# 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 106 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)?

2.74 x 10-10 m

3.77 x 10-14 m

PROBLEM $$\PageIndex{2}$$

What is the de Broglie wavelength of a 46 g baseball traveling at 94 mph?

3.43 x 10-34 m

PROBLEM $$\PageIndex{3}$$

Which of the following equations describe particle-like behavior? Which describe wavelike behavior?

1. $$c = λν$$
2. $$E=\dfrac{mν^2}{2}$$
3. $$r=\dfrac{n^2a_0}{Z}$$
4. $$E = hν$$
5. $$λ=\dfrac{h}{mν}$$

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

Red: 660 nm; 4.54 × 1014 Hz; 3.01 × 10−19 J. Green: 520 nm; 5.77 × 1014 Hz; 3.82 × 10−19 J. Blue: 440 nm; 6.81 × 1014 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?

$$4.56\times 10^{-19}J$$

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?

The frequency of (a) would be 3.79 × 1014 s-1.

The frequency of (b) would be 7.13 × 1014 s-1.

Because (a) would be in the near-IR, the compound would appear purple/blue based on the wavelength of (b).

PROBLEM $$\PageIndex{7}$$

The emission spectrum of cesium contains two lines whose frequencies are (a) 3.45 × 1014 Hz and (b) 6.53 × 1014 Hz. What are the wavelengths and energies per photon of the two lines? What color are the lines?

λ = 8.69 × 10−7 m; E = 2.29 × 10−19 J; red

λ = 4.59 × 10−7 m; E = 4.33 × 10−19 J; blue