6.6 Exercise 20

Show that Wien’s displacement law results from Planck’s radiation law. (Hint: substitute $x = h c / \lambda k T$ and write Planck’s law in the form $I \left(x , T\right) = A x^{5} / \left(e^{x} - 1\right) ,$ where $A = 2 \pi \left(k T\right)^{5} / \left(h^{4} c^{3}\right) .$ Now, for fixed T, find the position of the maximum in I(x,T) by solving for x in the equation $d I \left(x , T\right) / d x = 0 .$)