- #1
teme92
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Homework Statement
The Planck blackbody spectrum is given by
[tex]u(ω,t)=\frac{ħω^3}{π^2c^3(e^{βħω}-1)}[/tex]
Show that the peak of the Planck spectrum for a blackbody at a temperature T occurs at the wavelength
[tex]λ_{max}T=0.29[/tex]
where T is in Kelvin and λmax is in cm.
Homework Equations
[tex]\frac{d(ω,T)}{dω}=0[/tex]
The Attempt at a Solution
So using the equation above I get down to:
[tex](3-βħω)(e^{βħω})-3=0[/tex]
This is a transcendental equation. I said:
[tex]x=βħω[/tex]
I've tried using the bisection method to solve but my answer doesn't match up with what it should as from the Wien Displacement Law it should be 0.29 for λ in cm. If anyone could help explain the solving for x, I would greatly appreciate it.