High School

At 10.1 µm wavelength of maximum radiation emission, what are the corresponding temperatures (in K)?

Answer :

The wavelength of maximum radiation emission, known as the peak wavelength, is directly related to the temperature of an object according to Wien's displacement law.

Wien's law states that the product of the peak wavelength and the temperature is constant. Using this relationship, we can determine the corresponding temperatures for a given wavelength.

In the case of a wavelength of 10.1 µm (micrometers) or 10.1 x 10^-6 meters, we can apply Wien's displacement law. The constant in Wien's law is approximately 2.898 × 10^-3 m·K. Dividing this constant by the given wavelength (10.1 x 10^-6 meters) gives us the corresponding temperature.

Calculating the temperature:

Temperature = Constant / Wavelength

Temperature = 2.898 × 10^-3 m·K / 10.1 x 10^-6 meters

Temperature ≈ 28645.5 K

Therefore, at a wavelength of 10.1 µm, the corresponding temperature is approximately 28645.5 Kelvin (K).

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