As a refresher exercise in modern physics, I want to derive Wien's displacement law:(adsbygoogle = window.adsbygoogle || []).push({});

[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

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# Deriving Wien's Law from Planck's Formula

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