# Blackbody radiation over whole frequency spectrum

• CassiopeiaA
In summary, the conversation discusses the concept of black body radiation and how quantization of energy can solve the ultraviolet catastrophe. The speaker has a doubt regarding the behavior of charge particles in a black body cavity at thermal equilibrium and how they can radiate across all frequencies. The response clarifies that the assembly of harmonic oscillators in the cavity refers to the modes of the radiation field, not the electrons in the enclosure.
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

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.

CassiopeiaA said:
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).

## 1. What is blackbody radiation?

Blackbody radiation refers to the electromagnetic radiation emitted by a perfectly black, or ideal, object. It is the thermal radiation that an object emits due to its temperature, and is determined by its surface temperature and the material it is made of.

## 2. What is the whole frequency spectrum?

The whole frequency spectrum refers to the range of electromagnetic radiation that includes all possible frequencies, from the lowest radio waves to the highest gamma rays. This spectrum is continuous and has no gaps.

## 3. How is blackbody radiation distributed over the whole frequency spectrum?

According to Planck's law, the distribution of blackbody radiation over the whole frequency spectrum follows a specific curve known as the Planck curve. This curve shows that the intensity of radiation increases with frequency, reaching a peak at a certain frequency before decreasing again.

## 4. What is the significance of studying blackbody radiation over the whole frequency spectrum?

Studying blackbody radiation over the whole frequency spectrum helps us understand the physical properties of objects, such as their temperature and composition. It also has practical applications in fields such as astronomy, where the spectrum of blackbody radiation emitted by stars can reveal information about their temperature and composition.

## 5. How is blackbody radiation related to the concept of thermal equilibrium?

In thermal equilibrium, the rate of energy absorption and emission by an object is equal. Blackbody radiation is the result of this energy exchange, where the object absorbs energy at the same rate that it emits it. This is why a perfectly black object in thermal equilibrium appears to have a constant temperature and emits radiation in a continuous spectrum.

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