Using the basic physical constants, show that \(C_{1}=3.742 \times 10^{8} \mathrm{~W} \mu \mathrm{m}^{4} / \mathrm{m}^{2}\) and \(C_{2}=\) \(1.4389 \times 10^{4} \mu \mathrm{m} / \mathrm{K}\) in the Planck model.

Take the derivative of the Planck equation with temperature. Set this equal to zero, and verify Wien's displacement law.