The physics in my wallpaper

My wallpaper is six rounded bars on a black field. People assume it’s abstract art. It’s not — it’s the emission spectrum of hydrogen, remixed into gruvbox. Every time an electron in a hydrogen atom falls from a higher orbit down to the second one, it spits out a photon at one of a handful of exact wavelengths. Those are the bars.

The wavelengths come from the Rydberg formula:

$$\frac{1}{\lambda} = R_H \left( \frac{1}{2^2} - \frac{1}{n^2} \right), \qquad n = 3, 4, 5, \ldots$$

with $R_H \approx 1.097 \times 10^7\,\text{m}^{-1}$. Plug in the first few values of $n$ and you get the visible lines — the Balmer series:

transition	name	$\lambda$
$3 \to 2$	H-α	656 nm (red)
$4 \to 2$	H-β	486 nm (aqua-ish)
$5 \to 2$	H-γ	434 nm (blue)
$6 \to 2$	H-δ	410 nm (violet)

Here’s the whole mechanism, gruvboxed. Watch the electron fall to $n = 2$ and fire off the corresponding line:

The $\frac{1}{2^2}$ is the whole story of why this series is visible. Transitions down to $n = 1$ (the Lyman series) are ultraviolet; down to $n = 3$ (Paschen) is infrared. Landing on the second shell happens to drop photons right into the narrow band our eyes evolved to catch.

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The original wallpaper kept the physically accurate spacing and just took liberties with the colors. Which is very gruvbox of it: the palette isn’t trying to be accurate either. It’s trying to feel warm at 2am. Both goals are legitimate engineering constraints.

If you want it: the wallpaper is in my dotfiles, and the footer of this site is the same spectrum, same positions.