
#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: 11,863

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 


Register to reply 
Related Discussions  
The determination of frequency v from Planck's formula  Advanced Physics Homework  0  
Planck's Radiation Formula  Quantum Physics  4  
Planck's Formula  Help undressing the question needed!  Introductory Physics Homework  2  
question about the meaning of planck's formula  Quantum Physics  3  
Need some help on Planck's Formula  Introductory Physics Homework  9 