quantum mechanics - How large can an atom get? What's the farthest an electron can be from its nucleus?

For example, would it be possible to excite a hydrogen atom so that it's the size of a tennis ball? I'm thinking the electron would break free at some point, or it just gets practically harder to keep the electron at higher states as it gets more unstable. What about in theoretical sense?

What I know is that the atomic radius is related to the principal quantum number $n$. There seems to be no upper limit as to what $n$ could be (?), which is what led me to this question.

Answer

Atoms with electrons at very large principle quantum number ($n$) are called Rydberg atoms.

Just by coincidence the most recent Physics Today reports on a paper about the detection of extra-galactic Rydberg atoms with $n$ as high as 508(!), which makes them roughly 250,000 times the size of the same atom in the ground state. That is larger than a micrometer.

The paper is Astrophys. J. Lett. 795, L33, 2014. and the abstract reads

Carbon radio recombination lines (RRLs) at low frequencies ($\lesssim 500 \,\mathrm{MHz}$) trace the cold, diffuse phase of the interstellar medium, which is otherwise difficult to observe. We present the detection of carbon RRLs in absorption in M82 with the Low Frequency Array in the frequency range of $48-64 \,\mathrm{MHz}$. This is the first extragalactic detection of RRLs from a species other than hydrogen, and below $1,\mathrm{GHz}$. Since the carbon RRLs are not detected individually, we cross-correlated the observed spectrum with a template spectrum of carbon RRLs to determine a radial velocity of $219 \,\mathrm{km \,s^{–1}}$. Using this radial velocity, we stack 22 carbon-$\alpha$ transitions from quantum levels $n = 468$–$508$ to achieve an $8.5\sigma$ detection. The absorption line profile exhibits a narrow feature with peak optical depth of $3 \times 10^{–3}$ and FWHM of $31 \,\mathrm{km \, s^{–1}}$. Closer inspection suggests that the narrow feature is superimposed on a broad, shallow component. The total line profile appears to be correlated with the 21 cm H I line profile reconstructed from H I absorption in the direction of supernova remnants in the nucleus. The narrow width and centroid velocity of the feature suggests that it is associated with the nuclear starburst region. It is therefore likely that the carbon RRLs are associated with cold atomic gas in the direction of the nucleus of M82.