# 2.1 Electromagnetic radiation & Line emission spectra  (Page 10/27)

 Page 10 / 27

## Key equations

• c = λν
• $E=h\nu =\phantom{\rule{0.2em}{0ex}}\frac{hc}{\lambda },$ where h = 6.626 $×$ 10 −34 J s
• $\phantom{\rule{0.2em}{0ex}}\frac{1}{\lambda }\phantom{\rule{0.2em}{0ex}}={R}_{\infty }\left(\phantom{\rule{0.2em}{0ex}}\frac{1}{{n}_{1}^{2}}\phantom{\rule{0.2em}{0ex}}-\phantom{\rule{0.2em}{0ex}}\frac{1}{{n}_{2}^{2}}\phantom{\rule{0.2em}{0ex}}\right)$

## 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.

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?

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

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?

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

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?

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

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 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.

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?

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

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?

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.

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.)

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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At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
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how do you find theWhat are the wavelengths and energies per photon of two lines
The eyes of some reptiles are sensitive to 850 nm light. If the minimum energy to trigger the receptor at this wavelength is 3.15 x 10-14 J, what is the minimum number of 850 nm photons that must hit the receptor in order for it to be triggered?
A teaspoon of the carbohydrate sucrose contains 16 calories, what is the mass of one teaspoo of sucrose if the average number of calories for carbohydrate is 4.1 calories/g?
4. On the basis of dipole moments and/or hydrogen bonding, explain in a qualitative way the differences in the boiling points of acetone (56.2 °C) and 1-propanol (97.4 °C), which have similar molar masses
Calculate the bond order for an ion with this configuration: (?2s)2(??2s)2(?2px)2(?2py,?2pz)4(??2py,??2pz)3
Which of the following will increase the percent of HF that is converted to the fluoride ion in water? (a) addition of NaOH (b) addition of HCl (c) addition of NaF