Electron orbits Is there an upper limit to the number of orbits an electron can have around say a proton?
Aren't there states that are unstable (for $n\ne1$) with corresponding mean/half lives and therefore uncertainty in energy.
So how do we differentiate between 2 values of $n$ (say $\nu_1$,$\nu_2$) esp if the uncertainty associated with their energy levels gets larger to the order of the energy difference associated with the transition? 
Also is it known that we can predict the following data with only computational resources being a bottleneck?
The half lives of each state (decay rate).
The transition rate (from $\nu_2$ to $\nu_1$ given $\nu_2>\nu_1$).
 A: Interesting question! This article says that "The natural lifetime of an undisturbed Rydberg atom increases as $n^3$ for a given electronic angular momentum." That means that each state has a natural width $\Delta E_{w}\propto n^{-3}$. The energy levels go like $n^{-2}$, and differentiation tells us that the spacing between successive levels goes as $\Delta E_s\propto n^{-3}$. This means that $E_w/E_s$ is approximately independent of $n$ for large $n$. Since we know that $\Delta E_w/\Delta E_s << 1$ for small $n$, it sounds to me like this continues to be true for large $n$. In other words, the states are still well defined and non-overlapping for arbitrarily large $n$. (Of course there will still be degeneracy within each $n$ value.) This is all for a hydrogen atom in free space with zero external electric or magnetic field and no background of blackbody photons.
A: The decay rate from a certain state depends on the environment.  If the atom is in an optical cavity which is strongly detuned from all of the decay modes of the atom, it will stay in the excited state much longer.   Because how much longer it remains excited
 depends on the properties of the cavity, I don't think there's a hard "states with $n>something$ cannot be distinguished from other states" limit, at least in non-relativistic QM.
Density of states factors pop up in statistical physics, so you can still tell there's a bunch of states there even if you can't distinguish them.
