Blackbody radiation over whole frequency spectrum

[CassiopeiaA]

I was studying black body radiation and how quantization of energy solves the problem of ultraviolet catastrophe. But I have a very fundamental doubt. A black body can be assumed as a cavity with a small hole with radiation leaking out of it. As the temperature of the black body is increased we can assume the the charge particles, electrons, on the metal surface will behave as harmonic oscillators and the energy of the harmonic oscillation will be equal to the energy density of the radiation inside the cavity at thermal equilibrium.

My doubt is that at thermal equilibrium, the cavity(assuming it to be uniform) will have a uniform temperature. Since the oscillations of the charged particles is due to the thermal agitation, how can the charge particles radiate all over the frequency range? The temperature is uniform over the cavity, won't they all be experiencing same thermal agitation and oscillate at same frequency

 

[Nugatory]

The average energy of the particles mat be the same, but at any given monent some of the particles will carry more energy than the average and others less.

 

[WannabeNewton]

Since the oscillations of the charged particles is due to the thermal agitation, how can the charge particles radiate all over the frequency range?

The cavity consists of an enclosure that is in thermal equilibrium with electromagnetic radiation consisting of a discrete spectrum of modes. The electrons in the enclosure are constantly absorbing radiation of all available modes and remitting the radiation across all absorbed modes. This is the necessary situation if we wish to use equilibrium statistical mechanics. Thus the assembly of harmonic oscillators in the cavity refers to the modes of the radiation field, not the electrons in the enclosure (atomic vibrations in a lattice can be regarded as an assembly of harmonic oscillators but this is immaterial to the problem of blackbody radiation).