Question

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

Answer 1

Answer: 10615 nm

Step-by-step 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)=(C)/(T)` (2)

`\lambda_(p)=(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.