Radius of Atoms
What force (or theory) keeps the electrons in the 1s orbital from
hitting the nucleus or eventually running out of energy?
Also how does that relate or does it ever relate to the
decay of an atom?
The question you ask was actually exactly (or pretty close to)
the question that prompted the development of quantum mechanics.
The weird thing about quantum states is that they are quantized -they
are simply not able to go continuously from one energy state
to another - so in particular the 1s electrons are stuck in the
lowest possible energy state - there just is nothing lower
in energy - they have already run out of all they are allowed to.
They actually do "hit the nucleus" in a sense, but the nucleus
itself is also almost always in its lowest energy state, and so
it and the electron just very agreeably coexist. The one exception
to this is in a strong magnetic field, where the nucleus can have
a bunch of different energy states depending on the magnetization.
This does not effect the inner electrons at all, but the outer
electrons can see this effect, and you get all sorts of wonderful
stuff from which we can now do "NMR" or "MRI" imaging.
I am not sure what you mean by the decay of an atom - most
atoms do not decay, unless they start out in some unstable
high-energy state (for example the nucleus could be radioactive
and decay into something different).
Well, you could have K-shell capture...
that is not a decay in itself, but the excited nucleus
formed can decay into other nuclei, or (more likely)
kick off a gamma particle (photon).
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Update: June 2012