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CH3 - 3 The Quantum Theory of Light 3-2 Assume that your...

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3 The Quantum Theory of Light 3-2 Assume that your skin can be considered a blackbody. One can then use Wien’s displacement law, max T 0.289 8 10 2 m K with T 35 0 C 308 K to find max 0.289 8 10 2 m K 308 K 9.41 10 6 m 9 410 nm . 3-4 (a) From Stefan’s law, one has P A T 4 . Therefore, P A 5.7 10 8 W m 2 K 4 3000 K 4 4.62 10 6 W m 2 . (b) A P 4.62 10 6 W m 2 75 W 4.62 10 6 W m 2 16.2 mm 2 . 3-5 (a) Planck’s radiation energy density law as a function of wavelength and temperature is given by u , T 8 hc 5 e hc B T 1 . Using u 0 and setting x hc max k B T , yields an extremum in u , T with respect to . The result is 0   5 hc max k B T e hc max k B T e hc max k B T 1 1 or x 5 1 e x . (b) Solving for x by successive approximations, gives x 4.965 or max T hc k B 4.965 2.90 10 3 m K . 3-10 The energy per photon, E hf and the total energy E transmitted in a time t is Pt where power P 100 kW . Since E nhf where n is the total number of photons transmitted in the time t , and f 94 MHz , there results nhf 100 kW t 10 5 W t , or n t 10 5 W hf 10 5 J s 6.63 10 34 J s 94 10 6 s 1 1.60 10 30 photons s . 3-14 (a) K hf hc 1 240 eV nm 350 nm 2.24 eV 1.30 eV (b) At c , K 0 and hc 1 240 eV nm 2.24 eV 554 nm
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