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Question

Solve for d and e.

3 Lightbulb The intensity of light radiated by an object at temperature T over a small range of frequencies between f and f + df is given by f³ I(f): ehf/k₂T-1 4h where c is the speed of light, kg is Boltzmann's constant, and his Planck's constant. df is the range of frequencies. For this problem you may set df = 1 Hz. -df This is the blackbody radiation spectrum that applies to any hot object, including the tungsten filament in an incan- descent lightbulb. (a) Critical Thinking: In what part of the electromagnetic spectrum do you expect to find the maximum intensity from a lightbulb: radio, microwave, IR, visible, UV, X-ray, or gamma ray? Why? (b) The tungsten filament in an incandescent lightbulb is heated to about 2800 K. Plot I(f) for such a bulb for 0 Hz ≤ f≤ 2.0 x 10¹5 Hz. (c) Find the frequency at which the intensity is greatest. (Taking the derivative and setting it equal to zero gives a transcendental equation - one that cannot be solved with algebra. Find a numerical solution or estimate the frequency from your plot.) (d) At which wavelength is the intensity greatest? What part of the spectrum is this? Is this what you expected? (e) Find the fraction of the total power that is emitted in visible wavelengths: Pvisible Ptotal Use λg = 700 nm for red light and λy = 300 nm for violet light. q= v 1(f) 1(f) You can evaluate q using numerical integration or by approximately calculating the area under your plot from part (b): Plot it on graph paper and count the number of squares under the curve.
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Transcribed Image Text:3 Lightbulb The intensity of light radiated by an object at temperature T over a small range of frequencies between f and f + df is given by f³ I(f): ehf/k₂T-1 4h where c is the speed of light, kg is Boltzmann's constant, and his Planck's constant. df is the range of frequencies. For this problem you may set df = 1 Hz. -df This is the blackbody radiation spectrum that applies to any hot object, including the tungsten filament in an incan- descent lightbulb. (a) Critical Thinking: In what part of the electromagnetic spectrum do you expect to find the maximum intensity from a lightbulb: radio, microwave, IR, visible, UV, X-ray, or gamma ray? Why? (b) The tungsten filament in an incandescent lightbulb is heated to about 2800 K. Plot I(f) for such a bulb for 0 Hz ≤ f≤ 2.0 x 10¹5 Hz. (c) Find the frequency at which the intensity is greatest. (Taking the derivative and setting it equal to zero gives a transcendental equation - one that cannot be solved with algebra. Find a numerical solution or estimate the frequency from your plot.) (d) At which wavelength is the intensity greatest? What part of the spectrum is this? Is this what you expected? (e) Find the fraction of the total power that is emitted in visible wavelengths: Pvisible Ptotal Use λg = 700 nm for red light and λy = 300 nm for violet light. q= v 1(f) 1(f) You can evaluate q using numerical integration or by approximately calculating the area under your plot from part (b): Plot it on graph paper and count the number of squares under the curve.
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