How do you convert Planck's Radiation Formula into terms of wavelength?

In summary, to make Planck's Law in terms of wavelength, you need to substitute dv with -d(lambda) and then integrate over u(lambda) d(lambda). This is because u(v) dv is equal to c^3 / 8\pi v^3 (e^(hc/kT)-1) and by using the relation u = c/lambda, you can get dnu = -c/lambda^2 dlambda.
  • #1
nadeemo
19
0
Okay, so I know that Planck's Law states that,

u(v) dv = 8[tex]\pi[/tex] v[tex]^{}3[/tex] / c[tex]^{}3([/tex]e[tex]^{}(hc/kT)[/tex]-1)

to make this formula in terms of wavelength, do you just plug in c = v[tex]\lambda[/tex], or is there more to it? because what I get is not what I find on the net to be correct.
 
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  • #2
sry for the bad looking equation, I am new to the forum :P
 
  • #3
you cannot simply substitute because you are missing the dv, in the right hand side of the formula.

sure, you can just put lambda in terms of v, but at the end, you want to integrate over u(lambda) d lambda, so you need to change dv to dlambda, and that introduces the extra factors you found on the internet.
 
  • #4
so how should i change u(v)dv to u(lambda)d(lambda)

i found a relation
1.png


2.png


so i just replace dv with negative d(lambda)??
and then integrate?
 
  • #5
[tex]\nu = \frac{c}{\lambda}[/tex]

[tex]\frac{d \nu}{d \lambda} = - \frac{c}{\lambda^2}[/tex]

Therefore

[tex]d \nu = - \frac{c}{\lambda^2} d \lambda[/tex]
 

1. What is Planck's Radiation Formula?

Planck's Radiation Formula, also known as Planck's Law, is a mathematical equation that describes the spectral energy density of electromagnetic radiation emitted by a blackbody at a certain temperature. It was developed by German physicist Max Planck in 1900 and is considered one of the fundamental principles of quantum mechanics.

2. How does Planck's Radiation Formula work?

Planck's Radiation Formula takes into account the discrete nature of energy and the idea that electromagnetic radiation is made up of individual packets of energy, called photons. It relates the energy of a photon to its frequency and temperature of the blackbody, and describes the distribution of energy across different wavelengths of radiation.

3. What is a blackbody?

A blackbody is an idealized object that absorbs all incoming radiation and emits electromagnetic radiation at all wavelengths. This means that a blackbody is a perfect emitter and absorber of radiation. Planck's Radiation Formula was originally developed to describe the behavior of blackbodies, but it has also been found to accurately describe the radiation emitted by other objects, such as stars and planets.

4. What are the applications of Planck's Radiation Formula?

Planck's Radiation Formula has many applications in physics and engineering, including predicting the heat transfer between objects, calculating the energy output of stars, and understanding the behavior of light in different materials. It is also used in the field of astrophysics to study the thermal radiation emitted by objects in space.

5. Is Planck's Radiation Formula still relevant today?

Yes, Planck's Radiation Formula is still widely used and considered a fundamental principle in modern physics. It has been tested and verified through numerous experiments and is essential for understanding many phenomena, such as blackbody radiation, the photoelectric effect, and the quantization of energy. It also serves as the basis for more complex equations, such as the Boltzmann distribution and the Bose-Einstein distribution.

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