Wien's Displacement Law and Other Ways to Characterize the Peak of Blackbody RadiationWhen the temperature of a blackbody radiator increases, the overall radiated energy increases and the peak of the radiation curve moves to shorter wavelengths. When the maximum is evaluated from the Planck radiation formula, the product of the peak wavelength and the temperature is found to be a constant.
This relationship is called Wien's displacement law and is useful for the determining the temperatures of hot radiant objects such as stars, and indeed for a determination of the temperature of any radiant object whose temperature is far above that of its surroundings. The temperature can be found from the wavelength at which the radiation curve peaks.
It should be noted that the peak of the radiation curve in the Wien relationship is the peak only because the intensity is plotted as a function of wavelength. If frequency or some other variable is used on the horizontal axis, the peak will be at a different wavelength.
There are various rationales for using the alternate ways of plotting the blackbody radiation curve, as discussed by Heald. The process of finding the maximum in a given presentation is to set the derivative of the intensity equal to zero and then numerically solve the transcendental equation that results. The solutions for the processes included above are summarized below.
Blackbody radiation concepts