- #1
Piano man
- 75
- 0
Planck's radiation law:
[tex]I(\lambda)=\frac{2\pi hc^2}{\lambda^5(e^{\frac{hc}{\lambda kT}}-1)}[/tex]
I'm trying to calculate the peak of a graph, so setting the derivative equal to 0, I've gotten it down to
[tex]\frac{\lambda(e^{\frac{\alpha}{\lambda}}-1)}{e^{\frac{\alpha}{\lambda}}}=\frac{\alpha}{5}[/tex]
where [tex]\alpha=hc/kT[/tex]
Is it possible to solve for [tex]\lambda[/tex]?
[tex]I(\lambda)=\frac{2\pi hc^2}{\lambda^5(e^{\frac{hc}{\lambda kT}}-1)}[/tex]
I'm trying to calculate the peak of a graph, so setting the derivative equal to 0, I've gotten it down to
[tex]\frac{\lambda(e^{\frac{\alpha}{\lambda}}-1)}{e^{\frac{\alpha}{\lambda}}}=\frac{\alpha}{5}[/tex]
where [tex]\alpha=hc/kT[/tex]
Is it possible to solve for [tex]\lambda[/tex]?