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Key equations

  • c = λν
  • E = h ν = h c λ , where h = 6.626 × 10 −34 J s
  • 1 λ = R ( 1 n 1 2 1 n 2 2 )

Chemistry end of chapter exercises

The light produced by a red neon sign is due to the emission of light by excited neon atoms. Qualitatively describe the spectrum produced by passing light from a neon lamp through a prism.

The spectrum consists of colored lines, at least one of which (probably the brightest) is red.

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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?

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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?

3.15 m

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A bright violet line occurs at 435.8 nm in the emission spectrum of mercury vapor. What amount of energy, in joules, must be released by an electron in a mercury atom to produce a photon of this light?

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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)?

3.233 × 10 −19 J; 2.018 eV

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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?

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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?

ν = 4.568 × 10 14 s; λ = 656.3 nm; Energy mol −1 = 1.823 × 10 5 J mol −1 ; red

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When rubidium ions are heated to a high temperature, two lines are observed in its line spectrum at wavelengths (a) 7.9 × 10 −7 m and (b) 4.2 × 10 −7 m. What are the frequencies of the two lines? What color do we see when we heat a rubidium compound?

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The emission spectrum of cesium contains two lines whose frequencies are (a) 3.45 × 10 14 Hz and (b) 6.53 × 10 14 Hz. What are the wavelengths and energies per photon of the two lines? What color are the lines?

(a) λ = 8.69 × 10 −7 m; E = 2.29 × 10 −19 J; (b) λ = 4.59 × 10 −7 m; E = 4.33 × 10 −19 J; The color of (a) is red; (b) is blue.

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Photons of infrared radiation are responsible for much of the warmth we feel when holding our hands before a fire. These photons will also warm other objects. How many infrared photons with a wavelength of 1.5 × 10 −6 m must be absorbed by the water to warm a cup of water (175 g) from 25.0 °C to 40 °C?

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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?

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

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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?

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RGB color television and computer displays use cathode ray tubes that produce colors by mixing red, green, and blue light. If we look at the screen with a magnifying glass, we can see individual dots turn on and off as the colors change. Using a spectrum of visible light, determine the approximate wavelength of each of these colors. What is the frequency and energy of a photon of each of these colors?

Red: 660 nm; 4.54 × 10 14 Hz; 3.01 × 10 −19 J. Green: 520 nm; 5.77 × 10 14 Hz; 3.82 × 10 −19 J. Blue: 440 nm; 6.81 × 10 14 Hz; 4.51 × 10 −19 J. Somewhat different numbers are also possible.

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Answer the following questions about a Blu-ray laser:

(a) 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?

(b) 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?

(c) 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 and NA is the numerical aperture. 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?

(d) 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.)

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What is the threshold frequency for sodium metal if a photon with frequency 6.66 × 10 14 s −1 ejects an electron with 7.74 × 10 −20 J kinetic energy? Will the photoelectric effect be observed if sodium is exposed to orange light?

5.49 × 10 14 s −1 ; no

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Questions & Answers

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Source:  OpenStax, Chemistry. OpenStax CNX. May 20, 2015 Download for free at http://legacy.cnx.org/content/col11760/1.9
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