## Mastering Physics Solutions: The Electromagnetic Spectrum

The Electromagnetic Spectrum

Part A = They have different wavelengths, They have different frequencies, They propagate at different speeds through nonvacuum media depending on both their frequency and the material in which they travel.
Part B = All these technologies use radio waves, including low-frequency microwaves, Microwave ovens emit in the same frequency band as some wireless Internet devices, he radiation emitted by wireless Internet devices has the shortest wavelength of all the technologies listed above, All these technologies emit waves with a wavelength in the range 0.10 to 10.0 m.
Part C = The earth absorbs visible light and emits radiation with a longer wavelength, The earth absorbs visible light and emits radiation with a lower frequency
Part D = 320 nm

Solutions Below:

Electromagnetic radiation is more common than you think. Radio and TV stations emit radio waves when they broadcast their programs; microwaves cook your food in a microwave oven; dentists use X rays to check your teeth. Even though they have different names and different applications, these types of radiation are really all the same thing: electromagnetic (EM) waves, that is, energy that travels in the form of oscillating electric and magnetic fields.

Consider the following:

• radio waves emitted by a weather radar system to detect raindrops and ice crystals in the atmosphere to study weather patterns;
• microwaves used in communication satellite transmissions;
• infrared waves that are perceived as heat when you turn on a burner on an electric stove;
• the multicolor light in a rainbow;
• the ultraviolet solar radiation that reaches the surface of the earth and causes unprotected skin to burn; and
• X rays used in medicine for diagnostic imaging.

Part A

Which of the following statements correctly describe the various forms of EM radiation listed
above?

• They have different wavelengths.
• They have different frequencies.
• They propagate at different speeds through a vacuum depending on their frequency.
• They propagate at different speeds through nonvacuum media depending on both their frequency and the material in which they travel.
• They require different media to propagate.

They have different wavelengths, They have different frequencies, They propagate at different speeds through nonvacuum media depending on both their frequency and the material in which they travel.

Part B

The frequency and wavelength of EM waves can vary over a wide range of values. Scientists refer to the full range of frequencies that EM radiation can have as the electromagnetic spectrum. Electromagnetic waves are used extensively in modern technology. Many devices are built to emit and/or receive EM waves at a very specific frequency, or within a narrow band of frequencies. Here are some examples followed by their frequencies of operation:

• garage door openers: 40.0 MHz,
• standard cordless phones: 40.0 to 50.0 MHz,
• baby monitors: 49.0 MHz,
• FM radio stations: 88.0 to 108 MHz,
• cell phones: 800 to 900 MHz,
• Global Positioning System: 1227 to 1575 MHz,
• microwave ovens: 2450 MHz,
• wireless Internet technology: 2.4 to 2.6 GHz.

Which of the following statements correctly describe the various applications listed above?
Check all that apply.

• All these technologies use radio waves, including low-frequency microwaves.
• All these technologies use radio waves, including high-frequency microwaves.
• All these technologies use a combination of infrared waves and high-frequency microwaves.
• Microwave ovens emit in the same frequency band as some wireless Internet devices.
• The radiation emitted by wireless Internet devices has the shortest wavelength of all the technologies listed above.
• All these technologies emit waves with a wavelength in the range 0.10 to 10.0 m.
• All the technologies emit waves with a wavelength in the range 0.01 to 10.0 km.

All these technologies use radio waves, including low-frequency microwaves, Microwave ovens emit in the same frequency band as some wireless Internet devices, he radiation emitted by wireless Internet devices has the shortest wavelength of all the technologies listed above, All these technologies emit waves with a wavelength in the range 0.10 to 10.0 m.

Part C

Despite their extensive applications in communication systems, radio waves are not the only form of EM waves present in our atmosphere. Another form of EM radiation plays an even more important role in our life (and the life of our planet): sunlight.

The sun emits over a wide range of frequencies; however, the fraction of its radiation that reaches the earth’s surface is mostly in the visible spectrum. (Note that about 35% of the radiation coming from the sun is absorbed directly by the atmosphere before even reaching the earth’s surface.) The earth, then, absorbs this radiation and reemits it as infrared waves.

Based on this information, which of the following statements is correct?

• The earth absorbs visible light and emits radiation with a shorter wavelength.
• The earth absorbs visible light and emits radiation with a longer wavelength.
• The earth absorbs visible light and emits radiation with a lower frequency.
• The earth absorbs visible light and emits radiation with a higher frequency.

The earth absorbs visible light and emits radiation with a longer wavelength, The earth absorbs visible light and emits radiation with a lower frequency

Part D

A large fraction of the ultraviolet (UV) radiation coming from the sun is absorbed by the atmosphere. The main UV absorber in our atmosphere is ozone, O3. In particular, ozone absorbs radiation with frequencies around 9.38 * 10^14 Hz. What is the wavelength of the radiation absorbed by ozone?

C = λf
3.00 * 10^8 = λ * (9.38 * 10^14)
λ = 3.20 * 10^-7

λ = 320 nm

320 nm

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