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Big 3-Dimensional Atoms

Outline

Definitions of Atoms

In accordance with conventional chemistry various atoms are understood as combinations of protons, electrons and neutrons. These subatomic components have all been specified from quarks and reference sensations. So for EthnoPhysics, atoms are ultimately defined from sensations too. They are generically represented using bold, serified upper-case letters like  \mathbf{A} or  \mathbf{B}.

The smallest atom is hydrogen, noted by  \mathbf{H}. Hydrogen is also the smallest stable particle formed from a fully three-dimensional octet of sub-atomic components. Other bigger atoms can meet this requirement even more easily. So atomic events are all space-time events. Atomic events have positions and occurrence times that can be well-defined and perhaps measured.

Quantum Numbers for Atoms

Here are some quantum numbers for use in atomic descriptions that gloss over visual sensation. To objectively discuss atoms we adopt  \mathrm{n},  \ell,  s and  j instead of the four coefficients of rotating quarks  n^{\mathsf{u}},  n^{\mathsf{\overline{u}}},  n^{\mathsf{d}} and  n^{\mathsf{\overline{d}}} that previously accounted for achromatic visual sensations. Taken together, they are said to specify an atomic state. Note that  \mathrm{n} and  s are defined from simple sums and differences of quark coefficients, so they are always conserved. The principal quantum number is given by

\mathrm{n} \equiv  n^{\mathsf{d}}  / 4

This principal number was defined and discussed earlier. It is used to describe how an atom is excited by interactions with other particles. The azimuthal quantum number is also known as the orbital quantum number. It is defined by

\ell \equiv \dfrac{ \; n^{\mathsf{u}} + n^{\mathsf{\overline{u}}} - 3n^{\mathsf{d}} + n^{\mathsf{\overline{d}}} + \left| \, n^{\mathsf{u}} + n^{\mathsf{\overline{u}}} - n^{\mathsf{d}} - n^{\mathsf{\overline{d}}} \rule{0px}{9px} \; \right| \, }{8}

But recall that N^{\mathsf{Z}} \equiv n^{\mathsf{z}} + n^{\mathsf{\overline{z}}} so the azimuthal number can also be written as

\ell = \dfrac{ \; N^{\mathsf{U}} + N^{\mathsf{D}} + \left| N^{\mathsf{U}} - N^{\mathsf{D}} \rule{0px}{10px} \right| - 16\mathrm{n} \; }{8}

The spin angular momentum quantum number is defined by

s \equiv \dfrac{ \;  n^{\mathsf{u}} + n^{\mathsf{\overline{u}}} - 3 n^{\mathsf{d}}+ n^{\mathsf{\overline{d}}} \; }{8}

which may also be written as

s = \dfrac{ \;   N^{\mathsf{U}} + N^{\mathsf{D}} - 16\mathrm{n} \; }{8}

And finally, the total atomic angular momentum quantum number is given by

j \equiv \dfrac{ \; \left| \, n^{\mathsf{u}} + n^{\mathsf{\overline{u}}} - n^{\mathsf{d}} - n^{\mathsf{\overline{d}}} \rule{0px}{10px} \, \right| \; }{8} = \dfrac{ \; \left|  N^{\mathsf{U}} - N^{\mathsf{D}} \rule{0px}{10px} \right| \; }{8}

This is the same functional relationship used earlier to define \textsl{\textsf{J}}, the total angular momentum quantum number for nuclear particles. The duplication is so that we may use the lower case letter  j to identify the atom in problems that also involve an electron.

Chemical Quarks

The union of a conjugate seed and a chemical seed is called a chemical quark. Chemical quarks are symbolized using bold lower-case Roman letters with serifs like a b and d. (This is different from a b and d, the sans-serif font used for thermodynamic quarks.) So chemical quarks are defined by objectifying pairs of Anaxagorean sensations and named after their chemical seeds. Objectification changes narrative forms of description from using adjectives to identify sensations, to using nouns for identifying particles. Click on any icon in the table below for more detail.

Chemical Quark Definitions
tart taste on the right

+

acidic quark
tart taste on the left

+

acidic anti-quark
soapy taste on the right

+

basic quark
soapy taste on the left

+

basic anti-quark
brackish taste on the right

+

ionic quark
brackish taste on the left

+

ionic anti-quark
potable taste on the right

+

aqueous quark
potable taste on the left

+

aqueous anti-quark
sweet taste on the right

+

dextro quark
sweet taste on the left

+

dextro anti-quark
savory taste on the right

+

levo quark
savory taste on the left

+

levo anti-quark
Anaxagorean sensations are like these painted building-blocks.

Chemical quarks are building-blocks that we can combine to model more complicated particles. We use them to define atomic bonds. There are 6 different chemical seeds, so there are six different chemical quark types. Each type includes an ordinary-quark and an anti-quark, for a total of 12 particles. Chemical quarks are described by their internal energy  U as shown in the accompanying table. Note that this internal energy is reported in (eV) not (Mev), the chemical quarks are about a million times smaller than thermodynamic quarks.

Chemical Quark Traits

Quark Type

Quark IndexInternal Energy

\mathsf{Z}

 \zeta

U (eV)

11-2.216
12-1.801
13-2.114
14-2.549
15-0.02875
16-0.04894

Atomic Bonds and Molecules

WikiMechanics portrays molecules as compound atoms that are held together by atomic bonds. The bonds that we consider here are defined from pairs of electrons. We intend to treat these atomic bonds as countable entities, as for example in Lewis dot diagrams or VSEPR theory . So we need to follow some rules of logic and mathematics. Specifically, by Pauli’s exclusion principle we cannot have two identical electrons in the same set. So we need to distinguish electrons from each other. And, in molecules with more than one bond, we need to distinguish atomic bonds from each other too.

Seeds are not enough, so Mr. Quirky is here to remind us about other sensations.
Don’t forget about other sensations. Click for more.

Traditionally, we meet this requirement by saying that different bonds and electrons are distinct from each other because they are in different places. But, by the premise of EthnoPhysics, we cannot satisfy Pauli’s exclusion principle by resorting to a spatial explanation. And also we cannot use any visual sensation to make the distinction either, because the visual sensations used to define dynamic seeds have already been constrained by earlier hypotheses.

So instead, we differentiate them by association with different taste sensations. To satisfy Pauli’s exclusion principle, electrons are distinguished from each other by their union with various chemical quarks such as or . We use the letter  \mathbb{B} to identify specific bonds in the following discussion. Each bond is characterized by D_{\mathsf{o}} a bond dissociation energy given by

\displaystyle D^{\mathbb{B}}_{\mathsf{o}} \, \equiv H^{\mathbb{B}} - N^{\mathsf{e}} H^{\mathsf{e}} = \sum_{\mathsf{q} \in \mathbb{B}} \Delta n^{\mathsf{q}} U^{\mathsf{q}}

where H^{\mathbb{B}} is the bond’s enthalpy. The coefficients of quark  \mathsf{q} are noted by   \Delta n^{\mathsf{q}} . And  U notes the internal energy. The number of electrons in the bond is written as  N^{\mathsf{e}} .

Experimental observations1Bond Dissociation Energies in Simple Molecules , National Standard Reference Data Series Number 31, B. deB. Darwent, U.S. National Bureau of Standards, 1970., 2Bond Dissociation Energies of Organic Molecules , Stephen J. Blanksby and G. Barney Ellison, Accounts of Chemical Research 36 (4), 2003., 3Bond Dissociation Energies , Armen Zakarian, University of California Santa Barbara., 4Strengths of Chemical Bonds , J. Alistair Kerr and David W. Stocker, CRC Handbook of Chemistry and Physics 81st Edition, Lide, D.R. (Editor), Boca Raton, Florida, 2000. report D_{ \mathsf{o}} for the gaseous state.

Archetypical Single Bonds

Let us start by associating an acidic quark with one of the electrons in a covalent bonding pair. This simple arrangement is called \mathbb{B} \small{\mathsf{(semi \ acidic) }}. It is the first example of a bond formed predominantly from acidic quarks.

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

Single bonds are often indicated using a short line segment. For example, in the chemical structure diagram for  \mathrm{Au}_{\mathsf{2}} a diatomic gold molecule, the bond is represented as Au–Au. This is the only ligature defined from just one chemical quark. The archetypal acidic bond involves two acidic quarks like this

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

This arrangement accurately represents the bond in H–Cl, a strong acid. No more acidic quarks can be added to a pair of electrons without violating Pauli’s exclusion principle. So next we consider distinguishing electrons by association with basic quarks

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

This set of quarks and electrons accurately represents the bond in sodium hydroxide, Na–OH, also known as lye. Similar bonds can be defined using ionic and aqueous quarks for molecules of table salt, and water. These bonds are made from groups of quarks that are all the same quark-type. They are very homogeneous, so quark character may extend to molecular character.

Double Bonds

The single bonds discussed above all involve one pair of electrons. But we may also include more electrons to define double bonds which are made from four electrons. For example, here is a double acidic bond

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

This set correctly describes the bond strength in sulfur dimers, S=S. Here is a double basic bond

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

The strength of the double-bond in carbon dioxide, O=CO, is correctly represented by this arrangement. And here is a double aqueous bond

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

This bond accurately represents the link between oxygen atoms in the important diatomic gas molecule \mathrm{O}_{\sf{2}}. Stereochemical quarks have about 1% of the internal-energy of other chemical quarks, but nonetheless, they still play an important logical role by distinguishing between similar bonds. For example consider this bond

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

which accurately describes the strength of the double-bond in diazine, HN=NH. If we imagine that each single-bond of the pair is formed from one wet-quark and one stereochemical-quark, then there are two distinct possibilities. They can be written as

\mathbb{B} \mathsf{(double \ wet \ type1)} \equiv { { { \mathsf{e^{-}}, }, { \mathsf{e^{-}}, } }, { { \mathsf{e^{-}}, }, { \mathsf{e^{-}}, } } }

\mathbb{B} \mathsf{(double \ wet \ type2)} \equiv { { { \mathsf{e^{-}}, }, { \mathsf{e^{-}}, } }, { { \mathsf{e^{-}}, }, { \mathsf{e^{-}}, } } }

Both of these bonds contain the same quarks, but they are still logically different from each other. And in the laboratory, chemists do indeed find two different forms of diazine

Ball-and-stick model of the cis-diazene molecule, N2H2
cis-diazene
Ball-and-stick model of the trans-diazene molecule, N2H2
trans-diazene

The distribution of stereochemical quarks is thus associated with geometric isomerism.

Triple Atomic Bonds

The forgoing double-bonds all contain just four electrons, but we may also include another pair of electrons to define triple bonds such as

\mathbb{B} \mathsf{(triple \ wet \ acidic)} \equiv { { \mathsf{e^{-}}, }, { \mathsf{e^{-}}, , }, { \mathsf{e^{-}}, , }, { \mathsf{e^{-}}, }, { \mathsf{e^{-}}, }, \mathsf{e^{-}} }

The very strong triple-bond in carbon monoxide, C≡O, is correctly represented by this arrangement. And here is another triple-bond that accurately models the link in N≡N, a molecule of nitrogen gas

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

And here are some other double and triple bonds

Hydrides

Acidic quarks are featured prominently in models of binary hydrogen compounds. For example, this bond accurately represents the link between hydrogen atoms in \mathrm{H}_{\mathsf{2}}, a diatomic molecule of hydrogen gas

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

The following models give results that are within experimental uncertainty even though observations of the hydrides are so precise that ten quarks are required to include hydrogen deuteride.

Salts and Halogens

It is possible to construct models of salt molecules and halogen gases that make extensive use of ionic quarks.

But laboratory observations that report only two or three significant figures do not constrain the theory very much. So models that do not include ionic quarks are also possible. And more generally, the chemical characteristics of molecules are only weakly related to the quarks in their bonds. It is not even clear that the notion of an electron-pair bond is always a good idea. Van der Waals forces may be more relevant, especially for weak bonds. Nonetheless, we have working models for the bonding in a variety of other dimers.5For details about calculating bond strengths, please see the spreadsheets titled Atoms & Photons and Bond Data.

Sensory interpretation: All of the bonds discussed above are defined from three distinct classes of sensation; sour, salty and sweet tastes. They may vary independently from each other. So, in an upcoming article, we use these bonds to define a three-dimensional Cartesian coordinate system for making space-time descriptions of molecules. And after that, we stop worrying about Pauli’s principle.

Atomic Clocks

Atoms are objectified from eight-fold patterns of sensation, similar to the anthropomorphic motifs in this Indonesian textile
Two by Four Tampan, Paminggir people. Lampung region of Sumatra, 19th century, 55 x 59 cm. From the library of Darwin Sjamsudin, Jakarta. Photograph by D Dunlop.

Hydrogen atoms are the smallest stable particles defined from a fully three-dimensional octet of space-time events. And so, they are also the smallest particles to be precisely represented in three-dimensional space. The locations of larger atoms are easier to establish. So we assume that a position  \bar{r}, and a time of occurrence  t, can be associated with anything that happens to an atom. Assigning a position to an atom is discussed later in an article about molecular models. But we can readily assign a time-of-occurrence to atomic events by thinking of atoms as atomic clocks.

Atoms oscillate and jostle about in complex ways. So many different modes of atomic vibration have been examined in the laboratory, compared with historical standards of timekeeping, and assessed for their practical use as clocks. Some are excellent. Atomic fountain clocks can make time measurements that are good to one part in 1014 and they are still being improved. High precision laboratory work often uses atoms of caesium. But here is a way to tell time using a generic atom,  \mathbf{A} . Let  \mathbf{A} be described by a repetitive chain of events

\Psi^{\mathbf{A}} = \left(\mathsf{\Omega}_{\mathsf{o}}, \, \mathsf{\Omega}_{1}, \, \mathsf{\Omega}_{2} \, \ldots \, \mathsf{\Omega}_{k} \, \ldots \right)

where orbital cycles are composed of  N quarks as

\mathsf{\Omega}^{\mathbf{A}} = \left( \mathsf{q}_{1}, \, \mathsf{q}_{2}, \, \mathsf{q}_{3} \, \ldots \, \mathsf{q}_{N} \right)

Since  \mathbf{A} is being used as a clock, we assume it has been sufficiently stabilized and isolated so that its vibrations are steady and regular. We assume their period  \widehat{\tau} has been measured, so that  \mathbf{A} is calibrated. Then we can determine an elapsed time just by counting atomic cycles to determine k. We write

\Delta t \equiv t_{k} - t_{\mathsf{o}} = k \widehat{\tau}

Without loss of generality, let t_{\mathsf{o}} = 0 so that t_{k} = k \widehat{\tau}. And recall that the period is given by \hat{\tau}= 1/ \nu where  \nu is the frequency of  \mathbf{A}. Then t_{k} = k / \nu . Also, by definition the frequency is \nu \equiv N \omega / 2 \pi where  \omega is the angular frequency of  \mathbf{A}. And so event  k occurs at a time given by

t_{k} = \dfrac{2\pi k}{N \omega}

Recall that the phase angle  \theta of  \mathbf{A} is given by \theta_{k} = \theta_{\mathsf{o}} + 2\pi k/N. So we can write

t_{k} = \dfrac{\theta_{k} - \theta_{\mathsf{o}}}{\omega}

This relationship expresses the time-of-occurrence of the  kth event as a function of the phase-angle. Time is thus told. However, we often think of time as the independent parameter and write the phase-angle as a function of time; the  k-subscript is dropped, and   \theta ( t ) is substituted for   \theta_{ k}. Then rearranging gives

\theta (t) =    \theta_{\mathsf{o}} + \omega t

This form is good for describing the rotating motion of particles when they are framed in a Cartesian view.

Next we consider how to assemble the foregoing ideas into an account of EthnoPhysics faviconAtomic Hydrogen.

References
1Bond Dissociation Energies in Simple Molecules , National Standard Reference Data Series Number 31, B. deB. Darwent, U.S. National Bureau of Standards, 1970.
2Bond Dissociation Energies of Organic Molecules , Stephen J. Blanksby and G. Barney Ellison, Accounts of Chemical Research 36 (4), 2003.
3Bond Dissociation Energies , Armen Zakarian, University of California Santa Barbara.
4Strengths of Chemical Bonds , J. Alistair Kerr and David W. Stocker, CRC Handbook of Chemistry and Physics 81st Edition, Lide, D.R. (Editor), Boca Raton, Florida, 2000.
5For details about calculating bond strengths, please see the spreadsheets titled Atoms & Photons and Bond Data.