Evaluating R(λ): What to Do When Stuck?

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To evaluate R(λ) from the given equation, it's crucial to understand that energy per unit wavelength requires a transformation of both frequency and its differential. The correct formulation is dE/dλ = (dE/dν)(dν/dλ), which highlights the need to differentiate with respect to wavelength. Participants in the discussion emphasize the importance of not simply substituting frequency with wavelength in the original equation. Clarification on the differentiation process is sought to accurately compute R(λ). Understanding these transformations is essential for solving the problem effectively.
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I was given this problem, but I don't know where to start?

R(v) = dE/dv = (8(pie)(h)(v^3)/ (c^3(e^(hv/kT-1))).
Recall that if you want the energy per unit wavelength, you cannot
simply replace the argument v with c/wavelength. Instead you must write
R(wavelength) = dE/dv = (dE/dv)(dv/d wavelength).

Evaluate R().

Any help is appreciated!
 
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You have to replace both the frequency and its differential.

Daniel.
 
And the last formula that u've written,it should have been
\frac{dE}{d\lambda}=\frac{dE}{d\nu}\frac{d\nu}{d\lambda}

Daniel.
 
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