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what happens to the motion of electrons in the their respective orbits when a substance is cooled down to zero kelvin? assuming they stop moving then are they gonna stick to the nucleus? if yes what happens when it's brought back to ordinary temperature, will it still be stuck? what about the entropy in the whole process?

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  • $\begingroup$ Electrons don't have classical orbits. Classical trajectories don't make sense when the effects of Heisenberg's uncertainty principle are significant. $\endgroup$ – PM 2Ring May 5 at 22:03
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In the case of conductors, the zero temperature state is the ground state of the electronic system. The electrons still move and the energy of this state is the Fermi energy. In any case, electrons certainly do not stop moving. Sticking to the nucleus would imply that matter is unstable at low temperatures, which is not the situation when you cool down substances to that level.

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In a world described by Classical Physics, temperature would always be proportional to kinetic energy. Therefore, $T=0$ would correspond to a state with no kinetic energy, which in turn would imply all velocities equal to zero , i.e. no movement.

However, world is not always well described by Classical Physics and the most fundamental description we have is Quantum Mechanics (QM).

QM breaks the argument for no movement at $T=0$ in correspondence of two conceptual points:

  1. movement in the sense of change of observations with time is still there. But it cannot be described by using the concept of trajectory as in Classical Physics. The classical definitions of velocity and orbit break down completely and have to be abandoned. Momentum remains a key ingredient in QM but it should be looked as a quantity independent on the classical definition in term of velocity. So, it is possible to keep the concept of kinetic energy, even without trajectories and velocities. It turns out that the minimum allowed energy, which for a classical system would correspond to the global minimum of the potential energy and zero kinetic energy, in QM corresponds to a non-zero kinetic energy (the so called zero-point energy.
  2. The classical relation between kinetic energy and temperature (equipartition theorem) breaks for quantum systems. It is still possible to introduce the thermodynamic definition of temperature ( $T=\frac{\partial{U}}{\partial{S}}$ ) but in this case $T=0$ does not imply zero kinetic energy.

And this is valid for every system (not only conductors).

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