# The uncertainty principle

bapowell
Excuse me if this is off-topic, but I have to ask... How does (or does it) the the uncertainty principle forbids the electron to "hit" the nucleus?
It doesn't forbid the electron from hitting the nucleus. In fact, as Drakkith pointed out somewhere above, there is a small but finite probability that the electron will find itself in the nuclear because its wavefunction (in the H atom at least) overlaps with the nucleus slightly. It does sometimes occur in a process called electron capture. However, the bulk of the probability amplitude lies outside the nucleus. This is no accident, and has to do with the fact that we are looking at a central force problem -- while the central force seeks to confine the electron to an ever decreasing region about the nucleus, the variance in the electron's momentum becomes larger as a result of the HUP.

Drakkith
Staff Emeritus
The electron in the hydrogen atom does not fall into the nucleus on account of the HUP, not the PEP.

Principles aside, I actually thought I had read that it doesn't "fall" into the nucleus because the atom is in a more stable and less energetic situation with electrons orbiting it than it is for the electron to combine with a proton and turn one of the protons into a neutron in the nucleus. (Hence why only immense pressure, like what you find in a neutron star, cause electrons to combine in mass with protons) What principle that might be, I don't know.

The PEP forbids that more than a certain number of fermions (this number depends on their spin) be in the same energy level thus its effect during the collapse of an atom as in a neutron star is to resist that electrons on the outer shells be pushed to the inner shells where other electrons sits but in hydrogen(one electron) or even hellium(two electrons) its the HUP that prevents the collapse.

what is field theory? is this related to quantum mechanics?

It doesn't forbid the electron from hitting the nucleus. In fact, as Drakkith pointed out somewhere above, there is a small but finite probability that the electron will find itself in the nuclear because its wavefunction (in the H atom at least) overlaps with the nucleus slightly. It does sometimes occur in a process called electron capture. However, the bulk of the probability amplitude lies outside the nucleus. This is no accident, and has to do with the fact that we are looking at a central force problem -- while the central force seeks to confine the electron to an ever decreasing region about the nucleus, the variance in the electron's momentum becomes larger as a result of the HUP.
Thank you bapowell. I think your statement is the clearest example of the HUP in this thread.