# Is there way to thermalize an electron to room temperature?

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kiwaho
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?

Mentor
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.

kiwaho
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.

Mentor
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.

kiwaho
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 Boltzman distribution. I see. thank you!

Mentor
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.

kiwaho
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).

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So, it sounds they obey Boltzman 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.

kiwaho
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.

Mentor
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.
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.