# Measurement of Hydrogen 1s 4s transition frequency

1. Apr 16, 2015

### neilparker62

Has this been accurately measured yet? Google searches yield results for H 1s-2s and H 1s-3s transitions but not 1s-4s.

2. Apr 16, 2015

### phyzguy

The hydrogen spectrum has been measured in exquisite detail. The line you are referring to is called the Lyman-γ line. If you search on "Lyman series", you will find the wavelength.

3. Apr 16, 2015

### neilparker62

Ok thanks - I tried. Don't find much at all. I am looking for measurement in the same order of accuracy as the 1s-2s and 1s-3s transition frequencies have been measured.

4. Apr 16, 2015

### phyzguy

This site at NIST I think has the accuracy you are looking for (12 significant figures). When you are talking this level of accuracy, you need to specify which of the transitions you are talking about, taking into account the fine structure, hyperfine structure, etc. This site, also at NIST, gives the energy levels to about the same level of accuracy (12-13 figures).

Edit: I see the links don't work the way I've done them. Try going here, I entered H I for the spectrum, and 97.2 and 97.3 for the upper and lower wavelengths. Then at the bottom you can click on "Levels" and again put in H I to get the energy levels.

5. Apr 16, 2015

### neilparker62

Thanks again - I think I tried that but the problem is the 12 sf figures seem to be calculated ones. I am interested in accurately observed data. It somehow doesn't make sense to calculate something to 12 sf when your measured is only accurate to about 7 sf ?? For example in the 1s-3s transition, the NIST site gives a measured wavelength of 102.5728 nm and that seems to be for 1s-3p rather than 1s-3s. I think they might need to update their observed data in light of more recent measurements such as those I mentioned in the previous post - you can easily convert to wavelength from v = fλ with v=c. When you do this you see the calculated numbers (Ritz wavelengths) are pretty good tracking the measured wavelength down to about 9 sf. Wonder what the formula for that is ?? I have a formula which tracks down to about 7sf on the 1s-2s and 1s-3s transitions.

6. Apr 16, 2015

### phyzguy

Sounds like you know more than I do about it. However, the NIST Energy level page explicitly says " Most of the given level values are essentially experimental ones." It also gives a link to the paper by Kramida, which seems to have a wealth of information, but more than I want to delve into:

"A critical compilation of experimental data on spectral lines and energy levels of hydrogen, deuterium, and tritium",

7. Apr 16, 2015

### neilparker62

Thanks all the same for the NIST references - they certainly provide very thorough coverage of the various transition wavelengths in the Hydrogen spectrum.

From what I can understand, the Ritz wavelengths seem to be 'quasi calculated' so not really experimental. I think science become a bit hazy when we can't really distinguish between theoretical and measured data - the whole idea is to put up theories which are ultimately judged by the degree to which they concur with actual measurement. To date the only really accurate measured values I can find are those for the H 1s-2s and H 1s-3s transition frequencies. For interest here are references for these measurements:

Improved Measurement of the Hydrogen 1S–2S Transition Frequency

Optical frequency measurement of the 1S-3S two-photon transition in hydrogen

8. Apr 16, 2015

### Quantum Defect

1s-ns are going to be two photon transitions. There might not be much reason to do the1s-4s measurement directly, though, because you can do separate experiments to measure say 1s-2p (one photon) and measure 2p-4s (one photon). The precise measurement of the 2s-2p energy difference (Lamb shift) is something you can read about. QED is needed to explain the shift.

9. Apr 18, 2015

### neilparker62

Thanks - I think I read somewhere that accurate determination of 1s-2s, 1s-3s, 1s-4s etc transition energies/frequencies was needed to resolve the proton radius anomaly

Some more data I am looking for if anyone can help: accurate values of wavelengths for Fraunhofer lines stretching into the UV region for the H I Lymann series. I found this reference:

http://www.coseti.org/9006-025.htm

but it only seems to cover lines in the visible spectrum.

10. Apr 20, 2015

### neilparker62

Just by way of history, there were a lot of rocket missions in the late 50s, early 60s to photograph the solar spectrum in the UV region. Various Lymnan series lines are clear in these photos. Of particular note is the Lyman alpha line which shows up as a bright emission band with a very sharp absorption dip right in the centre (I hope I interepreted the plates I saw correctly). It seems surprising that interest in this region of the solar spectrum seems to have subsequently waned - one would of thought that with today's technology , much higher resolution photos of the spectrum would be available and it should also be possible to measure the important wavelengths to a great degree of precision. In particular the Lymann Alpha absorption dip. Or am I just missing something in my Google searches ??

Reference for the 50s/60s missions here.