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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 λ

_{max}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.