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## Homework Statement

Show that the maximum of the Planck energy density occurs for a wavelength of the form λ

_{max}= b/T, where T is the temperature and b is a constant that needs to be estimated.

## Homework Equations

Planck energy density

u (v,T) = 8πv

^{2}/ c

^{3}* hv / e

^{hv/kT}-1

## The Attempt at a Solution

v= c / λ

dv = |dv / (dλ)| dλ = (c/λ

^{2}) dλ

I get up to this bit and I'm stuck...

v= c / λ

c = v*λ

∴ v = v*λ / λ

dv = dv*dλ / dλ

dv = (dv / dλ) * dλ

I'm confused how dv = |dv / (dλ)| dλ turns into (c/λ

^{2}) dλ. Sorry if my question is a bit vague -- haven't posted on here in a while and I just started taking QM.