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# ps01 - Homework(1 for Physics 316 Modern Physics...

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Homework (1) for Physics 316, Modern Physics I (Hoffstaetter/Drasco/Thibault) Due Date: Friday, 02/04/05 - 09:05 in 132 Rockefeller Hall Exercise 1: Express Planck’s radiation formula for the emitted power per area R T ( ν ) = 2 πh c 2 ν 3 e kT - 1 (1) in terms of the wavelength λ = c/ν . The result should have the form ˜ R T ( λ ) = F ( λ ) dλ , (2) for which you have to determine F ( λ ). (from [2, 2.2,2]) Exercise 2: a) A 1kW radio transmitter operates at a frequency of 900kHz. How many photons per second does it emit. Use Planck’s formula for the energy per photon, E = . (from [2, 2.3,7]) b) Approximate the emission of a 100W light bulb as that of a black body at 4000K. How many photons are emitted? You may use R 0 x 3 / ( e x - 1) dx = π 4 / 15 and R 0 x 2 / ( e x - 1) dx = 2 ζ (3) = 2 . 4. c) (Bonus) What fraction of the energy emitted by this bulb is in the visible region? You may need to use numerical integration, for example with Mathematica using: Integrate[x ^ 3/(Exp[x]-1), x] .
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