As a refresher exercise in modern physics, I want to derive Wien's displacement law: [tex]\lambda_{max}T=2.898x10^{-3}mK[/tex] from Planck's formula: [tex]R(\lambda)=(\frac{c}{4})(\frac{8\pi}{\lambda^4})(\frac{hc}{\lambda})(\frac{1}{\exp^(\frac{hc}{\lambda\kT})-1})[/tex] by differentiating R([tex]\lambda[/tex]) and setting dR/d[tex]\lambda[/tex] = 0. I get to an expression like this: [tex]\exp^(\frac{hc}{\lambda\kT})(hc - 5kT\lambda)+5kT\lambda=0[/tex] If it wasn't for the "5kT[tex]\lambda[/tex]" term by itself on the left-hand side of the equation, the solution would simply be: ([tex]\lambda[/tex]) (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
Yes, you're dealing with a typical transcendental equation, to which exact solutions cannot be found in most cases, this one included. Daniel.
http://en.wikipedia.org/wiki/Wien_approximation check this link you will see why the 5kt(lamda) shouldnt be there