# Ultraviolet Catastrophe / Rayleigh-Jeans Black Body Cavity

## Main Question or Discussion Point

In reading about the “Ultraviolet Catastrophe” in dealing with black body radiation, my book says that at the ultraviolet frequencies and beyond, the Rayleigh-Jean equation for the energy density of the radiation would be infinite (and thus a catastrophe).
If this is the Rayleign-Jeans equation:
p(v)dv = (8 * pi * v^2 * k * T * dv) / c^3
with v being the frequency of light…how does this number come out to be infinite at some finite frequency?
For example, 1 E16 Hz would be well within the ultraviolet part of the EM spectrum. If I plug this value into the above equation I will get a very large number to be sure, but it will not be infinity. Or do they just mean that as the frequency goes to infinity, so does the energy, when we know otherwise experimentally.

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jtbell
Mentor
Objects don't radiate at a single frequency only. The problem is the total energy that you get when you integrate over all frequencies. In the classical Rayleigh-Jeans analysis, there's no upper limit on the frequency.

Last edited:
Haelfix