The peak of the thermal radiation power spectrum (dR/dλ)

[Andres123]

Homework Statement

The peak of the thermal radiation power spectrum (dR/dλ) is at a wacelength of about λ_m=hc/5kT. Why is the peak of the same power spectrum plotted as dR/df not at f_m=c/λ_m= 5kT/h?

Homework Equations

dR/dλ= 2πhc²/(λ⁵(e^(hc/λkT)-1))
f=c/λ

The Attempt at a Solution

 

[BvU]

Hello Andres, welcome to PF

The idea at PF is that you post your efforts under attempt at solution and that helps us to guide you further as best we can. After all, you don't want someone else to do the exercise for you -- you want to learn by doing the exercise. See the guidelines for more info.

In the mean time: how do you find a peak ? What is the expression for dR/df ?

 

[Andres123]

the equation for dR/df= 2πhf³/(c²(e^hf/kt-1))
I am currently trying to differentiate both equation and setting them equal to zero to see if i find a relationship or reason for this. so far no success

 

[BvU]

Also think about the relationship between df and d$\lambda$

Spoiler

I strongly advise you not to fall for this and explore by yourself. Spoilers are exactly what the name says.You are much better of thinking this over than getting the answer on a plate

Spoiler

Here is a thread from before you joined -- same subject. You see it's causing some confusion with others too...