Talk:Planck's law

Symbol for spectral radiance

The symbol for spectral irradiance used in the Wikipedia article of the same name is L not B. L is also the ISO 80000 recommended symbol for this quantity. This article should use L instead of B for consistency.

Equation errors?

It looks to me as though there are errors in at least one of the six "Different forms" equations. When I tried using the form that used wavelength instead of frequency, my answers were ridiculous. I'm not an expert so I don't want to change anything for fear of being mistaken, however a simple substitution of nu = c / lambda in the first equation yields an answer quite different than the equation right below it. I'm hoping someone knowledgeable will see this and take a look. 47.14.123.228 (talk) 18:23, 20 April 2023 (UTC)

There is no error. It is not the spectral densities that are equal to each other, but rather their integrals. For this reason e.g. frequency and wavelength forms are related by

$$B_{\lambda }(\lambda ,T)=-\frac{d\nu }{d\lambda }{B}_{\nu }(\nu (\lambda ),T),$$

which includes a factor from the change of variables. The relation between the different forms is discussed in the text after the table. Jähmefyysikko (talk) 18:59, 20 April 2023 (UTC)

Thanks for the clarification. I understand. 47.14.123.228 (talk) 14:47, 26 April 2023 (UTC)

Another Equation Error?

In the fractional bandwidth form for Planck's function, the numerator of the second factor is x⁴. I think it ought to be x³. The integral of Planck's function w.r.t. ν is the Stefan-Boltzmann law, and the coefficient of T⁴ after integration is the Stefan-Boltzmann constant σ. With the numerator being x⁴, the constant is wrong, and contains a factor of ζ(5). With the numerator being x³ the constant after integration is the Stefan-Boltzmann constant. — Preceding unsigned comment added by Van.snyder (talk • contribs) 04:02, 5 November 2023 (UTC)

its distribution with respect to ln(x) so you have an extra x. EditingPencil (talk) 03:16, 6 November 2023 (UTC)

Also constants follow from Planck's spectral radiance law for frequency. B_ln(x) = B_nu d(nu)/d(lnx). Please don't mind my lazy reply ;p EditingPencil (talk) 03:22, 6 November 2023 (UTC)

Bibliography for "Planck, M. (1901)" link not yet available

In Bibliography for "Planck, M. (1901)", as original Ando file is not yet available,

I propose to add a link to a new translated version on wikimedia, which respects as faithfully as possible the form of the german original:

https://upload.wikimedia.org/wikipedia/commons/4/4e/On_the_Law_of_the_Energy_Distribution_in_the_Normal_Spectrum.pdf

(https://commons.wikimedia.org/wiki/File:On_the_Law_of_the_Energy_Distribution_in_the_Normal_Spectrum.pdf) Malypaet (talk) 21:47, 18 October 2023 (UTC)

Typo on graph

It seems there is a typo error on the ordinate-axis of the spectral radiance graph, namely, numeral 22 should be 2 and numeral 44 should be 4. Esem0 (talk) 06:03, 2 January 2024 (UTC)

Planck's law of black-body radiation

Can I add this note in the page

https://duckduckgo.com/?t=ffab&q=black-body+radiation

He discoverd this on October 19 1900... but not noted in the page Scottsdesk (talk) 22:31, 21 August 2024 (UTC)

There's an obvious error in the equations of intensity vs wavelength and frequency.

Either the intensity vs wavelength equation is correct, or the intensity vs frequency equation is correct. But the two, as shown here, are NOT mathematically equivalent. One of them is wrong.

The one shown for frequency is $B_{\nu }(\nu ,T)=\frac{2h{\nu }^3}{c^2}\frac{1}{e^{h\nu /(k_{\mathrm{B}}T)}-1}$

The one shown for wavelength is $B_{\lambda }(\lambda ,T)=\frac{2h{c}^2}{{\lambda }^5}\frac{1}{e^{hc/(\lambda k_{\mathrm{B}}T)}-1}$

Each equation has 2 fractions. The second fractions are equivalent. That is $\frac{1}{e^{h\nu /(k_{\mathrm{B}}T)}-1}$ is indeed equivalent to $\frac{1}{e^{hc/(\lambda k_{\mathrm{B}}T)}-1}$. But the first fractions are not equivalent.

That is, $\frac{2h{\nu }^3}{c^2}$ is not equivalent to $\frac{2h{c}^2}{{\lambda }^5}$.

If you break down the power raising (like v^3 broken down into v*v*v) you will be able to see where the problem is. The one in terms of frequency is (2*h*v*v*v)/(c*c), and the one in terms of wavelength is (2*h*c*c)/(wl*wl*wl*wl*wl) where "wl" means wavelength. And remember, that v=c/wl. So if you try to convert (2*h*v*v*v)/(c*c) to be in terms of wl instead of in terms of v, you will do the following simple algebra.

Starting at (2*h*v*v*v)/(c*c)

Replace every v with c/wl like this (2*h*c*c*c)/(wl*wl*wl*c*c)

Then several of the c's will cancel out like this (2*h*c)/(wl*wl*wl).

Putting it back in terms of powers instead of multiplication, you get this $\frac{2hc}{{\lambda }^3}$.

And I can definitely say that $\frac{2hc}{{\lambda }^3}$ is NOT equal to $\frac{2h{c}^2}{{\lambda }^5}$.

Now this doesn't prove WHICH of the original equations is the correct one, only that one of them must NOT be correct, because the two are NOT equivalent, and they MUST be equivalent for both of them to be correct.

Now I myself don't know which of the equations is the wrong one, so hopefully an actual physics professor, who knows the CORRECT equations, will also be reading this, and help out by fixing the wrong equation. That way, this Wikipedia article will FINALLY have the correct equations in it. Benhut1 (talk) 10:47, 12 April 2025 (UTC)

Indeed these are not equivalent, because these are not the same functions. This is explained in the article here, where

$\frac{B_{\lambda }(T)}{B_{\nu }(T)}=\frac{c}{{\lambda }^2}=\frac{{\nu }^2}{c}$

Headbomb {t · c · p · b} 14:04, 12 April 2025 (UTC)