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Ch.6 - Electronic Structure of Atoms
All textbooksBrown 14th EditionCh.6 - Electronic Structure of AtomsProblem 16
Chapter 6, Problem 16

Determine which of the following statements are false and correct them. Determine which of the following statements are false and correct them. (a) The frequency of radiation increases as the wavelength increases. (b) Electromagnetic radiation travels through a vacuum at a constant speed, regardless of wavelength. (c) Infrared light has higher frequencies than visible light. (d) The glow from a fireplace, the energy within a microwave oven, and a foghorn blast are all forms of electromagnetic radiation.

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Step 1: Analyze statement (a): 'The frequency of radiation increases as the wavelength increases.' Use the relationship between frequency (\(f\)) and wavelength (\(\lambda\)) given by the equation \(c = f \cdot \lambda\), where \(c\) is the speed of light. Determine if the statement is true or false.
Step 2: Analyze statement (b): 'Electromagnetic radiation travels through a vacuum at a constant speed, regardless of wavelength.' Recall that the speed of light in a vacuum is constant (approximately \(3.00 \times 10^8\) m/s) for all electromagnetic waves. Determine if the statement is true or false.
Step 3: Analyze statement (c): 'Infrared light has higher frequencies than visible light.' Compare the typical frequency ranges of infrared and visible light. Infrared light has longer wavelengths than visible light, which affects its frequency. Determine if the statement is true or false.
Step 4: Analyze statement (d): 'The glow from a fireplace, the energy within a microwave oven, and a foghorn blast are all forms of electromagnetic radiation.' Consider the nature of each example: the glow from a fireplace (visible light), energy in a microwave oven (microwave radiation), and a foghorn blast (sound wave). Determine if the statement is true or false.
Step 5: Correct any false statements identified in the previous steps by providing the accurate scientific explanation or fact.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Relationship Between Wavelength and Frequency

The frequency of electromagnetic radiation is inversely related to its wavelength, as described by the equation c = λν, where c is the speed of light, λ is the wavelength, and ν is the frequency. This means that as the wavelength increases, the frequency decreases. Therefore, the statement that the frequency increases as the wavelength increases is false.
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Speed of Electromagnetic Radiation

Electromagnetic radiation travels through a vacuum at a constant speed of approximately 3.00 x 10^8 meters per second, regardless of its wavelength or frequency. This principle is fundamental to understanding how different types of electromagnetic waves, such as radio waves and gamma rays, propagate through space. Thus, the statement about the speed being dependent on wavelength is incorrect.
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Electromagnetic Spectrum

The electromagnetic spectrum encompasses all types of electromagnetic radiation, arranged by frequency and wavelength. Infrared light has lower frequencies than visible light, which means it occupies a different region of the spectrum. Therefore, the assertion that infrared light has higher frequencies than visible light is false, as visible light has higher frequencies than infrared.
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Related Practice
Textbook Question

Label each of the following statements as true or false. For those that are false, correct the statement. (a) Visible light is a form of electromagnetic radiation.

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Textbook Question

Label each of the following statements as true or false. For those that are false, correct the statement. (b) Ultraviolet light has longer wavelengths than visible light.

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Textbook Question

Label each of the following statements as true or false. For those that are false, correct the statement. (c) X rays travel faster than microwaves.

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Textbook Question

Arrange the following kinds of electromagnetic radiation in order of increasing wavelength: infrared, green light, red light, radio waves, X rays, ultraviolet light.

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Textbook Question

(a) What is the frequency of radiation that has a wavelength of 10 µm, about the size of a bacterium?

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