Question

Estimate the peak wavelength for radiation from ice at 273 k.

Answer 1

Answer: 10615 nm

Explanation:

This problem can be solved by the Wien's displacement law, which relates the wavelength  $\lambda_{p}$ where the intensity of the radiation is maximum (also called peak wavelength) with the temperature $T$ 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:

$\lambda_{p}.T=C$    (1)

Where:

$T$ is in Kelvin (K)

$\lambda_{p}$ is the wavelength of the emission peak in meters (m).

$C$ is the Wien constant, whose value is $2.898(10)^{-3}m.K$

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 $\lambda_{p}$:

$\lambda_{p}=\frac{C}{T}$   (2)

$\lambda_{p}=\frac{2.898(10)^{-3}m.K}{273K}$  

Finally:

$\lambda_{p}=10615(10)^{-9}m=10615nm$  This is the peak wavelength for radiation from ice at 273 K, and corresponds to the infrared.