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Back in the middle school (which I guess was about 10 years ago) I remember being taught that the temperature of an atom is basically the speed of electrons circling the nucleus which kinda made sense - lower temperature, lower speed so the matter is better at holding together (being solid).

I don't really know if this was outdated knowledge or simplification (or I remember incorrectly) but my question is:

How true is it that temperature is defined by the speed of the electrons and, thus, the lower the temperature the slower the electrons go around the nucleus?

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In a given orbital, electron motion has nothing to do with temperature.

Atoms do have a variety of electronic states and, at higher temperatures, the higher energy states are more likely to be populated.

Temperature, however, is most commonly determined by the translational motion of the nucleus of the atoms. Let $v$ be the speed of a nucleus of an atom in a gas. Let $\langle v^2 \rangle$ be the average square speed of those nuclei. Temperature and mean energy of translational motion in a gas are related as follows: $$\frac{3}{2} kT = \frac{1}{2} m \langle v^2\rangle$$ where $k$ is Boltzmann's constant, $T$ is temperature, and $m$ is the atom's mass.

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  • $\begingroup$ Electrons in orbitals do not have a velocity distribution. That is dangerous semi-classical nonsense that one should never propagate. Your formula for the average kinetic energy of ideal gas molecules is wrong. $\endgroup$
    – CuriousOne
    Commented Jun 29, 2015 at 22:25
  • $\begingroup$ Just to see if we are on the same page, would allow that the orbital wavefunction defines a position distribution? $\endgroup$
    – John1024
    Commented Jun 29, 2015 at 22:27
  • $\begingroup$ No, but this is not the place for me to give you a lesson in quantum mechanics. $\endgroup$
    – CuriousOne
    Commented Jun 29, 2015 at 22:30
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    $\begingroup$ The Born rule gives you a distribution for a measurement, it doesn't give you a distribution for the position of an electron (or any other particle). That is a fine but very important difference between classical physics and quantum mechanics. In order to measure a position, you have to exchange real quanta with the atom, while there is no such exchange for the unmeasured atom. I know, we don't teach this stuff right in beginners classes and layman literature... but we should. Remove your first sentence and correct your formula and I will retract the down vote. Fair? $\endgroup$
    – CuriousOne
    Commented Jun 29, 2015 at 22:55
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    $\begingroup$ I apologize for speaking in shorthand: you are right that it is a distribution for a measured value. Answer updated. $\endgroup$
    – John1024
    Commented Jun 29, 2015 at 23:01
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it seams to me that a low temperature would cause energy to dissipate from the electron orbit. This would more importantly cause the orbit of the electron decrease its distance from the proton/Nucleus core. causing the electron to actually move more quickly around the core. this is the real reason for Thermal Expansion. I find it highly improbable that there is ever a distance between electrons as stated in so many. I understand the scientific communities desire to be correct. but, everything that i read about the atom, makes me think that nobody has really got a grasp of real physics. One last thing. electrostatic shock has been blamed on lack of humidity for too long. If the electrons are moving faster in colder temperature, then it seams to me that this is the reason for ESD in colder environments

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