Textbook Question
The distance from the sun to Earth is 1.496×108 km. How long does it take light to travel from the sun to Earth?
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Ch.8 - The Quantum-Mechanical Model of the Atom
Chapter 8, Problem 39b
List these types of electromagnetic radiation in order of (ii) increasing energy per photon.
a. visible light
b. radio waves
c. X-ray
d. ultraviolet radiation
Verified step by step guidance1
Understand the relationship between the energy of a photon and the frequency of electromagnetic radiation. The energy of a photon (E) is given by the equation E = h \( \nu \), where h is Planck's constant and \( \nu \) is the frequency of the radiation.
Recognize that the frequency of electromagnetic radiation is inversely proportional to its wavelength (\( \lambda \)), as given by the equation c = \( \lambda \nu \), where c is the speed of light.
Identify the general order of electromagnetic radiation types by their wavelengths, from longest to shortest: radio waves, visible light, ultraviolet radiation, and X-rays.
Using the inverse relationship between wavelength and frequency, deduce that the order of increasing frequency is the same as the order of decreasing wavelength: radio waves, visible light, ultraviolet radiation, and X-rays.
Conclude that the order of increasing energy per photon, which is directly proportional to frequency, is: radio waves, visible light, ultraviolet radiation, and X-rays.
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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, arranged by wavelength and frequency. It includes radio waves, visible light, ultraviolet radiation, X-rays, and more. Each type of radiation has distinct properties and applications, with energy inversely related to wavelength; shorter wavelengths correspond to higher energy.
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Electromagnetic Spectrum
Photon Energy
Photon energy is determined by the equation E = hν, where E is energy, h is Planck's constant, and ν (nu) is the frequency of the radiation. Higher frequency radiation, such as X-rays, has more energy per photon compared to lower frequency radiation like radio waves. Understanding this relationship is crucial for ranking types of radiation by energy.
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Order of Increasing Energy
To list types of electromagnetic radiation in order of increasing energy, one must consider their respective frequencies and wavelengths. Radio waves have the lowest energy, followed by visible light, ultraviolet radiation, and finally X-rays, which possess the highest energy. This order reflects the inverse relationship between wavelength and energy in the electromagnetic spectrum.
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Related Practice
Textbook Question
The nearest star to our sun is Proxima Centauri, at a distance of 4.3 light-years from the sun. A light-year is the distance that light travels in one year (365 days). How far away, in km, is Proxima Centauri from the sun?
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Textbook Question
List these types of electromagnetic radiation in order of (i) increasing frequency and (ii) decreasing energy per photon.
a. gamma rays
b. ultraviolet radiation
c. infrared radiation
d. microwaves
Textbook Question
Calculate the frequency of each wavelength of electromagnetic radiation: a. 632.8 nm (wavelength of red light from helium–neon laser) b. 503 nm (wavelength of maximum solar radiation) c. 0.052 nm (wavelength contained in medical X-rays)
Textbook Question
Calculate the energy of a photon of each wavelength and state what part of the electromagnetic spectrum is associated with the wavelength.
a. 105 nm
b. 715 nm
c. 2.52 cm