5.0 Wein's displacement law

Thermal radiation, once emitted are electromagnetic waves and they obeys all the laws of wave theory.

As the wave lengths are still small compared to obstacles (lies in the infrared region), so the rules of optics are also valid.

The radiation emitted are a mixture of wavelengths.

The wavelength decreases when the temperature increases.

If the intensity of radiation near a given wave length is plotted against wavelength for temperatures. We can observe that, if temperature is increased, the wavelength corresponding to the highest intensity decreases.

So, the the wavelength ${\lambda _m}$ is inversely proportional to the absolute temperature. So,$${\lambda _m}T = b$$where $b$ is a constant.

The equation is known as Wein's displacement law and for a black body the constant $b$ is measured to be 0.288$cmK$ and it is known as Wein's constant.