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I've derived Planck's Law for frequency from his law for wavelength, and I got this: $$u(f)=\frac {8\pi f^2} {c^3} \frac {hf} {e^{\frac {hf}{kT}}-1}$$

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.

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    $\begingroup$ For high frequency limit, $hf>>kT$ and for low frequency limits, $hf<<kT$. What effect these arguments produce on the exponential term? $\endgroup$ – UKH Sep 22 '16 at 5:14
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If we take the low frequency limit, i.e. $hf\ll kT$, then we can expand the exponential $$e^x\ =\ 1\ +\ x\ +\ \frac{x^2}{2}\ +\ \ldots$$ 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 $hf\gg kT$, we can ignore the $1$ in the denominator. This leads to the Wien's law.

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  • $\begingroup$ You shouldn't post complete homework solutions to such blunt problems. We are not homework-helping service. $\endgroup$ – user36790 Sep 22 '16 at 6:32
  • $\begingroup$ Sorry, I wasn't aware of the 'homework and exercises' policy that well. I'll keep this in mind. Thanks, @MAFIA36790! $\endgroup$ – Sucheta Sep 22 '16 at 6:50

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