3.0.1.0: Atomic Spectroscopy and the deBroglie Wavelength (Problems)
PROBLEM \(\PageIndex{1}\)
Assume the mass of an electron is 9.11 x 10 -31 kg.
a. Calculate the wavelength of an electron traveling with a speed of 2.65 x 10 6 m/s.
b. What would the wavelength of the helium atom be if it were traveling at the same speed as the electron in part a (1 amu = 1.6606 x 10 -24 g)?
- Answer a
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2.74 x 10 -10 m
- Answer b
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3.77 x 10 -14 m
PROBLEM \(\PageIndex{2}\)
What is the de Broglie wavelength of a 46 g baseball traveling at 94 mph?
- Answer
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3.43 x 10 -34 m
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PROBLEM \(\PageIndex{3}\)
Which of the following equations describe particle-like behavior? Which describe wavelike behavior?
- \(c = λν\)
- \(E=\dfrac{mν^2}{2}\)
- \(r=\dfrac{n^2a_0}{Z}\)
- \(E = hν\)
- \(λ=\dfrac{h}{mν}\)
- Answer
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e. describes particle-like behavior
a&d describe wavelike behavior
PROBLEM \(\PageIndex{4}\)
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
- Answer
-
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.
PROBLEM \(\PageIndex{5}\)
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?
- Answer
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\(4.56\times 10^{-19}J\)
PROBLEM \(\PageIndex{6}\)
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?
- Answer
-
The frequency of (a) would be 3.79 × 10 14 s -1 .
The frequency of (b) would be 7.13 × 10 14 s -1 .
Because (a) would be in the near-IR, the compound would appear purple/blue based on the wavelength of (b).
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PROBLEM \(\PageIndex{7}\)
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?
- Answer a
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λ = 8.69 × 10 −7 m; E = 2.29 × 10 −19 J; red
- Answer b
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λ = 4.59 × 10 −7 m; E = 4.33 × 10 −19 J; blue
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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