The Wien Displacement Law states that the product of the wavelength at which the emission of a black body spectrum is maximized (\lambda_{max}) and the absolute temperature (T) is a constant, represented as x. To prove this relationship using Planck's formula, one must take the derivative with respect to wavelength (\lambda) and solve for the maximum. This mathematical approach confirms the validity of Wien's Law through the application of Planck's radiation law.
PREREQUISITESPhysicists, students of thermodynamics, and anyone interested in the mathematical foundations of black body radiation and its implications in various scientific fields.