Talk:Rydberg formula

$n_{1}$ and $n_{2}$

It would be very useful to have a description of what the numbers n1 and n2 mean physically. Just saying that the Balmer series, for example, is created by setting n1 equal to 2 and letting n2 run from 3 to infinity is all well and good, but it won't help someone understand what these numbers represent.

I've now added something more about that. Is that clearer? SBHarris 03:41, 16 January 2007 (UTC)

An obvious mathematical mistake in this article

"Rydberg rewrote this in terms of wavenumbers as n = no − 4no/m ².

"This shows that hydrogen is a special case with m = 0 and C0=4no. Co is a universal constant common to all elements."

This immediately gives division by zero in the first line when m = 0 from the second line is substituted in.

My master's degrees are in electrical engineering and mathematics, and I don't remember enough from my long Modern Physics course to correct the expressions here.74.249.82.7 (talk) 03:21, 18 September 2008 (UTC)

I added a prime-sign, it is m-prime in the formula before that is zero. Thank you for pointing this out. /Pieter Kuiper (talk) 11:39, 11 October 2008 (UTC)

A visual comparison of the hydrogen spectral series for n1 = 1 to n1 = 6 on a log scale

[Note: This section refers to the image of the Hydrogen Spectrum in PNG format which was originally used in the article:] — Preceding unsigned comment added by Hops Splurt (talk • contribs) 12:43, 18 February 2023 (UTC)

Very nice figure (maybe display a larger thumbnail) but: It doesn't seem to be on a log scale (factors of 1,2,3,4,5 are evenly spaced), and I think the units are actually m, not nm (10^-6 nm would be beyond x-rays and gamma rays). But then I may be confused about this, too. Eaberry (talk) 04:06, 28 December 2022 (UTC)

I agree that the diagram does not make much sense.

• The scale (showing the wavelength) is linear, not logarithmic as the description states.
• The numerical values are apparently in meters, with e.g. 1 μm (1000 nm) being in the middle of the Paschen series. The unit "nm" on the right should then be "m", or all the "×10⁻⁶" bits should be removed, leaving the values simply as micrometers.
• What is marked as the $\alpha$ line in each series is actually the $\beta$ line. See article Hydrogen spectrum for the known values. E.g. the line marked Pa-$\alpha$ in the diagram is at about 1280 nm. This corresponds to the measured value of Pa-$\beta$ of 1282 nm. The actual Pa-$\alpha$ is at 1875 nm, putting it inside the Bracket series (yellow in the diagram) as it should be. Similarly "Pf-$\alpha$" at about 4650 nm matches Pf-$\beta$ at 4654 nm (Note that the small scale divisions mark out 200 nm intervals.)
• The Humphreys series is a complete mess. It should be mostly beyond the right of the diagram. Note how the "Pf-$\alpha$" and the "Hu-$\alpha$" are shown to be nearly the same.

I get the urge to replace this diagram with a better one. Since Wikimedia recommends re-creating the image as an SVG file, I intend to use a script to generate the image as an SVG, where the script can calculate the correct positions for the lines. Seeing how the Humphreys series mostly falls outside the range of the current diagram (Hu-$\alpha$ has a wavelength of 12370 nm), including the whole Humphreys series would probably squash the other series into a single thick line, like the Lyman series is now. Using an actual logarithmic scale would solve this problem, and also un-squash the Lyman series. Alternatively, we could keep the linear scale and not show the Humphreys series. I would also include a marker for the series convergence (probably a dotted line), and some brackets below the scale indicating the ranges of UV, visible and IR. Hops Splurt (talk) 12:28, 30 January 2023 (UTC)

Further note: The metadata of the diagram shows it was created using Wolfram Mathematica 8.0, at 17:07, 20 July 2013. It might be feasable to use Wolfram again to create and export an improved diagram in SVG format. Hops Splurt (talk) 14:27, 30 January 2023 (UTC)

Further, further note: There already exists an SVG file with spectral lines on a logarithmic scale:

It's a bit uglier, but pretty much has all the features I wanted. It is also far more widely used. So, I'm not going to bother making my own, but will replace the link to the wonky PNG file with a link to this one. Hops Splurt (talk) 16:45, 30 January 2023 (UTC)

Formulas given are not the ones Rydberg or Bohr published.

The formulas in the "For hydrogen" and "For any hydrogen-like element" are not present in the publications cited in this article. Johnjbarton (talk) 16:11, 11 July 2023 (UTC)

The published formula

$\pm {\frac {n}{N_{0}}}={\frac {1}{(m_{1}+\mu _{1})^{2}}}-{\frac {1}{(m_{2}+\mu _{2})^{2}}}:$

Note in particular the formula is written in terms of wave number not wavelength.

The formula may be fine, but is unreferenced material. Johnjbarton (talk) 16:24, 11 July 2023 (UTC)

Added Rydberg's published formula, Added ref to Bohr's derivation of Rydberg formula and connected the two.

Resolved

Johnjbarton (talk) 00:21, 12 July 2023 (UTC)