I Wien's displacement law from Plank's formula

1. Aug 19, 2015

En Joy

2. Aug 19, 2015

Staff: Mentor

Show us what you tried, and maybe someone can point out your mistake. Or we can verify that you did it correctly and the book has a mistake!

3. Aug 19, 2015

lightarrow

The "5" does not refer to the previous equation written in the book but to the one which results from the Planck's law written in terms of the wavelenght (which is not merely the one written in terms of frequency substituting $$c/\lambda$$ to the frequency).

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lightarrow

Last edited: Aug 19, 2015
4. Aug 19, 2015

En Joy

5. Aug 19, 2015

lightarrow

No, x is not that, it's $$\hbar c/\lambda k T$$ infact it then writes the Wien's displacement law in terms of wavelenght, but the book omits to write that then you should use the other Planck equation (with wavelenght) and it's a quite bad omission; I understand your concern.

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lightarrow

6. Aug 19, 2015

Avodyne

The book is wrong. If you follow the steps, the 5 should indeed be a 3.

The book is apparently trying to follow the "Derivation from Planck's Law",
https://en.wikipedia.org/wiki/Wien's_displacement_law
but used the wrong $u$ (radiance per unit frequency instead of radiance per unit wavelength).

What book is this?? Bad books like this one should be flagged and made known, so we can all avoid them.

7. Sep 10, 2016

Ranjan Das

I have noticed these discussions on Wien's displacement law (and number 3 vs 5). I happened to write an article trying to clarify these very issues last year in Journal of Chemical Education. Please take a look at it. Its reference is:
R. Das, Wavelength and frequency-dependent formulations of Wien's displacement
law, J. Chem. Educ. 92 (2015) 1130–1134.