Average wavelength for blackbody radiation

[jimjohnson]

The maximum wavelength for blackboby radiation is .29/Temperature. Is the average wavelenght 1.84 times the maximum for all temperatures?

 

[Naty1]

Unless you have something very esoteric in mind, your premise is wrong...there is no "maximum" wavelength...see http://en.wikipedia.org/wiki/Blackbody_radiation

see the first chart at the top...or for more, try

here http://en.wikipedia.org/wiki/Wien's_Law

 

[jimjohnson]

As shown in both ref., the wavelength where the emission intensity is maximum is .29/T. But I want to know the avg wavelenght at that temperatue. So I think the wavelenght where the area under the intensity ghaph is equal on both sides would be the average, but I do not know how to calculate it from gragh equation. My estimate working back from other calculations was 1.84 times the max wavelenght.

 

[Bob S]

You can calculate the following:

Use Planck's Law for the blackbody radiation power as a function of T and λ

http://en.wikipedia.org/wiki/Planck's_law

u(T,λ) = [2hc²/λ⁵]/[e^(hc/λkT) - 1]

The average wavelength is then given by:

λ_avg = ∫λ u(T,λ) dλ / ∫ u(T,λ) dλ

where both integrals are from 0 to ∞. The appendix of the above wiki solves the important integrals.

Bob S

 

[jimjohnson]

Do you know if the average is 1.84 the maximum for all temperatures? I can not do the math. The following quote from the source may relate: This function peaks for hc = 4.97λkT, a factor of 1.76 shorter in wavelength (higher in frequency) than the frequency peak. Thanks jimj