Question

Why is the displacement term used in Wien’s displacement law?

Answer 1

In order to explain the statement in question we will use the information regarding the thermodynamic law that is Wien’s displacement law we will use the relation of wavelength and temperature that is in kelvin and the Wien’s displacement constant so as to proof the statement

Formula used:
$\lambda T = b$
Where, $\lambda$ represents the wavelength, $T$ represents the temperature and $b$ represents the Wien’s displacement constant.

Complete step by step answer:
Wien’s displacement law states that wavelength corresponding to maximum energy is indirectly proportional to the temperature and the unit used for temperature is kelvin.We use the Wien’s displacement law in order to state that in the blackbody radiation curve for different temperature this law show us the peak at different wavelength,
$\lambda \propto \dfrac{1}{T}$
$\Rightarrow \lambda = \dfrac{b}{T}$
$\therefore \lambda T = b$
Here, $b$ states the Wien’s displacement constant. The value of Wien's displacement constant (b) is $2.89 \times {10^{ - 3}}mK$.

When the temperature increases the wavelength moves toward the lower part of the spectrum and when the temperature decreases the wavelength is displaced toward the higher end of the spectrum that is why displacement term is used in Wien’s displacement law.

Note: Many of the students make the common mistake by thinking that the wavelength is independent of the energy but they are dependent on each other therefore when it is mentioned the maximum wavelength it is corresponding to the maximum energy.