Question

State and explain wien's displacement law.

Answer 1

Hint: The black-body radiation curve at various temperatures will peak at distinct wavelengths that are inversely proportional to the temperature, according to Wien's displacement law. Wilhelm Wien, who formulated the law in 1893 based on a thermodynamic argument, is the name given to it.

Complete answer:
The black-body radiation curve at various temperatures will peak at distinct wavelengths that are inversely proportional to the temperature, according to Wien's displacement law. The Planck radiation law, which defines the spectrum brightness of black-body radiation as a function of wavelength at any given temperature, causes that peak to move. Wilhelm Wien found it some years before Max Planck established the more general equation, and it explains the whole change of the spectrum of black-body radiation toward shorter wavelengths as temperature rises.

The spectrum brightness of black-body radiation per unit wavelength, according to Wien's displacement law, peaks at the wavelength peak given by:
\[{\lambda _{{\text{peak}}}} = \dfrac{b}{T}\]
$T$ stands for absolute temperature \[{2.897771955...10^{ - 3}}{\text{ }}mK\], or b = 2898 mK, is a proportionality constant termed Wien's displacement constant. The wavelength and temperature have an inverse relationship.

As a result, the wavelength of thermal radiation is shorter or smaller as the temperature rises. The wavelength of thermal radiation is longer or bigger as the temperature drops. Hot things emit blue light more than cold ones when it comes to visual radiation. If the peak of black body emission is measured per unit frequency or proportional bandwidth, a separate proportionality constant must be used.

The law's shape, however, stays the same: the peak wavelength is inversely proportional to temperature, whereas the peak frequency is directly proportional. Wien's displacement law is also known as "Wien's law," which is also the name given to the Wien approximation.

Note: A piece of metal burned with a blow torch becomes "red hot" as the very longest visible wavelengths look red, then turns more orange-red as the temperature rises, and finally becomes "white hot" as shorter and shorter wavelengths dominate the black body emission spectrum at extremely high temperatures. The thermal emission was mostly at longer infrared wavelengths, which are not visible, before it reached the red hot temperature; nonetheless, that radiation could be felt when it warmed one's adjacent skin.