Hydrogen_line - Wikiparency

# Hydrogen line  ## Microsims — three.js ### Hydrogen line (three.js) <div class="microsim-player"> <iframe src="https://wikitube-3d-microsims.netlify.app/Hydrogen_line.html" width="100%" height="620" frameborder="0" loading="lazy" sandbox="allow-scripts allow-same-origin" title="Hydrogen line — three.js microsim"></iframe> </div> **Open it full-screen:** [Hydrogen_line.html](https://wikitube-3d-microsims.netlify.app/Hydrogen_line.html) · library `threejs` · route `microsim/threejs/` ### Related microsims Live sims on neighbouring articles: - [[Hydrogen_atom]] - [[Diatomic_molecule]] - [[Ammonia]] - [[Metallic_hydrogen]] *Sim hosted off-article; the article owns the reference, not the runtime (WIKI_RULES §10.4). Placed by `g08_place_microsims.py`.*  ## Overview In a neutral hydrogen atom the proton and the electron each carry spin, and the two spins can sit parallel or antiparallel. The two arrangements are not the same energy. They differ by 5.874 micro-eV, the parallel one lying higher because the electron's moment opposes its spin, and when an atom drops from the upper arrangement to the lower it emits a single photon of wavelength 21 cm. Left alone, one atom waits about 11 million years for that flip. It does not matter. There is so much hydrogen in the Galaxy that the sky glows steadily at 21 cm, and radio waves that long pass straight through the dust that stops optical light within a few kiloparsecs. One forbidden transition in the commonest atom is therefore the most important probe of galactic structure we have. ## The physics Hyperfine structure is the coupling of the electron's magnetic moment to the *proton's*. It is a nuclear-spin effect, and a different thing from fine structure, which is the electron's spin coupling to its own orbital motion plus relativistic corrections and involves the nucleus not at all. The proton's moment is built on the nuclear magneton, e hbar / 2 m_p, smaller than the Bohr magneton by the mass ratio m_e/m_p = 1/1836, so hyperfine energies fall below fine-structure energies by roughly that ratio times g-factors of order a few. In the ground state the n = 1 fine-structure correction is about 1.8 x 10^-4 eV, some 31 times the hyperfine gap -- not the factor of 10^4 that often gets repeated. The numbers: nu = 1420.405 751 768 MHz, lambda = c/nu = 21.106 cm in vacuum, and an energy gap h nu = 5.874 micro-eV. The spontaneous emission coefficient is A = 2.85 x 10^-15 s^-1 (Wild 1952), refined in later work to 2.8843 x 10^-15, so the mean lifetime 1/A is about 3.47 x 10^14 s, near 11.0 million years (the sim runs on Wild's value and prints 11.12 Myr). Both levels are 1s. Same parity, same orbital angular momentum, so the electric-dipole matrix element vanishes identically and the transition is forbidden to first order. It proceeds by magnetic dipole instead, so A sits 23 orders of magnitude below Lyman-alpha's 4.7 x 10^8 s^-1. We see it anyway because of column density: a sight line through the plane carries of order 10^21 atoms per square centimetre, three quarters of them in the upper state at any interstellar temperature. The long lifetime is then a feature: the line stays optically thin, so the area under the profile is a linear measure of how much hydrogen is there. Hendrik van de Hulst worked the transition out in occupied Leiden and presented it at Oort's colloquium in 1944 (published 1945). Harold Ewen and Edward Purcell detected it in 1951 from a plywood-and-copper horn on a Harvard windowsill (*Nature* 168, 356), and Muller and Oort confirmed it from Kootwijk in the same issue that September (*Nature* 168, 357). What it bought was the Galaxy. Within a decade the Dutch and Australian surveys had drawn the first maps of the spiral arms, because radio goes where optical astronomy cannot. It also gave the rotation curve. On any sight line that dips inside the solar circle there is a tangent point where the orbital motion lies entirely along the beam; the gas there sets the extreme velocity in the profile, so V(R) falls out of the line's edge with no distance measurement. Pushed past the optical edges of other galaxies, the same line found rotation curves that stayed flat where the light had run out -- Bosma's 21 cm survey of spirals (*AJ* 86, 1825, 1981) and Begeman's NGC 3198 curve (*A&A* 223, 47, 1989). Rubin and Ford's famous M31 curve (*ApJ* 159, 379, 1970) was optical; it was the H I extension beyond the starlight that made dark haloes hard to escape. None of this reaches molecular hydrogen, which is homonuclear, has no permanent dipole moment and is nearly invisible ([[Diatomic_molecule]]) -- exactly why the atomic 21 cm line carries so much. ## Controls -> what each maps to | Control | Maps to | Range / values | Physical meaning | |---|---|---|---| | l (deg) | galactic longitude | 0 to 359 | Aims the beam; adds a row to the longitude-velocity diagram and, inside the solar circle, a measured rotation-curve point | | sweep l | -- | on / off | Drives l automatically so the l-v diagram builds up | | curve | rotation-curve model | flat 235 km/s / Keplerian (light) | Changes how the clouds actually move, so the spectrum and every measured point change with it | | dark halo | pseudo-isothermal halo | on / off | Pushes the Keplerian curve back up onto the observed flat one. That is the whole dark-matter argument | | clouds | Monte Carlo sample size | 200 to 2600 | Dots drawn from the same n_HI(R) the spectrum integrates; changes the grain, not the Galaxy and not the spectrum | | E scale | energy-axis exaggeration | 10^4 to 10^7 | Vertical stretch of the F = 1 / F = 0 ladder; the panel states the factor and the true gap in pixels | | spectrum | -- | on / off | Shows the synthesised profile and the l-v diagram | | v colour | -- | on / off | Blue/red Doppler colouring of the clouds by line-of-sight velocity | | running | -- | on / off | Pauses the clock, which advances 18 Myr per wall-clock second | | flip a spin | -- | button | Forces the transition now instead of waiting a mean 11 Myr for it | | reset | -- | button | Reseeds the clouds, the clock and the measurements | ## Learning objective After playing, a learner can explain why a transition with a mean lifetime of 11 million years is one of the brightest lines in radio astronomy, and how the tangent-point method turns the edge of a profile into a rotation curve and the rotation curve into an argument for dark matter. ## Limits and connections The Galaxy here is schematic: a two-arm logarithmic-spiral density wave over a smooth axisymmetric disc, where the Milky Way has roughly four arms. The spectrum is not a histogram of the dots on screen. It is the line integral a telescope performs, taken through the modelled density and the same live rotation curve the dots obey, which keeps the profile free of the Monte Carlo noise that would swamp a measurement made on its edge. Two things on the atom panel are drawn at arbitrary scale and cannot be otherwise: the spin precession, really of order GHz, and the photon, whose 21 cm wavelength is some 4 x 10^9 Bohr radii. Underneath all of it is one proton and one electron, which is [[Hydrogen_atom]]. ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Hydrogen_line) : [Wikitube](https://en.wikitube.io/wiki/Hydrogen_line) ## Previous hub tags Tree parent: [[Hydrogen]]. Legacy hubs: `HYDROGEN`. --- *Created 2026-08-05 - append-only - authored to WIKI_REPOPULATION_PROTOCOL v1.0 section 5 (PORTAL_Hydrogen batch 1) - 0 deletions*