# Deriving Wien's Law from Planck's Formula

by Dorje
Tags: deriving, formula, planck, wien
 P: 26 As a refresher exercise in modern physics, I want to derive Wien's displacement law: $$\lambda_{max}T=2.898x10^{-3}mK$$ from Planck's formula: $$R(\lambda)=(\frac{c}{4})(\frac{8\pi}{\lambda^4})(\frac{hc}{\lambda})(\f rac{1}{\exp^(\frac{hc}{\lambda\kT})-1})$$ by differentiating R($$\lambda$$) and setting dR/d$$\lambda$$ = 0. I get to an expression like this: $$\exp^(\frac{hc}{\lambda\kT})(hc - 5kT\lambda)+5kT\lambda=0$$ If it wasn't for the "5kT$$\lambda$$" term by itself on the left-hand side of the equation, the solution would simply be: ($$\lambda$$) (T) = hc / 5k which is Wien's law. There must be something wrong though, or maybe there's a trick involved that I'm not seeing? Thanks