Atomic Hydrogen

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

Atomic hydrogen is formed by the union of a proton $\sf{p}^{+}$ with an electron $\sf{e^{-}}$, bound together by $\mathscr{F}$, a force-carrying collection of field quanta. An atom of hydrogen is noted by $\mathbf{H}$, so we write

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

The proton is represented by these quarks.

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

The electron is modeled from this selection

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

And the field for hydrogen in its spin-down ground-state is given by

${{\mathscr{F}}} \left( {\mathbf{H}} \right) \leftrightarrow 4\bar{\sf{d}} + + 2\bar{\sf{m}} + 2\sf{m} + 2\bar{\sf{a}} + 2\sf{a}$

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 quark-model of hydrogen. The reference frame is suggested by shading in the background. See these spreadsheets for more detail about this and other similar models that describe hydrogen in different excited states.

## Excited States of Hydrogen

$\begin{array}{rl} E_{j\,n} & = -\mu c^2\left[1-\left(1+\left[\dfrac{\alpha}{n-j-\frac{1}{2}+\sqrt{\left(j+\frac{1}{2}\right)^2-\alpha^2}}\right]^2\right)^{-1/2}\right] \\ & \approx -\dfrac{\mu c^2\alpha^2}{2n^2} \left[1 + \dfrac{\alpha^2}{n^2}\left(\dfrac{n}{j+\frac{1}{2}} - \dfrac{3}{4} \right) \right] \end{array}$

The principal quantum number, $\rm{n}$

## 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 understanding that the temperature of a hydrogen atom in its ground state is $\ T=0 \ \sf{\text{(K)}}$. Quark models for all nuclear particles have been carefully adjusted to try to get this. But, despite much effort, the closest obtained from current models is $\ T=-8.9 \times 10^{-6} \ \sf{\text{(K)}}$. We think that this number has no physical significance. Rather, it shows the limits of our calculation technique.

The stability of a nuclear particle depends on a balance of competing effects. And so temperature calculations are based on a few small differences between large numbers. Some 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 which are nothing more than ordinary office equipment. This problem is probably trivial for large computers run by professionals with expertise doing highly precise calculations.

 Next step: length.

Related WikiMechanics articles.

page revision: 630, last edited: 13 Apr 2019 21:16