# 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.

• The size of the atom is in some sense infinite, no matter what $n$ you're talking about. The wavefunction tails off exponentially at large $r$, but it's never zero.
– user4552
Nov 13 '14 at 3:07
• See also my closely related question physics.stackexchange.com/q/144819/2818 Nov 13 '14 at 4:07

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.

• One of my favourite illustrations of just how comparatively large Rydberg atoms are is that their typical length scales would be more familiar to a biologist than an atomic physicist. For example, a Rydberg atom in an $s$ state with principal quantum number $n = 508$ can hold about 100 human red blood cells within the mean radius of the electronic orbital. Nov 13 '14 at 17:58
• I looked at the article briefly, I already got stuck at the first half of the first sentence of the abstract. "Carbon radio recombination lines (RRLs)..." so in this paper, are these "lines" between bound states, or is it radiative capture of free but very low energy electrons such that the radiation is narrow, thus the word "line", or are the lines from subsequent de-excitation after capture? Also second sentence of second paragraph: "When free electrons recombine with atoms..." is it really electrons and ions recombining to form atoms (the use of 'atom' here include ion?)? Thanks!
– uhoh
Jul 20 '16 at 4:28

In theory, a hydrogen atom is a proton with its corresponding electron "almost" at infinity! Therefore, n can be very large, in deed! However, on the "practical" side, if we accept the ionization point as the point at which hydrogen ceases to be hydrogen (around 13 ev), then n would be much smaller.