Prove Wien Displacement Law & Find x with Plank's Formula

In summary, the Wien Displacement Law is a scientific principle that states the wavelength at which a blackbody emits the maximum amount of radiation is inversely proportional to its absolute temperature. It was derived by the Austrian physicist Wilhelm Wien in 1893 using a mathematical analysis of blackbody radiation. Plank's Formula is a mathematical equation that describes the spectral energy density of blackbody radiation and can be used to find the peak wavelength of radiation emitted by a blackbody at a specific temperature. This information is significant in understanding the behavior of blackbody radiation and has various applications in fields such as astrophysics and thermodynamics.
  • #1
vahide
5
0
could you prove this
[tex]\lambda_{max}[/tex]*T=constant=x
and find x
by planks formula?
 
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  • #2
Yes, you can. You need to take the derivative wrt to [tex] \lambda [/tex] and solve.
 

1. What is the Wien Displacement Law?

The Wien Displacement Law is a scientific principle that states the wavelength at which a blackbody emits the maximum amount of radiation is inversely proportional to its absolute temperature. In simpler terms, as the temperature of a blackbody increases, the peak wavelength of its emitted radiation shifts to shorter wavelengths.

2. How is the Wien Displacement Law proven?

The Wien Displacement Law was derived by the Austrian physicist Wilhelm Wien in 1893. He used a mathematical analysis of the thermodynamic properties of blackbody radiation to come up with the law.

3. What is Plank's Formula?

Plank's Formula is a mathematical equation that describes the spectral energy density of blackbody radiation. It takes into account the temperature of the blackbody and the wavelength of the emitted radiation.

4. How is Plank's Formula used to find x?

In order to find x, which represents the peak wavelength of radiation, we can rearrange Plank's Formula to solve for x. The equation is x = b/T, where b is a constant known as Wien's displacement constant and T is the absolute temperature of the blackbody.

5. What is the significance of solving for x with Plank's Formula?

Solving for x with Plank's Formula allows us to determine the peak wavelength of radiation emitted by a blackbody at a specific temperature. This information is important in understanding the behavior of blackbody radiation and can be applied in various fields such as astrophysics and thermodynamics.

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