# Ultraviolet catastrope

1. Nov 18, 2004

### saiarun

How did Max Planck tackled the Ultra Violet catastrope? In one of the book I have read, it said that he considered the assumption of equal distribution of energy. Can you please Explain in detail.

2. Nov 18, 2004

### RedX

I think you mean Planck considered the assumption of equal energy units for each allowed frequency. So if f is an allowed frequency, the allowed energies for that mode are hf, 2hf, 3hf, 4hf, etc. That way at higher frequencies, since the smallest unit of energy (besides zero) is pretty big, the probability of occupation of this high energy state is low, so the expected energy for that state is low. Basically you have to treat things quantum mechanically, and not classically. If for each frequency you allow any energy, as in E=.5*m*w^2*x^2+.5*m*v^2 for a classical oscillator, then classical physics says the expected energy will be kT (kT/2 for storage as potential energy and kT/2 as storage for kinetic energy). As you increase frequency, the wavelength goes down, and is better able to fit in a box, and there are an infinite number of high frequency modes, and if each had kT, then the expected energy, which is the sum of the expected energy of all the modes, would go to infinity, and that's catastrophic, for everytime you open your oven, you'll be...well done.

Last edited: Nov 18, 2004
3. Nov 18, 2004

### chroot

Staff Emeritus