From Scientific American, February 2014: The Proton Radius Puzzle:

...we had to tune the laser so that it came in with exactly the right amount of energy. The atom would make the jump to the higher state only if the energy of the laser perfectly equaled the energy difference between the 2S and the 2P state. If the wavelength were a bit off, nothing would happen. How did we know if the atoms were making the jump? Any atom bumped up to the 2P state would quickly release a low-energy x-ray photon. If we found these photons, we knew we had the right energy...

But articles about the hydrogen spectral series say that even the highest-energy photons released, the so-called Lyman series, max out at about 91 nanons, which is UV territory, not X-ray....

Thinking further: when measuring the 'Lamb shift' of hydrogen, they also measured the Lamb shift of muonic hydrogen. Perhaps muonic hydrogen has much higher energy levels and level differences than regular hydrogen? Actually, the whole point of using muonic-hydrogen to measure Lamb-shifts was because its energy shifts are greater than regular hydrogen.

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    $\begingroup$ Low energy x-ray, high energy UV… Lots of overlap in various definitions. $\endgroup$
    – Jon Custer
    Jul 2, 2021 at 1:39
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    $\begingroup$ different but related: What is a “hydrogen-like” or “hydrogenic” atom? $\endgroup$
    – uhoh
    Jul 2, 2021 at 2:23
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    $\begingroup$ Similar as overlapping X ray and gamma ray regions, based on the way of creation, not on energy. $\endgroup$
    – Poutnik
    Jul 2, 2021 at 4:21
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    $\begingroup$ I believe this is about the muonic hydrogen experiment at PSI. The electron is replaced by a muon which is 200 times heavier and shifts the energies accordingly. $\endgroup$
    – Paul
    Jul 2, 2021 at 6:59
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    $\begingroup$ In an approximate calculation the hydrogen Rydberg constant $R_y$ is multiplied by $m_{\mu}/m_e=200$ and using the Balmer type equation the energies are 200 times larger as Paul writes, so the 2p-1s energy is $200\cdot3R_y/4$ $\endgroup$
    – porphyrin
    Jul 2, 2021 at 7:45

1 Answer 1


X ray photon energies are usually rendered in keV, so let's say that by the time we get to 1 keV energy we may reasonably call a photon "X-ray".

Normal hydrogen has an ionization energy from the ground state of only 13.6 eV, not enough really. It's less than five times the max for visible light, which peters out around 3 eV, and most people would allow more than that factor for the "ultraviolet" energy range.

But a muon is about 200 times as massive as an electron and, since this leaves the muon still lighter than even a hydrogen-1 nucleus, that means the ionization energy quoted above gets multiplied almost by that factor of 200. Now we're over 2 keV, with a 1s -> 2p transition taking three-quarters of that amount, and that may be reasonably considered as reaching "X-ray" territory.


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