To understand how the electromagnetic spectrum can be expressed in terms of wavelength, speed, and energy.

Electromagnetic radiation is energy radiated in the form of a wave, resulting from the motion of electric charges and the magnetic fields they produce. All types of electromagnetic radiation travel in the form of waves, at a speed of about 300,000 kilometers per second (the speed of light). The lengths of these waves determine the characteristics of each form of electromagnetic radiation. The distance from one wave crest to the next is called the wavelength. Radio waves have the longest wavelengths while gamma rays have the shortest wavelengths.

The various types of electromagnetic radiation can be arranged in a continuum, with the longest wavelengths at one end and the shortest at the other. This continuum is called the electromagnetic spectrum.

The electromagnetic spectrum can also be expressed in terms of frequency. Frequency is a property of a wave that describes how many wave patterns or cycles pass by in a period of time. Frequency is most often measured in Hertz (Hz), where a wave with a frequency of 1 Hz will pass by at 1 cycle per second. Short wave electromagnetic radiation, such as gamma rays have high frequency. Long wave electromagnetic radiation, such as radio waves have low frequency.

The frequency of electromagnetic radiation is equal to the ratio of the speed of light to the wavelength.

ν = ^{c}/_{Λ}

Where:

ν = frequency in Hertz (Hz) = (^{1}/_{sec})

c = speed of light (3.0 x 10^{17} ^{nm}/_{sec})

Λ = wavelength

Students create plots of the electromagnetic spectrum to get a sense of what part of the spectrum is visible to us and to understand the proportion of the other types of electromagnetic radiation in the spectrum.

sheets of paper, ruler, masking tape

- Have students tape four sheets of blank paper together to make one sheet 112 cm long.
- Instruct them to draw a vertical line 2 cm from the left edge of the paper and then draw two horizontal lines from that line, one about 8 cm from the top of the page, and one about 10 cm below the first line.
- Provide students the following table:

Frequency Range Table EMR Bands Frequency Range

(hertz)Log _{10}

Frequency

Range (hertz)10 ^{14}ConversionsRadio and Microwave Near 0 to 3.0 x 10 ^{12}0 to 12.47 -Infrared 3.0 x 10 ^{12}to 4.6 x 10^{14}12.47 to 14.66 -Visible 4.6 x 10 ^{14}to 7.5 x 10^{14}14.66 to 14.88 4.6 x 10 ^{14}to 7.5 x 10^{14}Red4.6 x 10 ^{14}to 5.1 x 10^{14}14.66 to 14.71 4.6 x 10 ^{14}to 5.1 x 10^{14}Orange5.1 x 10 ^{14}to 5.6 x 10^{14}14.71 to 14.75 5.1 x 10 ^{14}to 5.6 x 10^{14}Yellow5.6 x 10 ^{14}to 6.1 X 10^{14}14.75 to 14.79 5.6 x 10 ^{14}to 6.1 X 10^{14}Green6.1 x 10 ^{14}to 6.5 x 10^{14}14.79 to 14.81 6.1 x 10 ^{14}to 6.5 x 10^{14}Blue6.5 x 10 ^{14}to 7.0 x 10^{14}14.81 to 14.85 6.5 x 10 ^{14}to 7.0 10^{14}Violet7.0 x 10 ^{14}to 7.5 x 10^{14}14.85 to 14.88 7.0 x 10 ^{14}to 7.5 x 10^{14}Ultraviolet 7.5 to 10 ^{14}to 6.0 10^{14}14.88 to 16.78 -X-Ray 6.0 x 10 ^{16}to 1.0 10^{20}16.78 to 20 -Gamma RAy 1.0 x 10 ^{20}to . . .20 to . . . - - Tell students that they will be plotting the Log
_{10}frequency ranges of the electromagnetic spectrum on the top line. In order to do this, they must first mark off twenty-four 1-cm intervals starting at the left vertical line. They should label the marks from 1 to 24 (each number represents increasing powers of 10, from 10^{1}to 10^{24}). - Tell students to use the information from the table to divide their scales into the individual bands of electromagnetic radiation (for the visible band, they should use the entire band, not the individual colors).
- Tell students that they will be plotting the ranges of the electromagnetic spectrum on a linear scale on the lower horizontal line. In order to do this, they must first convert the range of frequencies that each band of radiation covers for the logarithmic scale. This will allow them to compare the width of the bands of radiation relative to each other. They should convert the frequency numbers for all bands (except visible) to 1014 and record them in the table. You may want to provide them the following example:

Example: 10^{17}is 1000 times greater than 10^{14}, so 2.5×10^{17}= 2500×10^{14}.

*Radio and Microwaves: 0 to 0.03x10*^{14}

Infrared: 0.03x10^{14}to 4.6x10^{14}

Ultraviolet: 7.5x10^{14}to 600 x10^{14}

X-Ray: 600x10^{14}to 1,000,000x10^{14}

Gamma Ray: 1,000,000x10^{14}to...

- Tell students that, on the lower horizontal line, they should mark off ten 10-cm intervals from the vertical line. Next, starting with the first interval, they should label each mark with a whole number times 10
^{14}, from 1 x 10^{14}to 10 x 10^{14}. Also, have them label this line "Frequency in hertz." - Instruct students to plot some of the 10
^{14}frequencies they calculated on the bottom line. They should plot the individual colors of the visible spectrum and color them. - Have students look at the range of ultraviolet radiation (which is electromagnetic radiation at wavelengths shorter than the violet end of visible light) and answer the following:
- How high do the ultraviolet frequencies extend (in hertz)?

*The ultraviolet band extends from 7.5x10*^{14}Hz to 6.0x10^{16}Hz. - Using the same linear scale that you constructed in Step 7 (10 cm = 1x10
^{14}Hz), calculate the width (in centimeters) of the ultraviolet electromagnetic radiation band.

*On the logarithmic scale, the UV is approximately 1.9 cm long. The ultraviolet (UV) band spans 5.925x10*^{16}Hz (7.5x10^{14}to 6x10^{16}). This equates to 592.5x10^{14}. Using the linear scale 10cm=1x10^{14}cm, this band would be 5925 cm long! - Using this same scale, what do you think you would need to measure the distance from the beginning of the ultraviolet band of the electromagnetic radiation to the end of the ultraviolet band of the electromagnetic radiation?

*Answers will vary, but should be something in excess of about 60 meters long.* - Using your calculations above and the linear scale you created, how much wider is the ultraviolet band than the entire visible band? How does this compare to the relative widths of these two bands on the log scale?

*The visible band on this linear scale was 29 cm long. From the calculation above, the UV band is 204.3 times as wide as the visible band. On the logarithmic scale, the UV band was 8.6 times as wide as the visible band (the UV band was 1.9 cm wide and the visible band was 0.22 cm wide).*

- How high do the ultraviolet frequencies extend (in hertz)?
- Have students look at the X-ray band of radiation and answer the following:
- Using the same linear scale (10 cm = 1x10
^{14}Hz), calculate the distance from the end of the ultraviolet band to the end of the X-ray band. Obtain a map from the Internet or use a local or state highway map to plot the distance.

*The X-ray band spans about 9.994x10*^{14}Hz. Converting so this number is expressed in terms of 10^{14}gives 999,400 (i.e., 999,400x10^{14}). Using the same 10 cm=1x10^{14}Hz linear scale yields a total length of the X-ray band of 9,994,000 cm, or 99.94 km. -
Based on your results for the width of the X-ray band, what would be your estimate for the width of the gamma-ray band of radiation? What would you need to measure the distance?

*Answers will vary. Students are not given an upper limit to the gamma-ray frequency range, so they should recognize that the value is quite large.*