Obtaining Wien's displacement law from Planck's law of radiation

Abstract

Wien’s displacement law states that the wavelength at which the radiated power is a maximum for a blackbody varies inversely with the temperature. This relationship is important in astrophysics for determining the temperature of stars. The objective of this note is to show that in teaching introductory (calculus-based) or intermediate physics, instead of simply stating Wien’s displacement law, instructors can ask students to derive if from Planck’s radiation law. A numerical solution to a transcendental equation is required, easily accomplished using a symbolic math program such as Maple or Mathematica.