Exercise 1 1.1 The distribution in wavelengths of the light emitted from a radiating black- body is a sensitive function of the temperature. This dependence is used to measure the temperature of hot objects. (a) Show that in the limit 2kgT >> 1, the maximum in a plot of p(1,7) vs. 1 is given by Wien's law: Imax 5kgT (b) At what wavelength does the maximum in p(1,7) occur for T = 450, 1500, and 4500 K? hc hc 1 Exercise 1 hc 1.3 For a black body, the temperature and the wavelength of emission maximum, imax, are related by Wien's law, Amax 5kg Values of Imax from a small pinhole in an electrically heated container were determined at a series of temperatures, and the results are given below. Deduce a value for Planck's constant. T/C 1000 1500 2000 2500 Amaxm 2181 1600 1240 1035 3000 878 3500 763 hc Exercise 1 1.2 In the discussion of a black-body radiation for ART the average energy of an oscillator Bose Acetc/kg-1) was approximated as Eost approx = kg. hc he h akt Calculate the relative error = Base-Roscapprox in making this approximation for Eos v = 4 x 10^2 - at temperatures of 6000, 2000, and 500 K. Exercise 1 1.4 Given that the following kinetic energies (Ex) were observed for photoejected electrons irradiated by radiation of the wavelengths noted. Determine the value of the work function and the Planck's constant h. 2m 320 330 345 385 Elev 1.17 1.05 0.885 0.735 0.511 360