Wien's displacement law

In physics, Wien's displacement law states that the black-body radiation curve for different temperatures will peak at different wavelengths that are inversely proportional to the temperature. The shift of that peak is a direct consequence of the Planck radiation law, which describes the spectral brightness or intensity of black-body radiation as a function of wavelength at any given temperature. However, it had been discovered by German physicist Wilhelm Wien several years before Max Planck developed that more general equation, and describes the entire shift of the spectrum of black-body radiation toward shorter wavelengths as temperature increases.

Formally, the wavelength version of Wien's displacement law states that the spectral radiance of black-body radiation per unit wavelength, peaks at the wavelength ${\displaystyle \lambda _{\text{peak}}}$ given by: $${\displaystyle \lambda _{\text{peak}}={\frac {b}{T}}}$$ where T is the absolute temperature and b is a constant of proportionality called Wien's displacement constant, equal to 2.897771955...×10⁻³ m⋅K,‍^[1][2] or b ≈ 2898 μm⋅K.

This is an inverse relationship between wavelength and temperature. So the higher the temperature, the shorter or smaller the wavelength of the thermal radiation. The lower the temperature, the longer or larger the wavelength of the thermal radiation. For visible radiation, hot objects emit bluer light than cool objects. If one is considering the peak of black body emission per unit frequency or per proportional bandwidth, one must use a different proportionality constant. However, the form of the law remains the same: the peak wavelength is inversely proportional to temperature, and the peak frequency is directly proportional to temperature.

There are other formulations of Wien's displacement law, which are parameterized relative to other quantities. For these alternate formulations, the form of the relationship is similar, but the proportionality constant, b, differs.

Wien's displacement law may be referred to as "Wien's law", a term which is also used for the Wien approximation.

In "Wien's displacement law", the word displacement refers to how the intensity-wavelength graphs appear shifted (displaced) for different temperatures.