Ch.6 - Electronic Structure of Atoms

Brown - Chemistry: The Central Science 14th Edition

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Brown 14th Edition

Ch.6 - Electronic Structure of Atoms

Problem 19a

Chapter 6, Problem 19a

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

Verified step by step guidance

Step 1: Understand that the frequency (ν) of a wave is inversely proportional to its wavelength (λ). This relationship is expressed by the equation c = λν, where c is the speed of light (3.00 x 10^8 m/s).

Step 2: Convert the wavelength from micrometers (µm) to meters (m) since the speed of light is given in meters per second. There are 1 x 10^-6 meters in a micrometer, so multiply the given wavelength by this conversion factor.

Step 3: Rearrange the equation c = λν to solve for frequency: ν = c / λ.

Step 4: Substitute the values for the speed of light (c) and the wavelength (λ) into the equation to calculate the frequency.

Step 5: Ensure your answer is in the correct units. The frequency should be in Hertz (Hz), which is equivalent to 1/s or s^-1.

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Key Concepts

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

Electromagnetic Spectrum

The electromagnetic spectrum encompasses all types of electromagnetic radiation, which vary in wavelength and frequency. It includes radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays. Understanding where a specific wavelength, like 10 µm, falls within this spectrum helps in identifying its properties and applications.

Wavelength and Frequency Relationship

Wavelength and frequency are inversely related properties of electromagnetic waves, 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, and vice versa. This relationship is crucial for calculating the frequency of radiation given its wavelength.

Units of Measurement

In chemistry and physics, it is essential to use consistent units when performing calculations. Wavelength is often measured in meters (m) or micrometers (µm), while frequency is measured in hertz (Hz). Converting units appropriately is necessary to ensure accurate calculations, especially when dealing with wavelengths in micrometers.

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Units of Radiation Measurement

Related Practice

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

(d) What distance does electromagnetic radiation travel in 0.38 ps?

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Textbook Question

(b) What is the wavelength of radiation that has a frequency of 5.50 × 10¹⁴ s^-1?

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

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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Textbook Question