Textbook Question
The speed of sound in dry air at is 343 m/s, and the middle C on a piano keyboard has a frequency of 261 Hz. a. What is the wavelength of the sound wave corresponding to a middle C?
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Ch.6 - Electronic Structure of Atoms
Brown15th EditionChemistry: The Central ScienceISBN: 9780137542970
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Table of contents
- Ch.1 - Introduction: Matter, Energy, and Measurement111
- Ch.2 - Atoms, Molecules, and Ions166
- Ch.3 - Chemical Reactions and Reaction Stoichiometry138
- Ch.4 - Reactions in Aqueous Solution127
- Ch.5 - Thermochemistry104
- Ch.6 - Electronic Structure of Atoms109
- Ch.7 - Periodic Properties of the Elements107
- Ch.8 - Basic Concepts of Chemical Bonding102
- Ch.9 - Molecular Geometry and Bonding Theories120
- Ch.10 - Gases122
- Ch.11 - Liquids and Intermolecular Forces79
- Ch.12 - Solids and Modern Materials102
- Ch.13 - Properties of Solutions99
- Ch.14 - Chemical Kinetics153
- Ch.15 - Chemical Equilibrium83
- Ch.16 - Acid-Base Equilibria109
- Ch.17 - Additional Aspects of Aqueous Equilibria117
- Ch.18 - Chemistry of the Environment60
- Ch.19 - Chemical Thermodynamics109
- Ch.20 - Electrochemistry113
- Ch.21 - Nuclear Chemistry79
- Ch.22 - Chemistry of the Nonmetals52
- Ch.23 - Transition Metals and Coordination Chemistry57
- Ch.24 - The Chemistry of Life: Organic and Biological Chemistry7
Brown15th EditionChemistry: The Central ScienceISBN: 9780137542970Not the one you use?Change textbook
Chapter 6, Problem 2a
A popular kitchen appliance produces electromagnetic radiation with a frequency of 2450 MHz. With reference to Figure 6.4, answer the following: (a) Estimate the wavelength of this radiation.
Verified step by step guidance1
Convert the frequency from MHz to Hz for easier calculation. Remember that 1 MHz equals 1,000,000 Hz, so multiply the given frequency by 1,000,000.
Use the speed of light equation, which is c = \(\lambda\) \(\nu\), where c is the speed of light (approximately 3.00 \(\times\) 10^8 m/s), \(\lambda\) is the wavelength, and \(\nu\) is the frequency. Rearrange the equation to solve for the wavelength (\(\lambda\)).
Substitute the frequency value in Hz and the speed of light into the rearranged equation \(\lambda\) = \(\frac{c}{\nu}\).
Calculate the wavelength by dividing the speed of light by the frequency. Ensure your units are consistent (meters for wavelength and Hz for frequency).
Express the final wavelength in meters, which is the standard unit for wavelength in the context of electromagnetic radiation.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Electromagnetic Radiation
Electromagnetic radiation encompasses a range of waves, including radio waves, microwaves, and visible light, characterized by their frequency and wavelength. The frequency, measured in hertz (Hz), indicates how many cycles of the wave occur per second, while the wavelength, measured in meters, is the distance between successive peaks of the wave. Understanding this relationship is crucial for estimating wavelength from frequency.
Wavelength and Frequency Relationship
The relationship between wavelength (λ) and frequency (f) of electromagnetic radiation is described by the equation c = λf, where c is the speed of light (approximately 3.00 x 10^8 m/s). This equation allows us to calculate the wavelength when the frequency is known, and vice versa. In this case, knowing the frequency of 2450 MHz enables us to determine the corresponding wavelength.
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Frequency-Wavelength Relationship
Unit Conversion
In scientific calculations, unit conversion is often necessary to ensure consistency in measurements. For instance, the frequency given in megahertz (MHz) must be converted to hertz (Hz) for use in the wavelength formula. Since 1 MHz equals 10^6 Hz, converting 2450 MHz to Hz is essential for accurately calculating the wavelength of the electromagnetic radiation produced by the kitchen appliance.
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Related Practice
Textbook Question
The speed of sound in dry air at is 343 m/s, and the middle C on a piano keyboard has a frequency of 261 Hz. b. What would be the frequency of electromagnetic radiation with the same wavelength?
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Textbook Question
Stars do not all have the same temperature. The color of light emitted by stars is characteristic of the light emitted by hot objects. Telescopic photos of three stars are shown below: (i) the Sun, which is classified as a yellow star, (ii) Rigel, in the constellation Orion, which is classified as a blue-white star, and (iii) Betelgeuse, also in Orion, which is classified as a red star. (a) Place these three stars in order of increasing temperature. (i) sun (ii) Rigel (iii) Betelguese
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Textbook Question
A popular kitchen appliance produces electromagnetic radiation with a frequency of 2450 MHz. With reference to Figure 6.4, answer the following: (d) Which of the following is the appliance likely to be? (i) A toaster oven, (ii) A microwave oven, or (iii) An electric hotplate.
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Textbook Question
A popular kitchen appliance produces electromagnetic radiation with a frequency of 2450 MHz. With reference to Figure 6.4, answer the following: (c) If the radiation is not visible, do photons of this radiation have more or less energy than photons of visible light?
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