# [I=(1/4)cE]? Relation between radiation emittance and energy density in a black body

1. Jul 4, 2009

### sharomi

I am looking to prove the relation
I=(1/4)cE
Where I is the radiation emittance which is the energy emitted by a black body per unit area per unit time and E is the radiation energy density (energy per wavelength summed over all wavelength/frequencies of electromagnetic radiation emitted).

I am familiar with the derivation for the intensity of a plane Electromagnetic wave: I=cE
which is just the amount of energy that flows through a unit area in a unit time and is easily understood as the total energy contained within a box of length C and unit width and height.

In this case i am trying to follow the same procedure but I don't get the above results (the relation can also be found at http://en.wikipedia.org/wiki/Planck's_law under overview except it's formulation is different: I=(1/4pi)cE

I encountered the topic in Alonso-Finn fundamental university physics in the discussion of Black body radiation and Planck's law.

If anyone can help me understand how to derive the relation at the top i'd appreciate it!