Express Planck's Law for blackbody radiation in terms of frequency

Asked Jan 28 '16 at 01:14

Active Jan 28 '16 at 02:52

Viewed 67 times

I'm having trouble with substituting $\lambda$ with frequency.

The problem:

Show that $$u(f)=\frac{8\pi f^2}{c^3} * \frac{hf}{e^{hf/kT}-1}$$

Where I'm at:

$$\frac{8 \pi f^2}{c^3} * \frac{hf^3}{ce^{hf/kT}-1}$$

As you can see, the left half of my solution matches what I'm supposed to get but there is a $\frac{f^2}{c}$ on the right side that I can't seem to eliminate. I used the relation $\lambda = c/f$ to do all this.

Side note - if anyone could make a tag for Planck's law that's be great. Or something related to this problem, like deriving equations....idk.

edited Jan 28 '16 at 02:52

Qmechanic

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asked Jan 28 '16 at 01:14

whatwhatwhat

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Isn't this one of those $F(x)dx=f(y)dy$ things? – Kyle Kanos Jan 28 '16 at 01:21
@KyleKanos not sure. But it's really just the derivation of a well known equation, I just can't seem to figure it out. – whatwhatwhat Jan 28 '16 at 02:23
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Possible duplicate of Planck's Law in terms of wavelength – ACuriousMind Jan 28 '16 at 02:25
@ACuriousMind I would have loved it if that question had solved my problem, but alas, it did not. The end result I am supposed to reach has an $8\pi$ in it and the other answer does not. It's very similar, but there seems to be some element missing that would explain where that $8\pi$ comes from. – whatwhatwhat Jan 28 '16 at 04:02

Express Planck's Law for blackbody radiation in terms of frequency

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