51. (a) Derive Wien's displacement law from Planck's law. S Proceed as follows. In Figure 39.3, notice that the wave- length at which a black body radiates with greatest inten- sity is the wavelength for which the graph of I(A,T) versus has a horizontal tangent. From Equation 39.6, evaluate the derivative dI/d. Set it equal to zero. Solve the result- ing transcendental equation numerically to prove that hc/AkT 4.965... or A the constant as precisely as possible and compare it with Wien's experimental value. T hc/4.965k (b) Evaluate max B max 51. (b) 2.897755 X 10- m. K

51. (a) Derive Wien's displacement law from Planck's law. S Proceed as follows. In Figure 39.3, notice that the wave- length at which a black body radiates with greatest inten- sity is the wavelength for which the graph of I(A,T) versus has a horizontal tangent. From Equation 39.6, evaluate the derivative dI/d. Set it equal to zero. Solve the result- ing transcendental equation numerically to prove that hc/AkT 4.965... or A the constant as precisely as possible and compare it with Wien's experimental value. T hc/4.965k (b) Evaluate max B max 51. (b) 2.897755 X 10- m. K

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter28: Quantum Physics

Section: Chapter Questions

Problem 2P

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