How do electrons keep out of the nucleus?

[Bob S]

RE question on how do electrons keep out of the nucleus: Quantum mechanics allows only certain radial and angular distributions of electrons in the central Coulomb field of a nucleus. These are defined by integer quantum numbers n and l (l = little L), with l <= n-1. The probability distribution of the n=1, l=0 state has a very very small (but non zero) probability of being inside the nucleus at any given instant in time.

Some nuclei are radioactive. For nuclei lighter than lead, the radioactvity is mostly beta decay (positron and electron decay, with neutrinos) when the nucleus is either neutron deficient or neutron excessive. Sometimes a proton "wants" to decay to a neutron, but does not have enough free energy to create both a neutron and a positron. In this case it will capture a n=1. l=0 electron (K shell) (see above), emit a neutrino, and change to a neutron. This is called K capture or electron capture. An example is beryllium 7, which decays to lithium 7 with a half life of about 53 days.

So the electron does not always keep out of the nucleus, but it needs to stay away from hungry protons.

 

[alxm]

The probability distribution of the n=1, l=0 state has a very very small (but non zero) probability of being inside the nucleus at any given instant in time.

Actually the nucleus (r=0) is the most probable location in space of any. But not the most probable radius.

 

[Vals509]

aren't there energy levels that the electrons can stay in, and it can only go from one energy level to another

 

[alxm]

aren't there energy levels that the electrons can stay in, and it can only go from one energy level to another

Yes, and the s-type orbitals have a non-zero value at the nucleus, so any ground-state atom will have a non-zero electron density at the nucleus.

There's also a cusp in the density at that point, since the coulomb potential 1/r has a singularity there.
An important result (Kato's theorem) states that, for a closed shell atom, that the spherical average of the density gradient at the nucleus is:

\frac{\partial\rho(r)}{\partial r}|_{r=0}=-\frac{2Z}{a_0}\rho(r=0)

Which is something density-functional theorists spend a great deal of time pondering about, because it's one of very few exactly known properties of the electronic density.