- #1
En Joy
- 16
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Wien's displacement law from Plank's formula
- Context: Undergrad
- Thread starter En Joy
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- Displacement Formula Law
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Discussion Overview
The discussion revolves around the derivation of Wien's displacement law from Planck's formula, specifically addressing discrepancies in a textbook's presentation of the equations. Participants explore the implications of using different formulations of Planck's law, particularly in terms of wavelength versus frequency.
Discussion Character
- Debate/contested
- Technical explanation
- Conceptual clarification
Main Points Raised
- Some participants suggest that the textbook contains an error regarding the use of the number "5," indicating it should be "3" based on the correct application of Planck's law.
- Others argue that the discrepancy arises from the book's failure to clarify the distinction between using Planck's law in terms of frequency versus wavelength.
- A participant mentions a specific equation involving \hbar, c, \lambda, k, and T, asserting that the omission of this detail in the textbook is significant.
- One participant references their own article that addresses these issues, suggesting it may provide further clarification on the topic.
Areas of Agreement / Disagreement
Participants express disagreement regarding the correctness of the textbook's presentation of Wien's displacement law, with multiple competing views on the implications of using different formulations of Planck's law. No consensus is reached on the accuracy of the textbook or the correct interpretation of the equations.
Contextual Notes
Limitations include potential missing assumptions about the context in which Planck's law is applied, as well as unresolved mathematical steps related to the derivation of Wien's displacement law.
- #2
jtbell
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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
lightarrow
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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).En Joy said:
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- #4
En Joy
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jtbell said: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!
- #5
lightarrow
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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.En Joy said:
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- #6
Avodyne
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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.
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
Ranjan Das
- 1
- 2
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.
R. Das, Wavelength and frequency-dependent formulations of Wien's displacement
law, J. Chem. Educ. 92 (2015) 1130–1134.
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