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 Originally Posted by CoccoBill
When I measure the width of a poker chip, should I do it at the edge of the outermost atomic nuclei, or at the farthest trajectory point of their electrons?
Somewhere in-between, but very nearly at the outermost electron's <r>
<r> = The EV of the electron's r
r is the electron's time-averaged distance from the center of mass of the atom
Originally Posted by CoccoBill
Also, how hard do I need to squeeze the chip to force the electrons to clump together with the nuclei, and is this observed in nature? Neutron stars, black holes?
If you exert this much pressure, you will turn your poker chip into a (very tiny) white dwarf star:
where h_bar is the reduced Plank constant, m_e is the mass of an electron, and rho_N is the number of free electrons per unit volume.
This is the electron degeneracy pressure. White dwarf stars are observed to exist.
Degeneracy pressure is an unexpected consequence of indistinguishable particles. If it were possible to tell electrons apart, like pool balls on a pool table, then this pressure wouldn't exist. There is no way to tell electrons apart because all of their intrinsic properties are exactly identical. The same is true for all fundamental particles. This gives rise to the Pauli Exclusion Principle.
The PEP states that no 2 identical fermions can be in the same state at the same time. Protons, neutrons, and electrons are all fermions. Photons are not fermions.
Neutron stars are a consequence of the pressure becoming great enough during a supernova to overcome the electron degeneracy pressure. The electrons are forced to no longer be indistinguishable particles of mass m_e within the volume they are constrained. It is emphatically not that they are "pushed into the nucleus." It's that the energy cost to be an electron + proton became greater than the energy requirement to become a neutron + neutrino + photon. So the particles "moved downhill" in terms of the energy required to fit the environmental conditions.
When the energy cost to be one thing is less than the energy cost to be another thing, and all else is equal, the universe tends to the lowest cost arrangement. <- Hints of Entropy.
Pretty cool, huh?
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