Questions about atoms

[Mike Helland]

How big is an electron shell/orbital thing in terms of Planck's Length?

Is the first shell bigger than the other one's? Or are they all the
same size?

According to QED, if a proton a neutron and an electron wander into the
same neighbor hood, under what conditions will they form an atom?

Thanks.

[paulaireilly]

Mike Helland asks:

>How big is an electron shell/orbital thing in terms of Planck's Length?

Off hand, I think the Bohr radius (which is also the average radius for
the real hydrogen atom wavefunction, if I recall correctly) is 0.53
Angstroms. If it's not that it's close. That's almost 25 orders of
magnitude bigger than the Planck length, 1.6 E-35 m.
So Planck Length: diameter of hydrogen atom::hydrogen diameter:.06
light-years.

>Is the first shell bigger than the other one's? Or are they all the
>same size?

For a given atomic number Z, an electron orbital with a higher n (outer
shell) will have a greater expectation value of distance from the
nucleus... so the outer shells are "bigger" in that sense.

>According to QED, if a proton a neutron and an electron wander into the
>same neighbor hood, under what conditions will they form an atom?

I'll leave out the neutron. If a proton and an electron wander near
each other, they will have too much energy to form an atom unless they
shed it; if there are no other particles in the vicinity they can do
that by interacting with virtual photons and kicking one out of the
vacuum to become real. They could also kick out two photons, but that
would be about a hundred times less probable. For the one-photon
process they need to shed one Planck unit of angular momentum as well
as some energy, because photons have angular momentum 1. So there are
some conditions on the details of their wavefunctions as they approach.
I will leave a more detailed answer to an expert if this is
insufficient.