# 1.2.1: Atomic Spectroscopy and the deBroglie Wavelength (Problems)

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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**-
2.74 x 10

^{-10}m

**Answer b**-
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**-
3.43 x 10

^{-34}m

**Click here for a video of the solution**-

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**-
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**-
\(4.56\times 10^{-19}J\)

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).

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

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**-
*λ*= 8.69 × 10^{−7}m;*E*= 2.29 × 10^{−19}J; red

**Answer b**-
*λ*= 4.59 × 10^{−7}m;*E*= 4.33 × 10^{−19}J; blue

## 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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