Ammonia - Wikiparency

# Ammonia  ## Microsims — three.js ### Ammonia (three.js) <div class="microsim-player"> <iframe src="https://wikitube-3d-microsims.netlify.app/Ammonia.html" width="100%" height="620" frameborder="0" loading="lazy" sandbox="allow-scripts allow-same-origin" title="Ammonia — three.js microsim"></iframe> </div> **Open it full-screen:** [Ammonia.html](https://wikitube-3d-microsims.netlify.app/Ammonia.html) · library `threejs` · route `microsim/threejs/` ### Related microsims Live sims on neighbouring articles: - [[Diatomic_molecule]] - [[Hydrogen_atom]] - [[Hydrogen_line]] - [[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 Ammonia is one nitrogen atom bonded to three hydrogens. It is not flat. The three hydrogens form a triangle, the nitrogen sits above its centre, and nitrogen's two remaining valence electrons -- the lone pair -- point away on the far side. The shape is a trigonal pyramid, and the lone pair on top of it governs nearly everything the molecule does. Two stories are told about the same object. The first is quantum: the nitrogen does not stay on one side. It passes through the plane of the three hydrogens and back, billions of times a second, across a barrier it cannot classically cross -- and in 1954 that motion built the first maser. The second is agricultural. Haber-Bosch ammonia supplies essentially all synthetic nitrogen fertiliser: on the order of 180 million tonnes a year, about 2 percent of the world's total final energy consumption, and by the most-cited estimates the food of roughly half of humanity. ## The physics Nitrogen has five valence electrons: three go into N-H bonds, two stay as a lone pair. Valence shell electron pair repulsion puts those four electron domains at the corners of a tetrahedron, which would give an H-N-H angle of 109.5 degrees. The measured angle is 106.7. A lone pair is held by one nucleus rather than shared between two, so it is fatter, sits closer in, and presses the three bonding pairs together. With an N-H bond length of 101.2 pm, that angle puts the nitrogen about 38 pm above the plane of the hydrogens. Flattening the molecule forces the lone pair out of a comfortable sp3-like orbital into a pure p one, and that costs around 2020 cm^-1 -- roughly 24 kJ/mol, 0.25 eV, or 2900 K. There are therefore two pyramids of identical energy with a hump between them, and at room temperature almost no molecule carries 2020 cm^-1 in this one mode. Classically each should stay in the pyramid it started in. It does not. The wavefunction leaks through the hump, and in a symmetric double well no eigenstate is a pyramid at all: every vibrational level splits into a close pair, symmetric and antisymmetric under reflection, and a molecule prepared as a pyramid is a superposition of the two. The pair drifts out of phase at the splitting frequency, and after half a beat the molecule is the other pyramid. The ground-state splitting is 0.7934 cm^-1, or 23.79 GHz, giving a tunnelling period T = 1/(2 nu) of about 21 ps -- the molecule turns itself inside out and back some twenty-four billion times a second. The barrier is not an activation energy; the inversion goes through it, not over it. Tunnelling depends exponentially on the mass moved, since the WKB action carries the square root of the mass inside an exponential. Deuterating the three hydrogens raises the reduced mass of the inversion coordinate from 2.487 u to 4.221 u, a factor of 1.70, and the splitting falls to 0.0531 cm^-1, or 1.59 GHz. The ratio 0.7934 / 0.0531 = 14.9, near enough 15: a 70 percent increase in mass buys a fifteenfold suppression. This is among the cleanest demonstrations of quantum tunnelling in any molecule. The NH3 inversion doublet is a microwave transition, and it was the first ever made to oscillate coherently. Gordon, Zeiger and Townes state-selected a beam of ammonia with an electrostatic quadrupole focuser, fed the upper-state molecules into a resonant cavity, and got stimulated emission near 24 GHz: J. P. Gordon, H. J. Zeiger and C. H. Townes, "Molecular Microwave Oscillator and New Hyperfine Structure in the Microwave Spectrum of NH3", *Physical Review* **95**, 282 (1954), with the full treatment in *Physical Review* **99**, 1264 (1955). They worked on the J = K = 3 rotational component at 23 870.1292 MHz, not the J = 0 splitting of 23.79 GHz, because the doubling depends on J and K. The maser is the direct ancestor of the laser: the same population inversion in the same kind of cavity, at shorter wavelength. Ammonia's other importance is the nitrogen it carries. Atmospheric N2 is inert and most plants cannot use it; Haber-Bosch breaks that triple bond with hydrogen over an iron catalyst at high pressure, and about 70 percent of world ammonia goes to fertiliser. The bill is 8.6 EJ of final energy -- near 2 percent of the world total -- and around 450 Mt of CO2 directly each year, about 2.4 tonnes per tonne of ammonia, nearly twice as emissions-intensive as crude steel. The human figure is an estimate, not a measurement, and it has risen each time it is re-derived: Smil near 40 percent of world population for 2000, Erisman and co-workers near 48 percent for 2008, later work near 50 percent for 2019. Roughly four billion people. ## Controls -> what each maps to | Control | Maps to | Range / values | Physical meaning | |---|---|---|---| | Isotope | mu, reduced mass of the inversion coordinate | NH3 / ND3 | 2.487 u against 4.221 u; the switch changes nothing else, and the splitting drops by about fifteen | | Barrier | V_b, height of the Gaussian hump in V(x) | 0 to 4000 cm^-1, step 20 | 2020 cm^-1 is the real molecule; raise it and the splitting collapses by orders of magnitude, drop it to zero and the double well becomes a single one | | Level pair | v, which vibrational doublet is occupied | v = 0 to 3 | Higher doublets sit nearer the top of the hump and split far more widely; above the barrier the inversion is free rather than tunnelled | | Slow motion | log10 of the slow-motion factor | 10^6 to 10^14, default about 1.5 x 10^11 | Real time runs that many times faster than screen time; at the default the 21 ps flip takes about three seconds to watch, and the HUD warns when the phase advance outruns the frame rate | | Lone pair | -- | on / off | Shows or hides the amber lobe that swings across with the nitrogen | | V(x) panel | -- | on / off | The double well, plotted rotated 90 degrees so the nitrogen's height on screen is literally its position on the curve | | Running | -- | on / off | Runs or pauses the wavepacket; the space bar on the canvas does the same | | Reset | -- | button | Back to NH3, 2020 cm^-1, v = 0 and the default slow-motion factor | ## Learning objective After playing, a learner can explain why the H-N-H angle falls below the tetrahedral 109.5 degrees, describe the inversion as tunnelling through a barrier rather than thermal passage over it, convert a level splitting into a tunnelling period, and predict what that period does when the tunnelling mass is raised. ## Limits and connections The splitting in the HUD is computed, not quoted. The sim solves the one-dimensional Schrodinger equation live, in a harmonic-oscillator basis, for V(x) = (1/2) k x^2 + B exp(-C x^2) -- a harmonic restoring force plus a Gaussian hump. Its three constants were fitted once, to three measured NH3 numbers: the ground-state splitting 0.7934 cm^-1 and the two nu2 umbrella components at 932.43 and 968.24 cm^-1. Everything else is prediction, and most of it lands -- barrier 2019 cm^-1 against about 2020, inversion amplitude 38.1 pm, and hence 106.7 degrees. The isotope prediction is where it departs. The model gives an ND3 splitting near 0.046 cm^-1 against the measured 0.0531, an isotope ratio of about 17 rather than 15: it runs the deuterated molecule too slow. That is the price of one dimension with a reduced mass held constant along the path, since the real inversion also stretches the N-H bonds. The HUD is candid about it, printing the model value beside the experimental one every frame -- though it rounds the ND3 experiment to 0.053 cm^-1 = 1.60 GHz, where the sourced values are 0.0531 cm^-1 and 1.59 GHz. The double well and its exponential mass dependence are the lesson, not the third digit. For the single-particle standing waves underneath all of this see [[Hydrogen_atom]]; for the vibrational ladder in a well with only one minimum, [[Diatomic_molecule]]. ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Ammonia) : [Wikitube](https://en.wikitube.io/wiki/Ammonia) ## 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-microsim-pass (PORTAL_Hydrogen batch 1) - 0 deletions*