3.0.0.0: The Nature of Light (Problems)
PROBLEM \(\PageIndex{1}\)
An FM radio station found at 103.1 on the FM dial broadcasts at a frequency of 1.031 × 10 8 s −1 (103.1 MHz). What is the wavelength of these radio waves in meters?
- Answer
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2.908 m
PROBLEM \(\PageIndex{2}\)
FM-95, an FM radio station, broadcasts at a frequency of 9.51 × 10 7 s −1 (95.1 MHz). What is the wavelength of these radio waves in meters?
- Answer
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3.15 m
PROBLEM \(\PageIndex{3}\)
Light with a wavelength of 614.5 nm looks orange. What is the energy, in joules, per photon of this orange light? What is the energy in eV (1 eV = 1.602 × 10 −19 J)?
- Answer
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\(3.233 \times 10^{-19} J\)
2.018 eV
PROBLEM \(\PageIndex{4}\)
Heated lithium atoms emit photons of light with an energy of 2.961 × 10 −19 J. Calculate the frequency and wavelength of one of these photons. What is the total energy in 1 mole of these photons? What is the color of the emitted light?
- Answer
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Frequency: \(4.469\times 10^{14} Hz\)
Wavelength: \(6.709\times 10^{-7} m\) = Red Light
Total energy: \(1.783\times 10^{5} J \)
PROBLEM \(\PageIndex{5}\)
A photon of light produced by a surgical laser has an energy of 3.027 × 10 −19 J. Calculate the frequency and wavelength of the photon. What is the total energy in 1 mole of photons? What is the color of the emitted light?
- Answer
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ν = 4.568 × 10 14 s; λ = 656.3 nm; Energy mol −1 = 1.823 × 10 5 J mol −1 ; red
PROBLEM \(\PageIndex{6}\)
One of the radiographic devices used in a dentist's office emits an X-ray of wavelength 2.090 × 10 −11 m. What is the energy, in joules, and frequency of this X-ray?
- Answer
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E = 9.502 × 10 −15 J; ν = 1.434 × 10 19 s −1
PROBLEM \(\PageIndex{7}\)
The eyes of certain reptiles pass a single visual signal to the brain when the visual receptors are struck by photons of a wavelength of 850 nm. If a total energy of 3.15 × 10 −14 J is required to trip the signal, what is the minimum number of photons that must strike the receptor?
- Answer
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\(1.3\times 10^{5}\, photons\)
PROBLEM \(\PageIndex{8}\)
Answer the following questions about a Blu-ray laser:
- The laser on a Blu-ray player has a wavelength of 405 nm. In what region of the electromagnetic spectrum is this radiation? What is its frequency?
- A Blu-ray laser has a power of 5 milliwatts (1 watt = 1 J s −1 ). How many photons of light are produced by the laser in 1 hour?
- The ideal resolution of a player using a laser (such as a Blu-ray player), which determines how close together data can be stored on a compact disk, is determined using the following formula: Resolution = 0.60( λ /NA), where λ is the wavelength of the laser (in nm) and NA is the numerical aperture (dimensionless). Numerical aperture is a measure of the size of the spot of light on the disk; the larger the NA, the smaller the spot. In a typical Blu-ray system, NA = 0.95. If the 405-nm laser is used in a Blu-ray player, what is the closest that information can be stored on a Blu-ray disk?
- The data density of a Blu-ray disk using a 405-nm laser is 1.5 × 10 7 bits mm −2 . Disks have an outside diameter of 120 mm and a hole of 15-mm diameter. How many data bits can be contained on the disk? If a Blu-ray disk can hold 9,400,000 pages of text, how many data bits are needed for a typed page? (Hint: Determine the area of the disk that is available to hold data. The area inside a circle is given by A = πr 2 , where the radius r is one-half of the diameter.)
- Answer a
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7.40 × 10 14 s -1
- Answer b
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3.67 × 10 19 photons
- Answer c
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255 nm
- Answer d
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1.67 × 10 11 bits
17,765 bits/page
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PROBLEM \(\PageIndex{9}\)
What is the threshold frequency for sodium metal if a photon with frequency 6.66 × 10 14 s −1 ejects a photon with 7.74 × 10 −20 J kinetic energy? Will the photoelectric effect be observed if sodium is exposed to orange light?
- Answer
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5.49 × 10 14 s −1 ; no
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Contributors and Attributions
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Paul Flowers (University of North Carolina - Pembroke), Klaus Theopold (University of Delaware) and Richard Langley (Stephen F. Austin State University) with contributing authors. Textbook content produced by OpenStax College is licensed under a Creative Commons Attribution License 4.0 license. Download for free at http://cnx.org/contents/85abf193-2bd...a7ac8df6@9.110 ).
- Adelaide Clark, Oregon Institute of Technology