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Molecular Hydrogen

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This bold letter H is an icon for hydrogen.


Cartesian Models Table

Ground State Proton

Magnetically Excited Proton

Ground State Electron

Ground State Hydrogen Atom

Electromagnetically Excited Hydrogen Atom

Excited Hydrogen Atom

Unitary Gas Molecules

  • note that even the fine-structure analysis of atomic hydrogen requires the use of just one type of stereochemical quark, i.e. so far shown as levo quarks
  • so it is possible to model another type of hydrogen hydrogen by substituting dextro quarks for levo quarks, i.e. the two types are levo-rotary and dextro-rotary hydrogen
  • to make a unitary model of molecular hydrogen gas, we need two distinct hydrogen atoms
  • traditionally, we meet this requirement to be distinguishable by saying that different atoms are distinct from each other because they are in different places. But, by the [[[premise |premise]]] of WikiMechanics, we cannot satisfy Pauli’s exclusion principle by resorting to a spatial explanation.
  • so instead we use stereo chemical quarks to distinguish the hydrogen atoms in hydrogen gas
  • then we can satisfy Pauli’s principle even for the form of hydrogen where spins are alligned
  • small differences in the constants //k//(levo) and //k//(dextro) can account for the energy differences between //ortho// and //para// forms of hydrogen gas.

Diatomic Hydrogen Molecules

A fully three-dimensional model of molecular hydrogen.
  • modeled as a two-body mechanical system in a [[[space-molecular |three dimensional]]], isotropic, homogeneous space
  • for spatial [[[spatial-homogeneity |homogeneity]]], both bodies must have integer quantum numbers
  • for spatial [[[spatial-isotropy |isotropy]]], both bodies must be at least a large as atoms
  • for spatial [[[spatial-isotropy |isotropy]]], the description of chromatic sensation is glossed-over. Direct discussion about the categorical description of color are overlaid by calibrated measurements
  • measurements of displacement and elapsed time are what space time descriptions are made from
  • the details of how these measurements are made is very diverse, many thousands of pages of detailed descriptions of how conditions are controlled, samples prepared, equipment arranged and information recorded. But there are some common characteristics:
  • First, lots of visual reports about macroscopic objects; dial positions, meter readings, digital numeric indicators like nixie-tubes, cathode-ray tubes, printer output, computer generated graphics, etc. This is where all the visual sensations are reported, before they get glossed over. And they all can be classified and described using a direct [[[binary |binary method]]]
  • Second, all communicants in the scientific literature are members of the biological species //homo sapiens//. Other species have made contributions to science, but humans are doing all the writing.
  • So third, all our measurement data, comes to us after filtering through a veil of sensory capabilities that are specifically tied to human biology.
  • This human perceptual filter has a strong influence on all our scientific knowledge. Especially the historical knowledge obtained by direct observation. These ‘visible to the naked eye’ experiences have had the longest and strongest effect on the development of our ideas about space and time.
  • knowledge about the direction of particle momentum is obtained by what can be measured: the velocity. But this vector is still constrained by quantization and conservation rules
  • the direction of motion \hat{p} is defined from

\hat{p} \equiv \begin{cases} (0, 0, 0)  &\sf{\text{if}} \; \parallel \mathsf{\overline{v}} \parallel = 0     \\    \dfrac{ \mathsf{\overline{v}} }{ \parallel \mathsf{\overline{v}} \parallel } &\sf{\text{if}} \;  \parallel \mathsf{\overline{v}} \parallel \ne 0 \end{cases}

  • in the new space, [[\hat{p}]] has no manifest relationship with [[\overline{\rho}]]. But the norm of the momentum, [[p]] is the same in both quark-space and Euclidean-space. So in the glossy descriptions we write [[\overline{p} = p \hat{p}]]. Then, in the Euclidean/Cartesian system, rules about the conservation of momentum are expressed by vector sums of this quantity.
  • so the smallest two-body system that is fully three-dimensional is diatomic hydrogen, [[\mathbf{H_{2}}]]
  • photons?
  • for ortho/para freedom or choice in view of Pauli’s principle, let [[\mathbf{H_{2}}]] contain one each of a levo-rotary and dextro-rotary hydrogen atom
  • Let one of the hydrogen atoms, [[\mathbf{H_{o}}]] or? [[\mathbf{H}_{\sf{F}}]], provide a [[[frames |reference frame]]] for describing the other hydrogen atom, [[\mathbf{H}]]. The position of this atom is called the //spatial origin//.
  • the [[[space-molecular |handedness]]] of the coordinate system depends in the chiral character of the hydrogen atom selected a the spatial origin. E.g., if [[\mathbf{H}_{\sf{F}}]] is dextro-rotary, then it is called a right-handed coordinate system.
  • The [[[quark-space |polar axis]]] of the reference frame is noted by [[\hat{z} \equiv (0, 0, 1)]]. The [[[axes |abscissa]]] is written as [[\hat{x} = (1, 0, 0)]], and the [[[axes |ordinate]]] is [[\hat{y} = (0, 1, 0)]]. We generally assume that the space has a [[[euclidean-metric |Euclidean metric]]] and that [[\hat{x}]], [[\hat{y}]] and [[\hat{z}]] are all [[[norm |orthogonal]]] to each other.
  • The [[[total-angular-momentum |total angular momentum]]] vector of [[\mathbf{H_{o}}]] is noted by [[{\rm{\overline{J}}}]]. We say that [[{\rm{\overline{J}}}]] and [[\hat{z}]] are aligned or parallel to each other.
  • The [[[position |separation]]] vector, [[\overline{r}]], notes the [[[position |position]]] of [[\mathbf{H}]].
  • The [[[velocity | velocity]]] of [[\mathbf{H}]], in a frame provided by [[\mathbf{H_{o}}]], is noted by the vector [[\mathsf{\overline{v}}]]. And the [[[displacement-atomic |net displacement]]] over one atomic cycle, of any atom, is always along its own polar axis. So if [[{\mathsf{\overline{v}}} \ne ( 0, 0, 0 )]], then it also indicates the direction of the total angular momentum vector of [[\mathbf{H}]]. In general, it is not aligned with the polar axis of the reference frame.
  • In principle, [[\overline{r}]] and [[\mathsf{\overline{v}}]] are established by [[[space-molecular |measurements]]] of sensation, and nothing else. [[[space-molecular |Space itself is defined]]] as an elaborate way of organizing and storing experimental data. And [[[space-one-dimensional |empty space is not defined]]].
  • the force binding hydrogen atoms together into the [[[excited |ground-state]]] of [[\mathbf{H_{2}}]] is accurately represented by a [[[bonds |chemical bond]]] composed of five [[span style=” display:inline-block ; “]][[[chemical-quarks |chemical quarks]]][[/span]] and two electrons

\mathbb{B} \mathsf{(1)} \equiv { { \mathsf{e^{-}}, , }, { \mathsf{e^{-}}, , }, }

Ground State Model of Atomic Hydrogen

  • three spatial dimensions
  • both atoms in ground-state, so no temporal dimension required because there is no net atomic motion, [[\mathbf{H}]] is static
  • [[\mathsf{\overline{v}} = ( 0, 0, 0 )]]
  • both atoms just do vibrations back and forth along the axes of their angular momenta
  • in general, the [[[position |separation]]] vector can take on any values for [[[cartesian-coordinates |Cartesian coordinates]]]; [[\overline{r} = ( x, y, z )]]

Hydrogen Excited by Electromagnetic Field

A three-dimensional model of electromagnetically excited hydrogen.
  • two spatial dimensions plus time coordinate in lieu of polar axis
  • [[\overline{r} = ( x, y, 0 )]]
  • [[\mathbf{H}]] has uniform linear motion along the axis of the momentum of [[\mathscr{F}]] which is limited to the xy plane by electromagnetic requirement. So no strange quanta or weak forces in this model.
  • [[\mathsf{\overline{v}} = ( \mathsf{v}<em>{x}, \mathsf{v}</em>{y}, 0 )]]
  • A Two-dimensional Model of Hydrogen Excited by Electromagnetic Field
A two-dimensional model of electromagnetically excited hydrogen.
  • no radiative transitions between homonuclear ortho and para forms (p.2 Habart)
  • electronic transitions, rotational spectra, vibrational spectra, Raman