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, maxT0.289 8102mKwith T350C308 Kto find max0.289 8102mK308 K9.41106m9 410 nm. 3-4 (a) From Stefan’s law, one has PAT4. Therefore, PA5.7108W m2K43000 K44.62106W m2. (b) AP4.62106W m275 W4.62106W m216.2 mm2. 3-5 (a) Planck’s radiation energy density law as a function of wavelength and temperature is given by u, T8hc5ehcBT1. Using u0and setting xhcmaxkBT, yields an extremum in u, Twith respect to . The result is 0 5hcmaxkBTehcmaxkBTehcmaxkBT11or x5 1ex. (b) Solving for xby successive approximations, gives x4.965or maxThckB4.9652.90103mK. 3-10 The energy per photon, Ehfand the total energy Etransmitted in a time tis Ptwhere power P100 kW. Since Enhfwhere nis the total number of photons transmitted in the time t, and f94 MHz, there results nhf100 kWt105Wt, or nt105Whf105J s6.631034J s94106s11.601030photonss. 3-14 (a) Khfhc1 240 eV nm350 nm2.24 eV1.30 eV(b) At c, K0and hc1 240 eV nm2.24 eV554 nm
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