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3063_ProblemSet4 - PHY3063 Spring 2007 Problem Set 4 PHY...

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PHY3063 Spring 2007 Problem Set 4 Department of Physics Page 1 of 2 PHY 3063 Problem Set #4 Due Thursday February 15 (in class) (Total Points = 70, Late homework = 50%) Reading: Continue reading Tipler & Llewellyn Chapter 3. Problem 1 (10 points): Consider a two dimensional conducting square with sides of length L . Show that if the electric field must vanish on the conductor then the allowed wavelengths (and frequencies) of the electrometric radiation within the cavity are given by 2 2 2 2 y x n n c Lf L + = = λ , where n x , n y = all positive integers. Problem 2 (25 points): Consider Planck’s formula 1 1 8 ) , ( / 5 = T k hc Planck e hc T λ λ π λ ρ , where ρ (T, λ )d λ is the energy per unit volume in a spherical “black-body” cavity at temperature T with wavelength between λ and λ +d λ ,, λ λ ρ d dU V T 1 ) , ( = . Part A (5 points): Show that 1 8 ) , ( / 3 2 = kT hf Planck e hf c f f T π ρ , where ρ (T,f)df is the energy per unit volume in the cavity at temperature T with frequency between f and f+df, df dU V f T 1 ) , ( = ρ .
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