4 Questions around this concept.
The earth radiates in the infrared region of the spectrum. The wavelength of the maximum intensity of the spectrum is correctly given by the :
Wien's displacement law states that the wavelength (i.e $\lambda_{\text {max }}$ ) for which the emissive power of a black body is maximum is inversely proportional to the absolute temperature ( T ) of the black body.
Or Mathematically we can write that
$$
\lambda_{\max } * T=b=\mathrm{constant}
$$
Where $\mathbf{b}$ is a constant of proportionality which is known as Wien's displacement constant.
Value of b is given as $b=2.89 * 10^{-3} \mathrm{mK}$
With the help of this law, we can say that
As the temperature of the body increases, the wavelength at which the spectral intensity () is maximum shifts towards left, as shown in the below figure.

I.e
If $T_1<T_2<T_3$
Then $\lambda_{m_1}>\lambda_{m_2}>\lambda_{m_3}$
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