Question

State: Wein’s displacement law

Answer 1

Hint: We encounter the Wein’s displacement law when we study the energy spectrum of a blackbody. It gives the relation between the peak wavelength of the radiation emitted by a blackbody and the temperature at which that peak in wavelength occurs.

Complete step-by-step solution:
Blackbody radiation can be described as a body, which can absorb or emit radiations of all wavelengths or frequencies. This radiation is known as the blackbody radiation and a blackbody is characterized by its temperature.
We study the properties of a blackbody on the basis of the energy spectrum of the blackbody radiation. It is a plot between the wavelength emitted or absorbed by a blackbody along the x-axis and the intensity of that radiation along the y-axis. This plotting is done at different values of temperature. The following diagram shows a blackbody spectrum.

Wein’s displacement law helps us in understanding this spectrum by giving us the expression for the relation between the peak wavelength of the plot and the temperature at which that peak occurs. It is given as follows:
${\lambda _{\max }} = \dfrac{C}{T}$
Here C is a constant.
The law implies that the wavelengths at which the peak occurs in the blackbody spectrum is inversely proportional to the temperature of the blackbody. In other words, the peak in radiation occurs at different wavelengths for different temperatures.
This is the required answer.

Note: 1. A perfect blackbody does not exist as there are always certain wavelengths, which are absent in the energy spectrum of the possible candidates for a blackbody.
2. The consequence of the Wein’s law is that in the energy spectrum, the peaks for lower temperatures are towards the right while that for higher temperatures is towards left.