(a) Derive Wiens displacement law from Plancks law.
Chapter 40, Problem 76(choose chapter or problem)
(a) Derive Wiens displacement law from Plancks law. Proceed as follows. In Figure 40.3, notice that the wavelength at which a black body radiates with greatest intensity is the wavelength for which the graph of I(l,T ) versus l has a horizontal tangent. From Equation 40.6, evaluate the derivative dI/dl. Set it equal to zero. Solve the resulting transcendental equation numerically to prove that hc/lmaxkBT 5 4.965 . . . or lmaxT 5 hc/4.965kB. (b) Evaluate the constant as precisely as possible and compare it with Wiens experimental value.
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