visible Light Color Red Orange Yellow Green Blue Violet Frequencies (Hz) 4.3 x 1014 - 4.8 x 1014 4.8 x 1014 - 5.2 x 1014 5.2 x 1014 - 5.6 x 1014 5.6 x 1014 - 6.2 x 1014 6.2 x 1014 - 7.0 x 1014 7.0 x 1014 - 7.5 x 1014
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Table 1. Characteristics of Electromagnetic radiation

Type of
Wave

Frequencies
(Hz)

Wavelengths
(m)

Wavelengths
(nm)

Energies
(J)

< 3 ∗ 109

> 0.1

> 1 ∗ 108

< 2.0 ∗ 10−24

3 ∗ 109 − 3 ∗ 1012

0.1 − 10−4

1 ∗ 108 − 1 ∗ 105

2.0 ∗ 10−24 − 2.0 ∗ 10−21

3 ∗ 1012 − 4.3 ∗ 1014

10−4 − 6.98 ∗ 10−7

1 ∗ 105 − 698

2.0 ∗ 10−21 − 2.8 ∗ 10−19

4.3 ∗ 1014 − 7.5
∗ 1014

6.98 ∗ 10−7 − 4.0 ∗ 10−7

698 − 400

2.8 ∗ 10−19 − 5.0 ∗ 10−19

7.5 ∗ 1014 − 3 ∗ 1017

4.0 ∗ 10−7 − 1.0 ∗ 10−9

400 − 1

5.0 ∗ 10−19 − 2.0 ∗ 10−16

X Rays

3 ∗ 1017 − 3 ∗ 1019

1.0 ∗ 10−9 − 1.0 ∗ 10−11

1 − 0.01

2.0 ∗ 10−16 − 2 ∗ 10−14

Gamma
Rays

> 3 ∗ 1019

> 1.0 ∗ 10−11

> 0.01

> 2 ∗ 10−14

Radio
Microwave
Infrared
Visible
Ultraviolet

Table 2. Characteristics of visible light

Color

Frequencies
(Hz)

Wavelengths
(m)

Wavelengths
(nm)

Energies
(J)

Red

4.3 ∗ 1014 − 4.8 ∗ 1014

6.98 ∗ 10−7 − 6.25 ∗ 10−7

698-625

2.8 ∗ 10−19 − 3.2 ∗ 10−19

Orange

4.8 ∗ 1014 − 5.2 ∗ 1014

6.25 ∗ 10−7 − 5.77 ∗ 10−7

625-577

3.2 ∗ 10−19 − 3.4 ∗ 10−19

Yellow

5.2 ∗ 1014 − 5.6 ∗ 1014

5.77 ∗ 10−7 − 5.36 ∗ 10−7

577-536

3.4 ∗ 10−19 − 3.7 ∗ 10−19

Green

5.6 ∗ 1014 − 6.2 ∗ 1014

5.36 ∗ 10−7 − 4.84 ∗ 10−7

536-484

3.7 ∗ 10−19 − 4.1 ∗ 10−19

Blue

6.2 ∗ 1014 − 7.0 ∗ 1014

4.84 ∗ 10−7 − 4.29 ∗ 10−7

484-429

4.1 ∗ 10−1...