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Comment by radioactivist | Hacker News Reader

This is generally true for anything to do with matter at the microscopic level: not just chemistry, but many things about things like insulators, metals and other solids just don't make sense without quantum mechanics.

Even in the stability of solids (i.e.) why things don't pass through each) relies on the Pauli exclusion principle (and not just Coulomb repulsion as is commonly thought).

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The Pauli exclusion principle is just a fancy way of saying two electrons (later extended to fermions) can't be in the same place at the same time

Yes, the point that is often missed is that Coulomb interactions aren't enough on their own.

They can, if their spins are opposite. (Speaking of 'place' specifically, different orbitals of the atom overlap in space, so in fact nothing prevents two electrons from occupying the same point in space. A striking example would be an observation that the maximum probability of finding an electron sitting on an s-orbital is inside the atom's nucleus.)

Are you forgetting a Jacobian? The maximum probability isn't inside the nucleus for an s-orbital. E.g. for hydrogen, the maximum probability for the electron is one bohr radius away from the center of the nucleus (and the expectation value of the radius is 1.5 bohr radii away).

Well let me just quote Wikipedia here: ...in three-dimensional space, the maximum probability density occurs at the location of the nucleus and not at the Bohr radius, whereas the radial probability density peaks at the Bohr radius, i.e. when plotting the probability distribution in its radial dependency.

Ah yup you're right, I read your sentence too fast, whoops. The most likely location is at the nucleus, but the most likely radius (integrating over all angles) is at 1 bohr radius.

That it is maximum at the nucleus is not of much significance. To quote a professor:[1]

> In some ways it does not provide the best description of the electron distribution, since the region around r= 0, where the wavefunction has its largest values, is a relatively small fraction of the volume accessible to the electron. Larger radii represent larger physical regions since.

If you were to do any kinds of measurements, you are most likely to find it at the Bohr radius, not closer to the nucleus.

[1] http://www.umich.edu/~chem461/QMChap7.pdf

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