Wien's Displacement and Rayleigh-Jeans Law from Planck's Law I've derived Planck's Law for frequen

Jordon Haley

Jordon Haley

Answered question

2022-05-20

Wien's Displacement and Rayleigh-Jeans Law from Planck's Law
I've derived Planck's Law for frequency from his law for wavelength, and I got this:
u ( f ) = 8 π f 2 c 3 h f e h f k T 1
I just have a quick question about this. This problem says I need to find the low-frequency limit (which will lead to the Rayleigh-Jeans), and I need to take the high-frequency limit, which is supposed to lead to Wien's distribution.
The thing is I have no idea what the high, or low frequency limit even means, I've looked in my book, I've looked online, I'm not sure exactly what it means.

Answer & Explanation

Maeve Holloway

Maeve Holloway

Beginner2022-05-21Added 25 answers

If we take the low frequency limit, i.e. h f k T, then we can expand the exponential
e x   =   1   +   x   +   x 2 2   +  
and truncate the series at x ignoring the higher order terms. This will gives us the Rayleigh-Jeans law.
Next, if we take the high frequency limit, where h f k T, we can ignore the 1 in the denominator. This leads to the Wien's law.

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