PROBLEM \(\PageIndex{1}\) 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? Answer 2.908 m PROBLEM \(\PageIndex{2}\) 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? Answer 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)? Answer \(3.233 \times 10^{-19} J\) 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? Answer 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? Answer ν = 4.568 × 10 14 s; λ = 656.3 nm; Energy mol −1 = 1.823 × 10 5 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? Answer E = 9.502 × 10 −15 J; ν = 1.434 × 10 19 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? Answer \(1.3\times 10^{5}\, photons\) PROBLEM \(\PageIndex{8}\) Answer the following questions about a Blu-ray laser: 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? 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? 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? 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.) Answer a 7.40 × 10 14 s -1 Answer b 3.67 × 10 19 photons Answer c 255 nm Answer d 1.67 × 10 11 bits 17,765 bits/page Click here to see a video of the solution PROBLEM \(\PageIndex{9}\) What is the threshold frequency for sodium metal if a photon with frequency 6.66 × 10 14 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? Answer 5.49 × 10 14 s −1 ; no Have a video solution request? Let your professors know here. ***Please know that you are helping future students - videos will be made in time for next term's class. Feedback Think one of the answers above is wrong? Let us know here .