Spring H7B 2012 Problem Set #2 Due in class by Tuesday, February 7, 2012 Problem 1: Giancoli 4th edition Ch 18 #56 Problem 2 Giancoli 4th edition Ch 18 #63 Problem 3: Giancoli 4th edition Ch 18 #67 Problem 4: Giancoli 4th edition Ch 18 #70 Problem 5: Giancoli 4th edition Ch 18 #75
#6 The Planck Distribution Function An object in thermal equilibrium will radiate heat through a process known as "blackbody radiation," where all properties of the radiation are determined by the body's temperature. In quantum mechanics, radiation means that massless particles called photons carry energy away from the body. All electromagnetic radiation (including visible light) consists of photons. Each photon carries energy equal to hc/, where is the wavelength of the photon, h is the Planck constant (6.6 x 10-34 Joule-sec in SI units), and c is the speed of light. Blackbody radiation is given the by Planck Distribution Function, which says that the number of photons with wavelength between and +d in a unit volume is given by:
n()d = (8 /) * 1/ (ehc/
kT
-1) d
where k is the Boltzmann constant and T is the temperature of the radiating object (in Kelvin). You should recognize the exponential term as the Boltzmann factor. a) At a given temperature T, at what wavelength will the photons be most abundant? b) What is the total energy of the photons per unit volume? You will need to look up this integral or do it numerically. c) The radiation from stars closely approximates blackbody radiation. If the temperature of the sun is 5800 K, at what wavelength will the sun radiate the most photons? Where on the electromagnetic spectrum does this lie? d) If the human body radiated energy as a blackbody, at what wavelength would it emit the most photons? Does this answer make sense?