Atomic Hydrogen

Notice: this page is under construction
Notice: this page is under construction

Atomic Hydrogen
$\Large{ k }$ $\large{ \delta _{\hat{m}} }$ $\large{ \delta _{\hat{e}} }$ $\large{ \delta _{\theta} }$ $\large{ \sf{P}_{\it{k}} }$
1 +1 0 +1 $\sf{d}\bar{\sf{d}} \ \sf{m}\bar{\sf{m}} \ \bar{\sf{t}}\sf{b}$
2 0 -1 +1 $\bar{\sf{u}} \ \bar{\sf{b}}\sf{t} \ \mathrm{2}\bar{\sf{g}}$
3 -1 0 +1 $\sf{d}\bar{\sf{d}} \ \sf{a}\bar{\sf{a}} \ \bar{\sf{t}}\sf{b}$
4 0 +1 +1 $\bar{\sf{u}} \ \bar{\sf{s}}\sf{c} \ \mathrm{2}\sf{e}$
5 +1 0 -1 $\sf{d}\bar{\sf{d}} \ \sf{m}\bar{\sf{m}} \ \bar{\sf{t}}\sf{b}$
6 0 -1 -1 $\bar{\sf{u}} \ \bar{\sf{b}}\sf{t} \ \mathrm{2}\bar{\sf{g}}$
7 -1 0 -1 $\sf{d}\bar{\sf{d}} \ \sf{a}\bar{\sf{a}} \ \bar{\sf{t}}\sf{b}$
8 0 +1 -1 $\bar{\sf{u}} \ \bar{\sf{s}}\sf{c} \ \mathrm{2}\sf{e}$

Definition: Atomic hydrogen is formed by the union of a proton $\sf{p}^{+}$, with an electron $\sf{e^{-}}$, bound together by a magnetic field $\mathscr{F}$. The letter $\mathbf{H}$ is used to note an atom of hydrogen.

$\mathbf{H} \equiv \left\{ \sf{p}^{+}, \sf{e}^{-}, \mathscr{F}_{\mathbf{H}} \right\}$

The proton is represented by these quarks

$\sf{p^{+}} \leftrightarrow 2\sf{d} + 2\bar{\sf{d}} + 4\sf{b} + 4\bar{ \sf{t} }$

The electron is

$\sf{e^{-}} \leftrightarrow 4\bar{\sf{u}} + 2\bar{\sf{b}} + 2\sf{t} + 2\bar{\sf{s}} + 2\sf{c} + 4\bar{\sf{g}}+ 4\sf{e}$

And the field is described by these $\sf{q}\bar{\sf{q}}$ pairs

$\mathscr{F}_{\mathbf{H}} \leftrightarrow \sf{ 2d\bar{d} + 2m\bar{m} + 2a\bar{a} }$

Then atoms of hydrogen are objectified from space-time events like the one shown in the accompanying table and movie.

Click on this image for a look around a two-dimensional quark model of the electron. The frame of reference is shown by shading in the background. Note that the mix of quarks versus anti-quarks may not be properly indicated in the images. See spreadsheets for the most up-to-date models.
Click on this image for a look around a two-dimensional quark model of the electron. The frame of reference is shown by shading in the background. Note that the mix of quarks versus anti-quarks may not be properly indicated in the images. See spreadsheets for the most up-to-date models.


Stability of Atomic Hydrogen

The stability of a particle is described by its mean life. And a quantitative analysis of particle lifetimes is set by a customary assumption that the temperature of a hydrogen atom in its ground state is $\ T=0 \ \sf{\text{(K)}}$. Our current quark models for all nuclear particles have been carefully adjusted to respect this convention.

But, despite much effort, the closest to zero we can get in our working calculations and spreadsheets is $\ T=-8.9 \times 10^{-6} \ \sf{\text{(K)}}$ for an atom of hydrogen in its ground state. This number has no physical significance. Rather, it shows the limits of our calculation technique.

Fundamentally, the stability of a nuclear particle is premised on a balance of competing effects. And so temperature calculations depend on a few small differences between some very large numbers. Some rounding errorsXlink.png are inevitable. And if the temperature is near zero, then these errors can add up to being a significant problem.

The non-zero result for hydrogen suggests that our temperature calculations are questionable for any result more exact than a few parts in a million.

This seems to be near the limit of what we can obtain from our present computing arrangements1 that are ordinary office equipment. This problem is trivial for large computers run by professionals with expertise doing highly precise calculations.


Gross Structure of Hydrogen Spectrum

Define $\mathit{ň}$ as the principal quantum number

$\begin{align} \mathit{ň} \equiv \frac{ n^{\sf{d}} }{4} \end{align}$

Consider an excited hydrogen atom $\mathbf{H}^{\ast}$ formed by the union of some photon $\large{\gamma}$ with a hydrogen atom in its ground state

$\mathbf{H}^{\ast} \equiv \left\{ \mathbf{H}, {\large{\gamma}} \right\}$

Down quarks are indestructible, the prinicpal quantum number is conserved when particles are combined or decomposed. So

$\mathit{ň} \left( \mathbf{H}^{\ast} \right) = \mathit{ň} \left( \mathbf{H} \right) + \mathit{ň} \left( {\large{\gamma}} \right)$

A hydrogen atom in its ground state $\mathbf{H}$ contains four down quarks, so $\begin{align} \mathit{ň} \left( \mathbf{H} \right) = 1 \end{align}$ and

$\mathit{ň} \left( \mathbf{H}^{\ast} \right) = 1 + \mathit{ň} \left( {\large{\gamma}} \right) > 1$


Photon Energy

When chemical quarks are considered, we can define photons that include no baryonic and no leptonic quarks, just rotating and chemical quarks. These photons are not gamma-rays. They are x-rays, radio-waves and all the photons in between; ultraviolet, visible and infrared. Their energies are typically measured in (eV), rather than (keV). For such low energies, effects from down-quarks are apparent.

From the penultimate equation in the discussion of the mechanical energy of photons

$\begin{align} E \left( {\large{\gamma}} \right) = 2 \left| \, H_{chem}^{\mathcal{A}} \vphantom{{H_{chem}^{\large{\gamma}}}^{9}} \right| \cdot \left[ \frac{64}{\left( \Delta n^{\sf{D}} \right)^{2} } - \frac{64}{ \left( N^{\sf{D}} \right)^{2} } \right] \end{align}$


The Rydberg Formula

Let

$\begin{align} \mathit{ň} \left( \mathbf{H}_{i} \right)= \frac{ \, N^{\sf{D}} (\gamma) \, }{8} \end{align}$

$\begin{align} \mathit{ň} \left( \mathbf{H}_{f} \right) = \frac{ \Delta n^{\sf{D}} (\gamma) }{8} \end{align}$

$\begin{align} \mathcal{R} \left( \mathbf{H} \right) = 2 \left| \, H_{chem}^{\mathcal{A}} \vphantom{{H_{chem}^{\large{\gamma}}}^{9}} \right| \end{align}$

Then

$\begin{align} E(\gamma) &= \mathcal{R} \left( \frac{1}{ \mathit{ň} _{f}^{2} } - \frac{1}{ \mathit{ň} _{i}^{2} } \right) \end{align}$

Right.png Next step: the spectrum of hydrogen.
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