- #1
En Joy
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Wien's displacement law from Plank's formula
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In summary, the conversation discusses a mistake in a book regarding the use of the "5" instead of the correct "3" in a derivation from Planck's law. The book also omits to mention the use of a different Planck equation when dealing with wavelength instead of frequency. The discussion also mentions an article that clarifies these issues and suggests flagging the book to avoid it.
- #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 wavelenght (which is not merely the one written in terms of frequency substituting [tex]c/\lambda[/tex] 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 [tex]\hbar c/\lambda k T[/tex] 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.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
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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.
1. What is Wien's displacement law and how does it relate to Planck's formula?
Wien's displacement law is an equation that describes the relationship between the wavelength at which a blackbody emits the most radiation and its temperature. It is derived from Planck's formula, which describes the energy distribution of blackbody radiation. In other words, Wien's displacement law is a more specific application of Planck's formula.
2. How is Wien's displacement law used in scientific research?
Wien's displacement law is used to determine the temperature of objects in space or in the laboratory. It is also used to analyze and interpret the spectrum of light emitted from stars and other celestial bodies, providing valuable information about their composition and temperature.
3. Can Wien's displacement law be applied to objects other than blackbodies?
No, Wien's displacement law is only applicable to ideal blackbodies, which are objects that absorb and emit all radiation that falls on them. Real objects, such as stars and planets, are not perfect blackbodies, but their radiation can often be approximated using Wien's displacement law.
4. How does Wien's displacement law relate to the peak wavelength of blackbody radiation?
Wien's displacement law states that the peak wavelength of blackbody radiation is inversely proportional to the temperature of the object. This means that as the temperature of a blackbody increases, the peak wavelength of its radiation decreases.
5. What are the practical applications of Wien's displacement law?
Wien's displacement law has many practical applications, including in the fields of astronomy, thermodynamics, and materials science. It is also used in the development of technologies such as infrared cameras and sensors, which rely on the detection of thermal radiation. Additionally, it is a fundamental concept in understanding the behavior of light and energy in various systems.
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