Max Freq & Temp Relation in Wien Displacement Law

In summary, Wien's displacement law states that the product of the maximum wavelength and temperature of a black body is equal to 2848 micrometers Kelvin. The relationship between frequency max and temperature can be obtained through the formula wavelength * frequency = speed of light. Using this formula and Wien's law, we can convert wavelength max to frequency max and determine the relationship between omega max and temperature.
  • #1
yellowgold
12
0
In Wien displacement law we know that

wavelength max * Temperature = 2848 micrometer Kelvin

How we can get the relationship between frequency max and Temperature ?
 
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  • #2
For a black body the shape of the amount of radiation at each wavelength only depends on the temperature.
The shape of the curve changes with temperature but the position of the peak happens to increase linerarly with temperature.

Edit - sorry did you just mean what's the relationship between wavelength and frequecny?
wavelength * frequency = speed of light (make sure you have the same distance units)
 
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  • #3
Mgb thank you for your answer but I meant that how can I get it by formula. I have Planck spectrum formula SB law and wien law but i don't how how I can covert wavelength max to frequency max and state relationship omega max and temp. ?
 
  • #4
wavelength * frequency = c (the speed of light)
ie wavelength = c/f
so substiuting in Wein's law
(c/f)* T = 2.848 mm kelvin

or, f = cT/2.848mm ( you will need to use c in mm/s)

Wein's law is only quoted in terms of wavelength because 3mm is such an easy constant to remember instead of it's equivalent in teraHz
 

1. What is the Wien displacement law?

The Wien displacement law is a principle in physics that describes the relationship between the wavelength at which an object emits the most radiation and its temperature. It states that the product of the peak wavelength and the temperature of an object is constant.

2. How is the Wien displacement law used in scientific research?

The Wien displacement law is used in various fields of science, such as astrophysics and thermodynamics, to study the temperature and spectral properties of objects. It can also be used to determine the temperature of stars and other celestial bodies by analyzing their emitted radiation.

3. What is the significance of the maximum frequency and temperature relationship in the Wien displacement law?

The maximum frequency and temperature relationship is significant because it allows scientists to understand the thermal properties of objects and determine their temperature based on their radiation. This relationship also helps in the study of blackbody radiation, which is the idealized emission of radiation from a perfectly absorbing and emitting object.

4. How does the Wien displacement law relate to the Stefan-Boltzmann law?

The Wien displacement law and the Stefan-Boltzmann law are both based on the concept of blackbody radiation. The Wien displacement law describes the peak wavelength of the radiation emitted by an object, while the Stefan-Boltzmann law describes the total energy emitted by an object at a given temperature.

5. Can the Wien displacement law be applied to all objects?

The Wien displacement law is applicable to all objects that emit thermal radiation, including stars, planets, and even everyday objects. However, it is most accurate for objects that behave like ideal blackbodies, meaning they absorb and emit all radiation that falls on them. Real objects may deviate from this behavior and therefore, the Wien displacement law may not be as accurate.

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