This problem is to derive the Wien displacement law, Equation 3-5. 

(a) Show that the energy density distribution function can be written u = Cλ^-5(e^a/λ -1)^-1, where C is a constant and a = hc/kT. 

(b) Show that the value of λ for which du/dλ = 0 satisfies the equation 5λ (1- e^-a/λ) = a. 

(c) This equation can be solved with a calculator by the trial-and-error method. Try λ = α a for various values of α until λ/a is determined to four significant figures.

(d) Show that your solution in (c) implies λ_m T = constant and calculate the value of the constant.

Transcribed Image Text:

AT = constant = 2.898 x 10³ m. K 3-5