# 1.1.1: The Nature of Light (Problems)

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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 \(\PageIndex{2}\)

FM-95, an FM radio station, broadcasts at a frequency of 9.51 ^{7} s^{−1} (95.1 MHz). What is the wavelength of these radio waves in meters?

**Answer**-
3.15 m

**Click here to see a video of the solution**-

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: \(1.783\times 10^{5} J \)

**Click here to see a video of the solution**-

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 X-ray of wavelength 2.090 ^{−11} m. What is the energy, in joules, and frequency of this X-ray?

**Answer**-
*E*= 9.502 × 10^{−15}J;*ν*= 1.434 × 10^{19}s^{−1} **Click here to see a video of the solution**-

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 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**-
7.40 × 10

^{14}s^{-1}

**Answer b**-
3.67 × 10

^{19}photons

**Answer c**-
255 nm

**Answer d**-
1.67 × 10

^{11}bits17,765 bits/page

**Click here to see a video of the solution**-

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

## Contributors

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

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