In this concise and insightful answer to Which is larger, all known, bound nuclear energy levels, or known, bound atomic energy levels? it was pointed out that atoms can have an extremely large (possibly infinite) number of bound excited states.

The Rydberg formula represents a simple model for the energy of transitions in a hydrogen-like (one-electron) atom. Originally written for the measured vacuum wavelength of the photon released by the transition:

$${1\over\lambda_{vac}}=\text{R}_{\infty}Z^2 \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right) $$

because the original work was done with grating spectrographs. Z is the atomic number of the nucleus. It is often written in terms of energy as well:

$$E=h\nu = \text{Ry}Z^2 \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right) $$

where the Rydberg energy Ry is roughly 13.6 eV.

As was pointed out, as $n$ increases, the number of energy levels for this simple model increases (mathematically, at least) without limit. So possible transitions can have arbitrarily small energy, and therefore long wavelength.

It's often the low energy transitions measured in radio astronomy that allow mapping gas temperatures and distribution, rather than the optical transitions.

My Question: What is the lowest energy atomic transition ever detected and clearly identified? I've added the discussion of the Rydberg model just to help explain why there can be extremely low energy transition. If there is a really compelling case for a lowest energy record that was achieved in - for example - a diatomic molecule, that would be OK here - as long as it is a well defined and unambiguously identified transition.

Naturally occurring atomic hyperfine transitions are fine (no pun intended) but I want to rule out things like NMR, where the transitions and their energy are caused and defined by (respectively) an externally applied fields. This should be about transitions of the atom itself.

  • $\begingroup$ goldstone modes have arbitrarily low excitation energy. $\endgroup$
    – user18764
    Commented Jul 19, 2016 at 15:16
  • 1
    $\begingroup$ No such thing exists. $\endgroup$
    – CuriousOne
    Commented Jul 19, 2016 at 15:16
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    $\begingroup$ I wrote an answer to an earlier question involving megahertz band (lower energy than AM radio) signals from Rydbeg atom transitions in the $n > 500$ regime. That's certainly a very low energy transition and supports the notion that $n$ can take on arbitrarily high values. $\endgroup$ Commented Jul 19, 2016 at 20:43
  • $\begingroup$ @dmckee Wow, that's fascinating! I noticed that the paper is open access too. Thank you for your comment! $\endgroup$
    – uhoh
    Commented Jul 20, 2016 at 0:25

1 Answer 1


The 21cm line from atomic hydrogen is pretty low. Caused by the transition from parallel to anti-parallel spins between the atom and the electron.

  • $\begingroup$ Thanks for your answer! Next we'll have to show that no astronomical Rydberg-Rydberg transitions have ever been detected before we can be sure this is the lowest. You can start by reviewing this comment under my question. $\endgroup$
    – uhoh
    Commented Sep 15, 2022 at 20:58

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