Blackbody radiation derivative exercise

[Syrus]

Homework Statement

The problem (18.1a) can be found here:

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

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/(e^hv/kT-1)

Homework Equations

The Attempt at a Solution

To show that v_max 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 v_max). Using the quotient rule we have, after some simplifications (as the derivative of R(v) with respect to v): 3(e^hv/kT-1) = (vh/kT)e^hv/kT.

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

 

[Syrus]

Anybody?