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

2.908 m
PROBLEM \(\PageIndex{2}\)
FM95, 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

3.15 m
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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

\(3.233 \times 10^{19} J\)
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

Frequency: \(4.469\times 10^{14} Hz\)
Wavelength: \(6.709\times 10^{7} m\) = Red Light
Total energy: \(1.783\times 10^{5} J \)
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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

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 Xray of wavelength 2.090 × 10^{−11} m. What is the energy, in joules, and frequency of this Xray?
 Answer

E = 9.502 × 10^{−15} J; ν = 1.434 × 10^{19} s^{−1}
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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

\(1.3\times 10^{5}\, photons\)
PROBLEM \(\PageIndex{8}\)
Answer the following questions about a Bluray laser:
 The laser on a Bluray player has a wavelength of 405 nm. In what region of the electromagnetic spectrum is this radiation? What is its frequency?
 A Bluray 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 Bluray 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 Bluray system, NA = 0.95. If the 405nm laser is used in a Bluray player, what is the closest that information can be stored on a Bluray disk?
 The data density of a Bluray disk using a 405nm laser is 1.5 × 10^{7} bits mm^{−2}. Disks have an outside diameter of 120 mm and a hole of 15mm diameter. How many data bits can be contained on the disk? If a Bluray 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 onehalf of the diameter.)
 Answer a

7.40 × 10^{14} s^{1}
 Answer b

3.67 × 10^{19} photons
 Answer c

255 nm
 Answer d

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

5.49 × 10^{14} s^{−1}; no
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