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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Ch.6 - Electronic Structure of Atoms
Chapter 6, Problem 19b
(b) What is the wavelength of radiation that has a frequency of 5.50 × 1014 s-1?
Verified step by step guidance1
Start by recalling the relationship between wavelength and frequency, which is given by the equation: , where is the speed of light, is the wavelength, and is the frequency.
The speed of light is a constant, approximately . Use this value in the equation.
Rearrange the equation to solve for wavelength : .
Substitute the given frequency into the equation.
Calculate the wavelength using the rearranged formula. Ensure your units are consistent, and remember that the result will be in meters.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Wave-Particle Duality
Wave-particle duality is a fundamental concept in quantum mechanics that describes how every particle or quantum entity exhibits both wave and particle properties. This duality is crucial for understanding electromagnetic radiation, which can be characterized by its wavelength and frequency.
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Subatomic Particles
Relationship Between Wavelength and Frequency
The relationship between wavelength and frequency is described by the equation c = λν, where c is the speed of light (approximately 3.00 × 10^8 m/s), λ is the wavelength, and ν is the frequency. This equation allows us to calculate one property if the other is known, highlighting the inverse relationship between wavelength and frequency.
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Units of Measurement
Understanding the units of measurement is essential in chemistry. Frequency is measured in hertz (s^-1), while wavelength is typically measured in meters (m). Converting between these units is necessary when applying the wave equation to solve problems related to electromagnetic radiation.
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Related Practice
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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Textbook Question
(c) Would the radiations in part (a) or part (b) be detected by an X-ray detector?
Textbook Question
(d) What distance does electromagnetic radiation travel in 0.38 ps?
Textbook Question
A laser pointer used in a lecture hall emits light at 650 nm. What is the frequency of this radiation?