# How does quantization of energy solve the ultraviolet catastrophe?

• Shawn Garsed
In summary, classical physics says that an electron can always emit photons with the energy E=hv, but quantum mechanics says that only certain energy levels are allowed and therefore an electron can only emit low energy photons.

#### Shawn Garsed

Hi everybody,

I have a question concerning uv catastrophe.
I know light is quantized (photons) and I know the energy of a photon depends on the frequency (E=hv). However, I don't quite understand how this 'solves' the problem of uvc. I know the emission of light in a black body is due to oscillating electrons, but how do these things all relate.

Shawn Garsed said:
Hi everybody,

I have a question concerning uv catastrophe.
I know light is quantized (photons) and I know the energy of a photon depends on the frequency (E=hv). However, I don't quite understand how this 'solves' the problem of uvc. I know the emission of light in a black body is due to oscillating electrons, but how do these things all relate.

It is simple. Classical charge radiates all frequencies if accelerated, so a low energy charge can formally radiate a photon with the energy E=hv even higher than the charge proper kinetic energy. Here quantum mechanics forbids higher frequencies, the energy conservation law is different. It suppresses high frequency intensity so the total radiated energy becomes finite.

Bob.

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So, according to classical physics, when an electron is oscillating it radiates all frequencies so long as it has enough energy, which depends on the amount of oscillation, which in turn depends on the overall temperature of the black body, but then Planck said that the amount of energy given of by an oscillating electron comes in 'packages' or photons and the energy-level of these photons depend on the amount of oscillation. And since electromagnetic waves with short wavelengths and therefore high frequencies have 'powerful' photons (E=hv), it follows that electrons can never radiate at all frequencies since their photons wouldn't be 'powerful' enough.

Is this the right picture?

Not quite.
Classical theory say that it will radiate all frequencies - but the energy of the individual photons isn't limited to the energy of individual electrons. Classically all the energy is distributed among the photons in some Gaussian distribution, so a coal fire could put out some small number of x-rays.
Quantum theory says that you can only have energy in discrete packets and more importantly this also applies to things like electrons.
A single photon comes from a single electron transition - so you can't take the energy from a few different electrons add them up and get a higher energy photon.

## 1. What is the Ultraviolet Catastrophe?

The Ultraviolet Catastrophe, also known as the Rayleigh-Jeans Catastrophe, is a problem in classical physics that arises when trying to explain the emission of radiation by a perfect blackbody. According to classical physics, the amount of radiation emitted should increase infinitely as the frequency increases, leading to a catastrophic amount of energy.

## 2. Why is it called the Ultraviolet Catastrophe?

The term "Ultraviolet Catastrophe" comes from the fact that the classical theory predicts an infinite amount of energy in the ultraviolet range, which was a major problem for physicists at the time. It was later resolved by the development of quantum mechanics.

## 3. When was the Ultraviolet Catastrophe first discovered?

The Ultraviolet Catastrophe was first predicted by Lord Rayleigh and Sir James Jeans in the late 19th and early 20th century. They were attempting to explain the distribution of energy in blackbody radiation, which had been observed to deviate from predictions at high frequencies.

## 4. How was the Ultraviolet Catastrophe resolved?

The Ultraviolet Catastrophe was resolved by the development of quantum mechanics in the early 20th century. Max Planck proposed the idea of quantized energy levels, which explained the observed distribution of energy in blackbody radiation and avoided the infinite energy problem predicted by classical physics.

## 5. What impact did the Ultraviolet Catastrophe have on the development of quantum mechanics?

The Ultraviolet Catastrophe played a crucial role in the development of quantum mechanics. It highlighted the limitations of classical physics and provided evidence for the existence of quantized energy levels, which paved the way for the revolutionary theories of quantum mechanics that followed.