# Homework Help: Blackbody radiation derivative exercise

1. Sep 6, 2012

### Syrus

1. The problem statement, all variables and given/known data

The problem (18.1a) can be found here:

http://www.suagm.edu/umet/paginas/dbacelo/chem464/scan-probcap18-levine-pag1.pdf [Broken] .

For reference, the equation (referred to as 18.2 in the problem statement) for the frequency distribution of blackbody radiation is give as:

R(v)=(2∏h/c2)v3/(ehv/kT-1)

2. Relevant equations

3. The attempt at a solution

To show that vmax is of the form kTx/h, the derivative of R(v) with respect to v is taken and set equal to zero. This equation is then solved for v (or, what should now be referred to as vmax). Using the quotient rule we have, after some simplifications (as the derivative of R(v) with respect to v): 3(ehv/kT-1) = (vh/kT)ehv/kT.

I am having trouble solving this equation for v (in this case v = vmax). Any suggestions?

Last edited by a moderator: May 6, 2017
2. Sep 6, 2012

Anybody?