I was just asked this looking trivial question ... and honestly it doesn't look so simple.

Atom is just a bunch of particles hold mainly by electromagnetic interactions - doesn't pure Coulomb repulsion tell that some electrons should immediately run away?

Would e.g. F- or Cl- atom be stable while just flying in empty vacuum? How stable?

 

My first answer is the magnetic attraction between oppositely directed magnets - electron couples?

But the distance between them seems to be too large for such attraction (1/r^4) ... however there are suggestions that magnetic conjugation still works on larger distance, like for Cooper pairs or that neutral positronium scatters like a charged particle: http://physicsworld.com/cws/article/news/44265

Thinking about it purely classically, two electrons on opposite side of a proton will repel each other less (by a factor of 4) than they will be attracted to the proton. So there is no inherent reason that you can't have more negative charges than positive, from a pure Coulomb repulsion standpoint.

Ok, you are right - there is no problem with single excessive electron ...

... it starts with two, like e.g. for S2- or some molecules - in this case the total electric potential energy would drop while single electron would go to infinity - so shouldn't one electron tunnel/escape to this lower energy?

 

Thanks for pointing out that electrons are on opposite sides of the nucleus - it is usually forgotten in QM times, but it applies not only to classical picture.

The standard in QM is approximating two electron wavefunction by tensor product of for single electrons - it's good enough to calculate energy corrections, but from the perspective of wavefunction it completely ignores the interaction.

If we would do it right (unfortunately impractical) - take wavefunction for two particles: psi(x,y), six-dimensional potential V(x,y) have strong repulsive barriers on the diagonal - wavfunction is practically nonzero only when electrons are on opposite sides of the nucleus.

And it doesn't need Pauli exclusion principle - this anticorrelation is the result of Coulomb repulsion only.