# 1.1.1: The Nature of Light (Problems)

PROBLEM $$\PageIndex{1}$$

An FM radio station found at 103.1 on the FM dial broadcasts at a frequency of 1.031 × 108 s−1 (103.1 MHz). What is the wavelength of these radio waves in meters?

2.908 m

PROBLEM $$\PageIndex{2}$$

FM-95, an FM radio station, broadcasts at a frequency of 9.51 × 107 s−1 (95.1 MHz). What is the wavelength of these radio waves in meters?

3.15 m

PROBLEM $$\PageIndex{3}$$

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)?

$$3.233 \times 10^{-19} J$$

2.018 eV

PROBLEM $$\PageIndex{4}$$

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?

Frequency: $$4.469\times 10^{14} Hz$$

Wavelength: $$6.709\times 10^{-7} m$$ = Red Light

Total energy: $$1.783\times 10^{5} J$$

PROBLEM $$\PageIndex{5}$$

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 × 1014 s; λ = 656.3 nm; Energy mol−1 = 1.823 × 105 J mol−1; red

PROBLEM $$\PageIndex{6}$$

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 × 1019 s−1

PROBLEM $$\PageIndex{7}$$

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?

$$1.3\times 10^{5}\, photons$$

PROBLEM $$\PageIndex{8}$$

1. 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?
2. 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?
3. 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 (in nm) and NA is the numerical aperture (dimensionless). 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?
4. The data density of a Blu-ray disk using a 405-nm laser is 1.5 × 107 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 = πr2, where the radius r is one-half of the diameter.)

7.40 × 1014 s-1

3.67 × 1019 photons

255 nm

1.67 × 1011 bits

17,765 bits/page

PROBLEM $$\PageIndex{9}$$

What is the threshold frequency for sodium metal if a photon with frequency 6.66 × 1014 s−1 ejects a photon with 7.74 × 10−20 J kinetic energy? Will the photoelectric effect be observed if sodium is exposed to orange light?