uncertainty and electron capture

[ahprice]

I have been struggling for some time now to reconcile quantum mechanics with radioactive decay, specifically electron capture. There is a decay process called electron capture whereby a proton captures an inner orbital electrons (does the proton "observe" the electron and collapse the wave function?) and emmits gamma or x radiation, a neutrino and an up quark becomes a down quark (and the proton becomes a neutron) thereby lowering its overall energy level.

 

The problem is Heisenberg says we can never know the position AND the momentum of an electron (not to mention that electrons cannot lose enough energy to be captured by the nucleus--zero point energy) and the decay above seems to violate this.

 

Electron tunnelling seems to come up alot in these situations, but electron capture seems to happen WAY too often to be the far end of the bell curve.

 

If this makes any sense and you have any insight I would love to have your input--gracias

[swansont]

Some electron wave functions don't vanish in the nucleus, i.e. the electron spends part of its existence there, where it has a chance of interacting with a proton. The electron isn't confined there, so there's no problem with the uncertainty principle.

[ahprice]

Can you explain this a bit further for me? What do you mean by "some electron wave functions"? Aren't all electrons identical? Furthermore, how can we disregard uncertainty? It would seem that if we know the electron is nearing the nucleus (i.e. the uncertainty of its position is decreasing) it's total energy (i.e. its momentum) would increase sending it to a higher orbital and away from the nucleus. Following this reasoning, an electron could never actually "spend part of its existence there" in the nucleus.

 

Please clarify. Thanks.

[swansont]

S-orbital wave functions, for instance, don't vanish near r=0 as quickly as some others, and the nucleus is not a point. So the electron will spend some of its time in the nucleus — if you were to localize it, some of the measurements would have it inside the nucleus.

 

Electrons will not hop from one orbital to another with a different energy unless energy is added (or removed) from the system (and if we're discussing a ground-state system, the electron can't drop to a lower energy). So no, it won't go to a "higher orbital" away from the nucleus. (remember, an orbital is not the same thing as an orbit)