Weins Displacement Law: Calculating Max Wavelength & Frequency

[pseudo]

in weins displacement law how can we calculate the maximum wavelength & the maximum frequency? is that equation applicable for all kinds of black body radiations even the hawking radiation ?

 

[Kurdt]

Wavelength and frequency are linked via $c=f\lambda$. As far as I know it should be applicable to Hawking radiation as well.

 

[tacman]

Wein's Displacement Law is a fundamental principle in physics that relates the maximum wavelength of radiation emitted by a black body to its temperature. This law states that the product of the maximum wavelength and the temperature of a black body is a constant, known as Wien's constant (denoted by the symbol "b"). Mathematically, this can be written as λmaxT = b.

To calculate the maximum wavelength, we can rearrange the equation to solve for λmax, which gives us λmax = b/T. Similarly, to calculate the maximum frequency, we can use the relationship between wavelength and frequency, which is given by the equation c = νλ, where c is the speed of light. Rearranging this equation to solve for the frequency (ν), we get ν = c/λ. Therefore, the maximum frequency can be calculated as νmax = c/λmax = c/(b/T) = T/b.

This equation is applicable for all kinds of black body radiations, including Hawking radiation. Hawking radiation is a type of thermal radiation predicted to be emitted by black holes due to quantum effects near the event horizon. While it is not a traditional black body radiation, it still follows Wein's Displacement Law as it is based on the temperature of the black hole.

In conclusion, Wein's Displacement Law is a powerful tool for understanding the relationship between temperature and the maximum wavelength and frequency of radiation emitted by black bodies. It can be applied to all types of black body radiations, including Hawking radiation. By using this law, we can gain a deeper understanding of the properties and behavior of various forms of radiation in the universe.