Is there way to thermalize an electron to room temperature?

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Discussion Overview

The discussion revolves around the possibility of thermalizing an electron to room temperature, exploring the implications of electron behavior at low energies, and the statistical mechanics governing electrons in metals. It touches on concepts from quantum mechanics, thermodynamics, and particle physics.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants note that at room temperature, the energy of particles is approximately 0.025 eV, and question the feasibility of cooling free electrons to such low velocities.
  • It is mentioned that bound electrons do not have a well-defined speed and their kinetic energy expectation value is generally above 1/40 eV, which is independent of temperature.
  • Participants discuss the existence of free thermal electrons in metals and the misconception that they have zero kinetic energy.
  • There is a claim that electrons at absolute zero would occupy the lowest energy states permitted by the Pauli exclusion principle.
  • Some participants argue that electrons in metals obey Fermi-Dirac statistics rather than Boltzmann distribution, which is relevant for understanding their energy distribution.
  • A hypothesis is presented regarding the interaction of electrons with protons or positive ions, suggesting a mechanism for electron capture and nuclear transmutation, though this is contested by others who assert that electrons are not classical particles.
  • There is a discussion about the specific heat contributions of neutrons and electrons in metals, with references to historical developments in statistical mechanics.

Areas of Agreement / Disagreement

Participants express multiple competing views regarding the thermalization of electrons, their statistical behavior, and the implications of their interactions with other particles. The discussion remains unresolved with no consensus reached.

Contextual Notes

Some claims depend on specific definitions of thermalization and kinetic energy, and there are unresolved assumptions regarding the behavior of electrons at low temperatures and their interactions with other particles.

kiwaho
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At room temperature, particle energy is 0.025eV.
Neutron capture reaction has big cross section when neutron is in room temperature. Theoretically, so does an electron. At 0.025eV, the electron velocity should be only 93.78km/s.
Unfortunately almost no way to cool down an free electron to so low velocity, even an outermost orbital electron of atom runs at least 1000km/s above, e.g. 2190km/s for hydrogen electron.
In absolute 0K temperature, do the atom orbital electrons no longer move and become standstill?
 
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Bound electrons do not have a well-defined speed, this is independent of the temperature of the material. They have an expectation value for the kinetic energy, which is above 1/40 eV in most (but not all) cases, but this is not related to a temperature.

Free thermal electrons exist (just heat a metal wire), and in metals you have "free" (only constrained to the metal) electrons with (nearly) zero kinetic energy.
 
mfb said:
Bound electrons do not have a well-defined speed, this is independent of the temperature of the material. They have an expectation value for the kinetic energy, which is above 1/40 eV in most (but not all) cases, but this is not related to a temperature.

Free thermal electrons exist (just heat a metal wire), and in metals you have "free" (only constrained to the metal) electrons with (nearly) zero kinetic energy.
Are you sure the "free" electron in metal has zero momentum? I don't think so.
 
In absolute 0K temperature, do the atom orbital electrons no longer move and become standstill?
No. The electrons would be at the lowest state permitted by Pauli exclusion.
 
kiwaho said:
Are you sure the "free" electron in metal has zero momentum? I don't think so.
Some of them do. Others have more.

The states start at zero kinetic energy, and get filled until all electrons have some state. The highest filled states are typically at kinetic energies way above thermal energies, but there are lower states as well.
 
mfb said:
Some of them do. Others have more.

The states start at zero kinetic energy, and get filled until all electrons have some state. The highest filled states are typically at kinetic energies way above thermal energies, but there are lower states as well.
So, it sounds they obey Boltzmann distribution. I see. thank you!
 
They do not, they follow the Fermi-Dirac statistics, where the actual energy distribution is given by the density of states in the metal which depends on its crystal structure.
 
Sure, electrons in your room are thermalized to room temperature.
 
If a proton or positive ion appears nearby an "standstill" free electron, of course, the electron will begin to run to embrace the proton or ion, but it never falls bluntly onto proton or ion, instead be bound to orbit. I think that is because the electron is accelerated too far above room temperature, e.g. 13.6eV or more.
If we could exert a pull back force to counteract the electric suck force while they are meeting together, then it would be possible to see the electron slowly landing on the nucleus surface without having to be bound to orbit, and then see nuclear transmutation (electron capture beta decay).
 
  • #10
kiwaho said:
So, it sounds they obey Boltzmann distribution. I see. thank you!
In fact, the electrons in a metal are one of the first examples in history of statistical mechanics, where Fermi-Dirac statistics rather than classical Maxwell-Boltzmann statistics must be applied. It solved the long-standing puzzle why the electrons do not significantly contribute to the specific heat of metals at room temperature. It saved the otherwise successful Drude theory of electric and heat conductivity. This discovery is due to Sommerfeld.
 
  • #11
vanhees71 said:
In fact, the electrons in a metal are one of the first examples in history of statistical mechanics, where Fermi-Dirac statistics rather than classical Maxwell-Boltzmann statistics must be applied. It solved the long-standing puzzle why the electrons do not significantly contribute to the specific heat of metals at room temperature. It saved the otherwise successful Drude theory of electric and heat conductivity. This discovery is due to Sommerfeld.
Neutron is Fermion too, so it should also obey the same statistics, and it will not significantly contribute to the specific heat of the metal U-235 of a fissile fuel.
But the fact is that all neutrons can precisely be thermalized to 0.025eV without an obvious distribution, as well as the specific heat is affected.
 
  • #12
kiwaho said:
If we could exert a pull back force to counteract the electric suck force while they are meeting together, then it would be possible to see the electron slowly landing on the nucleus surface without having to be bound to orbit, and then see nuclear transmutation (electron capture beta decay).
No, that does not work. Electrons are not classical particles.
kiwaho said:
Neutron is Fermion too, so it should also obey the same statistics, and it will not significantly contribute to the specific heat of the metal U-235 of a fissile fuel.
There are not enough free neutrons to fill any relevant fraction of the available states.
 

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