Wien's Displacement Law

One of the clearest quantitative features of the blackbody spectral-distribution curves (Section 3.14, observation 4) is that the wavelength $\lambda_{max}$ at which a blackbody's emissive power is maximum is inversely proportional to its absolute temperature $T$. This is Wien's displacement law:

where $b$ is Wien's constant, with measured value $b = 2.897\times10^{-3}$ m K.

$\lambda_{max}$ indicates the wavelength at which a blackbody's radiation is most intense -- so it corresponds to the dominant colour of the radiating body, and (via this law) is a direct function of the body's temperature. This is the physical basis for classifying stars by colour and temperature: white dwarfs are hot stars, with surface temperatures around 10,000 K (their dominant emission shifted toward shorter, bluer wavelengths), while red giants are comparatively cooler stars, with surface temperatures around 3,000 K (their dominant emission shifted toward longer, redder wavelengths) -- exactly consistent with Wien's law, since a higher temperature corresponds to a smaller $\lambda_{max}$. …