Homework (1)for Physics 316, Modern Physics I (Hoffstaetter/Drasco/Thibault)Due Date: Friday, 02/04/05 - 09:05 in 132 Rockefeller HallExercise 1:Express Planck’s radiation formula for the emitted power per areaRT(ν)dν=2πhc2ν3ehνkT-1dν(1)in terms of the wavelengthλ=c/ν. The result should have the form˜RT(λ)dλ=F(λ)dλ ,(2)for which you have to determineF(λ). (from [2, 2.2,2])Exercise 2:a)A 1kW radio transmitter operates at a frequency of 900kHz. How many photonsper second does it emit. Use Planck’s formula for the energy per photon,E=hν. (from [2, 2.3,7])b)Approximate the emission of a 100W light bulb as that of a black body at 4000K. How manyphotons are emitted?You may useR∞0x3/(ex-1)dx=π4/15 andR∞0x2/(ex-1)dx= 2ζ(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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