Wien's displacement law from Plank's formula

[En Joy]

 

[jtbell]

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!

 

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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 wavelength (which is not merely the one written in terms of frequency substituting $$c/\lambda$$ to the frequency).

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[En Joy]

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!

 

[lightarrow]

View attachment 87553

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

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[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.

 

[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.