Explanation:
This problem can be solved by the Wien's displacement law, which relates the wavelength [tex]\lambda_{p}[/tex] where the intensity of the radiation is maximum (also called peak wavelength) with the temperature [tex]T[/tex] of the black body.
In other words:
There is an inverse relationship between the wavelength at which the emission peak of a blackbody occurs and its temperature.
Being this expresed as:
[tex]\lambda_{p}.T=C[/tex] (1)
Where:
[tex]T[/tex] is in Kelvin (K)
[tex]\lambda_{p}[/tex] is the wavelength of the emission peak in meters (m).
[tex]C[/tex] is the Wien constant, whose value is [tex]2.898(10)^{-3}m.K[/tex]
From this we can deduce that the higher the black body temperature, the shorter the maximum wavelength of emission will be.
Now, let's apply equation (1), finding [tex]\lambda_{p}[/tex]:
[tex]\lambda_{p}=\frac{C}{T}[/tex] (2)
[tex]\lambda_{p}=\frac{2.898(10)^{-3}m.K}{273K}[/tex]
Finally:
[tex]\lambda_{p}=10615(10)^{-9}m=10615nm[/tex] This is the peak wavelength for radiation from ice at 273 K, and corresponds to the infrared.
