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Deriving Wien's Law from Planck's Formula 
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#1
Apr406, 10:01 PM

P: 26

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})(\f rac{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 lefthand 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 


#2
Apr506, 04:07 AM

Sci Advisor
HW Helper
P: 11,927

Yes, you're dealing with a typical transcendental equation, to which exact solutions cannot be found in most cases, this one included.
Daniel. 


#3
Dec511, 12:21 AM

P: 1

http://en.wikipedia.org/wiki/Wien_approximation
check this link you will see why the 5kt(lamda) shouldnt be there 


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