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## Homework Statement

At what wavelength does a cavity at 6000 degrees Kelvin radiate most per unit wavelength?

## Homework Equations

$$\rho_T(\lambda)d\lambda=\frac{8\pi{hc}}{\lambda^5}\frac{d\lambda}{e^{{hc}/{\lambda{kT}}}-1}$$

## The Attempt at a Solution

I'm pretty new to this whole topic, so don't judge me if I'm totally off...

First off can't the $$d\lambda$$'s cancel each other out? I'm not sure why the book I am using writes this equation like they did if they could cancel out that easily, but anyways I got rid of them because it seems to just make this more confusing for me otherwise.

So I figured if it wants the wavelength for highest radiation (per unit wavelength), I should take the derivative of $$\rho_T(\lambda)d\lambda$$ with respect to the wavelength, and set that expression equal to zero.

However now I am at an impasse, seeing as how solving for lambda would probably be really difficult, and I am not even sure if I am working in the correct direction. Any help would be appreciated much. Thanks