Question

Hi everyone! I am having the darndest time figuring out the answer to a test question and am wondering if anyone can shed some light and help me out. Here is the question:
The temperature (the average kinetic energy of the molecules) of a star is evidenced by its color (its stage of life). For example, red giants are cooler than yellow stars, which are, in turn, cooler than bluish-white stars. Reconcile this fact with what you already know about the ordering of frequencies in the electromagnetic spectrum (ROY-G-BIV). Based on this result, propose a very simple mathematical equation describing the relation between the energy and frequency of electromagnetic radiation.

Thanks everyone for any help!

The average amount of radiation emitted by a star or a blackbody per unit area is given by the Wien displacement law:
(wavelength)*(temperature) = [c/(frequency)]*(temperature) = constant
Therefore
frequency = constant' * temperature
or
frequency = constant'' * (average energy of stellar surface molecules)
(The values f the three constants are different)
Note that this is similar to the Planck relation
E = h*f
(Photon energy) = (constant)*(frequency)