Dayton PHY 250 - PROBLEMS EXAMPLE PART 2

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Slide 1Slide 2Slide 3Slide 4Slide 5Slide 6Slide 7Slide 8Slide 9Slide 10ExamplesA star radiates as a blackbody at a temperature of 1700 K. At what wavelength does the peak of the blackbody spectrum occur? If you were to look at the source, what color would it appear to be?λMax = (0.29 cm / T) T in KλMax = (0.29 cm / 1700) = 1.7 x 10-4 cm = 1.7 x 10-6 m = 1700 nmThis is outside of the visible spectrum in the IR region (long wavelength). Therefore, one would expect that only the long wavelength end of the visible spectrum would be present. The star would be red.ExamplesA particular object is moving away from the earth at 50% of the speed of light. What is the wavelength as measured on the earth of an electromagnetic wave which leaves the source with a wavelength of 600 nm? Can this wave be observed with an optical telescope? If not, in what part of the electromagnetic spectrum will it be observed?λApparent / λTrue = 1 + (speed of source / wave speed)λApparent / λTrue = 1 + (.5 c / c) = 1.5λApparent = 1.5 (600 nm) = 900 nmNo, infraredExamplesA particular object is moving away from the earth at 50% of the speed of light. What is the wavelength as measured on the earth of an electromagnetic wave which leaves the source with a wavelength of 600 nm? Can this wave be observed with an optical telescope? If not, in what part of the electromagnetic spectrum will it be observed?λApparent / λTrue = 1 + (speed of source / wave speed)λApparent / λTrue = 1 + (.5 c / c) = 1.5λApparent = 1.5 (600 nm) = 900 nmNo, infraredExamplesWhen the first astronauts landed on the moon, how long did it take radio transmissions to reach the earth?d = v t = c tt = d / c = (3.84 x 108 ) / (3.00 x 108 m/sec) = 1.28 secExamplesIf the sun just blew up, how long would it be before we would see the explosion?d = v t = c tt = d / c = (1.5 x 1011 m) / (3.00 x 108 m/sec) = 500 sec = 8.33 minutesExamplesLineLineλ (nm)λ (nm)LineLineλ (nm)λ (nm)LyαLyα122122UVUVHαHα656656VisibleVisibleLyβLyβ103103UVUVHβHβ486486VisibleVisibleLyγLyγ9797UVUVHγHγ434434VisibleVisibleExamplesShow that the wavelength of the Hβ line is 486 nm.EHβ = 13.6 (1/22 – 1/42) eV = 13.6 (3/16) eV = 2.55 eV.2.55 eV (1.6 x 10-19 J/eV) = 4.08 x 10-19 J = hf (4.08 x 10-19 J ) / (6.6 x 10-34 J – sec) = 6.18 x 1014 sec-1f = 6.18 x 1014 sec-1 = c / λλ = (3 x 108 m/sec) / (6.18 x 1014 sec-1) = 485 x 10-9 m = 485 nmExamplesHow many different energy photons can be emitted by a gas of hydrogen atoms if (by magic) all of the electrons start in the 3rd excited state?ExamplesHow many different energy photons can be emitted by a gas of hydrogen atoms if (by magic) all of the electrons start in the 3rd excited state?Energy-13.6 /12 -13.6 /22 -13.6 /32 -13.6 /42ExamplesHow many different energy photons can be emitted by a gas of hydrogen atoms if (by magic) all of the electrons start in the 3rd excited state?Energy-13.6 /12 -13.6 /22 -13.6 /32 -13.6 /42 Answer – SIX ! The red transition is


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Dayton PHY 250 - PROBLEMS EXAMPLE PART 2

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