Talk:Wien's displacement law

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[edit] Alternative form correction

Since

{\nu_{max}} \not= {c\over\lambda_{max}}

I deleted the alternative form section (sorry, metacomet). It is possible to derive a frequency version of Wien's law, but I don't have it on hand at the moment. ...and I forgot to do an edit summary, so that's mostly the reason for this entry. ...wow, I am soo inept. --UltraHighVacuum 02:54, 23 February 2006 (UTC)

Don't apologize for fixing something that was incorrect. If it's wrong, it's wrong. I didn't write that section, I merely updated it so that it was possible to follow the logic. I didn't realize that the logic was flawed, or I would have removed it myself. -- Metacomet 10:18, 23 February 2006 (UTC)
On the other hand, it depends on what the definition of nu-max is. If it is the frequency of peak emission, then perhaps you are correct. But if the definition is the frequency that corresponds to the wavelength of peak emission, then the section that you removed was actually correct as written, although it would probably need a brief explanation of the difference in definitions. -- Metacomet 10:21, 23 February 2006 (UTC)
I have added a new, corrected section entitled "Frequency form" to the article. The source is Weisstein's World of Physics, and the information is consistent with the discussion below. -- Metacomet 11:10, 23 February 2006 (UTC)
In all my experience (and quantumm mechanics books)nu max is defined as the actual maximum frequency, so this was my motivation. It seems a definition of nu-max as being the corresponsing frequency for lambda max is confusing, and maybe also a bit arbitrary, since there is no reason for the definition not to be the other way around. But you're right, this is kind of ambiguous, so thanks for that section in the article. --UltraHighVacuum 18:04, 23 February 2006 (UTC)
Isn't that exactly what the new section says? -- Metacomet 23:07, 23 February 2006 (UTC)

Your frequency version is incorrect.

{\nu_{max}} \not= {c\over\lambda_{max}}

That is because the curves for frequency and wavelength are different. In fact, using a similar derivation it can be shown that

{ \partial u \over \partial \nu}= (3-{{h\nu_{max}}\over\ kT})e^{{{h\nu_{max}}\over\ kT}}-3=0

This gives

{ \nu_{max}= {2.8kT \over\ h}}

It turns out that

{C\lambda_{max} \over\ \nu_{max}} \approx 1.76

I will go ahead and make the changes, but it would still be nice for someone to check me on this. --129.93.63.14 23:08, 9 February 2006 (UTC)

Any point is putting the frequency version in?

f_{max} \approx 10^{11} T

--Audiovideo 13:09, 16 May 2005 (UTC)


It's said that "This equation cannot be solved in terms of elementary functions. It can be solved in terms of Lambert's Product Log function but an exact solution is not important in this derivation. One can easily find the numerical value of x"

But this derivation is horrible. Looking back at history einstein used the wien displacement law in his paper on radiation, but in no was was the wien displacement law a derivation from plancks radiation theory. This should be noted. I suck at writing or else i would.

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