# Shouldn't a metal at 0K emit electromagnetic radiation?

• voila
In summary, at 0K, electrons in a metal occupy all energy levels and have a maximum velocity in k-space. This means that they are always in motion, but this does not necessarily result in radiation being emitted. The misconception that "moving charges radiate" is not always true in quantum mechanics. A charged particle will only emit radiation if it can do so while conserving energy and momentum, and if the temperature of the environment is higher than the temperature of the particle. At 0K, a metal will not radiate because it is colder than its surroundings and is instead absorbing radiation.
voila
Electrons pile up inside a metal up to a maximum value in k-space (meaning the have velocity) and occupying all levels at 0K, solving the Schroedinger equation as running waves. So electrons moving => radiation being emitted. But electrons can't move to a lower energy state, so that would mean energy being emitted without slowing the electrons down. I must be obviously not getting something.

Your reasoning correctly shows that a metal (or anything else) at 0K will *not* radiate.

voila said:
So electrons moving => radiation being emitted.

This is an oversimplification. In quantum mechanics it is not as simple as "moving charges radiate."

It may be simpler to consider an atom, because the situation is exactly the same there. Suppose we have a hydrogen atom in the ground state. The expectation value of the electron's kinetic energy is nonzero, so in some sense the electron is "moving." Nonetheless it cannot radiate because there is no lower energy state for the electron to go to.

voila
This is a common misconception about quantum mechanics in general, and the Hydrogen atom in particular. The angular momentum of the electron was interpreted as a real motion of the electron about the nucleus. The magnetic moment corresponds to a current. This interpretation was shown to be wrong and over-simplified time and again. Angular momentum, wave vectors, etc. do not imply any moving charges, hence there is no radiation emitted in the ground state or other Eigenstates of the Hamiltonian.

voila and bhobba
Thought the "real velocity" of the particle (excuse the term) was given by the group velocity of the wavefunction, which happens to be non-zero. So I don't really get when interpret this as a "moving electron" that would emitt radiation and when not, appart from comon sense.

voila said:
So I don't really get when interpret this as a "moving electron" that would emitt radiation and when not, appart from comon sense.

In some sense all particles are always "moving," because of the uncertainty principle. So in QM you should not try to use this as a guide to when charged particles will radiate.

A decent rule of thumb is probably: a charged particle will always radiate photons (at some rate) if it can do so while conserving energy and momentum.

voila
The_Duck said:
A decent rule of thumb is probably: a charged particle will always radiate photons (at some rate) if it can do so while conserving energy and momentum.

Guess you meant "if it can do so while lowering its energy (having lower energy states available) or if it has a something supplying energy" or something like that. Thanks for the help M Quack and The_Duck

You may also take into account that you can linearly combine the +k- and -k-waves of the ground state to a standing wave that does not move. (This is the same procedure that gets you the band gap in the weak potential limit.)

One way to think about it is:
Things that radiate electromagnetic waves will also absorb electromagnetic waves. (Moving electrons can also absorb light.) And they will only have a net radiation if the temperature of the thing is higher than the temperature of the surrounding environment. A metal at 0K (impossible) is colder than the surrounding environment, so it will be absorbing radiation from the environment.

## 1. Why doesn't a metal emit electromagnetic radiation at 0K?

At 0 Kelvin, also known as absolute zero, the atoms in a metal are in their lowest energy state. This means that the electrons in the metal are not moving and therefore cannot emit electromagnetic radiation.

## 2. Can a metal emit electromagnetic radiation at temperatures above 0K?

Yes, as the temperature of a metal increases, the atoms and electrons within it gain more energy and begin to move. This movement of electrons creates changes in the electric field, resulting in the emission of electromagnetic radiation.

## 3. What is the relationship between temperature and electromagnetic radiation emission in metals?

The emission of electromagnetic radiation from a metal is directly proportional to the temperature of the metal. As the temperature increases, so does the amount of radiation emitted.

## 4. Is it possible for a metal to emit electromagnetic radiation at 0K under certain conditions?

No, at 0K, the atoms in a metal are in their lowest energy state and cannot emit electromagnetic radiation. However, in theory, if the metal were to be exposed to strong external forces, such as high pressure or radiation, it may be possible for it to emit some radiation at 0K.

## 5. Why is it important to understand the emission of electromagnetic radiation from metals at different temperatures?

Understanding the emission of electromagnetic radiation from metals at different temperatures is important for various scientific and technological applications. For example, it is crucial in the development of efficient energy conversion devices, such as solar cells, and in the study of heat transfer and thermal radiation in materials.

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