State and explain Wien's displacement law.

(N/A) Thermal radiation emitted by a body consists of electromagnetic waves of different wavelengths, and these wavelengths form a continuous spectrum. However, the intensity of electromagnetic waves at certain definite frequencies is higher.
For example, in blackbody radiation at room temperature $(300 \; K)$, the majority of the radiation consists of electromagnetic waves of wavelength $95,500 \; \mathring{A}$ (infrared waves).
As the temperature increases, the intensity of waves with shorter wavelengths increases.
At about $1100 \; K$, the body appears red because the intensity of waves corresponding to the red color is higher.
Wien's displacement law states: "The wavelength $(\lambda_{m})$ corresponding to the maximum spectral emissive power of radiation emitted from the surface of a body is inversely proportional to the absolute temperature $(T)$ of the emitting surface."
Mathematically, $\lambda_{m} \propto \frac{1}{T}$ or $\lambda_{m} T = b$, where $b$ is Wien's constant.
The value of Wien's constant is $2.9 \times 10^{-3} \; m \cdot K$.
Note: Here, $\lambda_{m}$ is not the maximum wavelength, but the wavelength at which the radiation energy density is maximum.
This law explains why a piece of iron, when heated, turns from reddish to yellowish-green and finally to white.
Wien's law is useful for estimating the surface temperature of celestial objects like the Sun, Moon, and stars.