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HW03-key - Chemistry 111 Homework#3 Due(Wednesday 1...

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Chemistry 111 Homework #3 Due: September 21, 2005 (Wednesday) 1. Determine the frequency of an ultraviolet photon of light that has a wavelength of 35.4 Å. a) 3.00 × 10 8 s -1 . b) 1.18 × 10 –17 s -1 . c) 3.33 × 10 –9 s -1 . d) 8.47 × 10 16 s -1 . e) 2.82 × 10 8 s -1 . f) None of these. Remember that the speed of a wave (c for light) equals the product of the frequency and the wavelength c = ν x λ Also remember that I said in class that you can assume the speed of light is c = 3.00 x 10 8 m s -1 unless the problem says otherwise. That is, assume your light is in a vacuum. Finally, remember that an angstrom Å = 1.00 x 10 -10 m (exactly). ν = c / λ = (3.00 x 10 8 m s -1 ) / (35.4 x 10 -10 m) = 8.47 x 10 16 s -1 8.47 x 10 16 Hz 2. Consider the following diagram: Calculate the energy for six photons of that particular electromagnetic wave. a) 1.21 × 10 -29 J b) 3.27 × 10 -21 J c) 1.18 × 10 -20 J d) 1.18 × 10 -25 J e) 5.45 × 10 -22 J f) None of these. λ = distance from one point on a wave to the next identical point (e.g. peak to peak) In this problem, then, λ = 4 x 5.07 μ m = 20.3 μ m

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Chemistry 111 2 Homework #3 / Fall 2005 The energy of one photon is: E = h x ν h = Planck's constant = 6.626 x 10 -34 J s ν = frequency = c / λ E = (6.626 x 10 -34 J s) (3.00 x 10 8 m s -1 ) / (20.28 x 10 -6 m) = 9.80 x 10 -21 J The energy of six photons = 6 x (9.80 x 10 -21 J) = 5.88 x 10 -20 J 3. How many of the following statements concerning infrared radiation are TRUE ? 3 http://www.yorku.ca/eye/spectrum.gif Ok … what you need to remember to answer this problem is (1) The electromagnetic spectrum – to know the various types of light in order of the wavelength (or frequency) (2) The equation E = h x ν = (h x c) / λ – to know that the energy of a photon is inversely proportional to the wavelength and directly proportional to the frequency
Chemistry 111 3 Homework #3 / Fall 2005 1. It is less energetic than ultraviolet radiation. UV (ultraviolet) light has a shorter wavelength and therefore more energy than IR (infrared) light True 2. It is less energetic than visible radiation. Visible light has a shorter wavelength and therefore more energy than IR light True 3. It has a lower frequency than radio waves. Radio waves (see "FM" on the diagram above) have longer wavelengths, and therefore larger frequencies, than IR light False 4. It has a longer wavelength than X-Rays. X-rays are very energetic. They have short wavelengths. IR light is much less energetic and has longer wavelengths. So this statement is True 4. What is the wavelength of a given photon of light if you are told that a small stream of identical photons that contains a total of 25 photons has a total energy of 1.69 × 10 -18 J ? a) 118 nm b) 2.94 μ m c) 4.70 Å d) 470 nm e) 118 Å. f) None of these. The wavelength (or frequency) of light is related to the energy of one photon. If the energy of 25 photons is 1.69 x 10 -18 J then the energy of 1 photon is 1.69 x 10 -18 J / 25 Energy of one photon = 6.76 x 10 -20 J = h x c / λ = (6.626 x 10 -34 J s) x (3.00 x 10 8 m s -1 ) / λ Æ λ = (6.626 x 10 -34 J s) x (3.00 x 10 8 m s -1 ) / (6.76 x 10 -20 J) = 2.94 x 10 -6 m = 2.94 μ m

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Chemistry 111 4 Homework #3 / Fall 2005 5. The laser in an audio compact disc player uses light with a wavelength of 64.8 nm. What is the total energy of a beam of photons of this light if that beam contains one-third of a mole of these photons?
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This note was uploaded on 02/08/2010 for the course CHEM 111 taught by Professor Kenney during the Spring '08 term at Case Western.

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HW03-key - Chemistry 111 Homework#3 Due(Wednesday 1...

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