Big 3-Dimensional Atoms

Outline

In accordance with conventional chemistry various atoms are understood to be combinations of protons, electrons and neutrons. These atomic 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 $\mathbf{B}$ .

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Atoms are objectified from eight-part compound events like this. Click for more about space-time events.

The smallest atom is hydrogen, noted by $\mathbf{H}$ . Hydrogen is also the smallest stable particle defined from a fully three-dimensional array of orbital components. Other bigger atoms can meet this requirement for tridimensionality even more easily. So atomic happenings are all space-time events. That is, atomic events have positions and occurrence times that are well-defined and potentially measurable.

Quantum Numbers for Atoms

Here are some more quantum numbers for use in atomic descriptions that gloss over visual sensation. To objectively discuss atoms we adopt $\mathrm{n},$ $\ell,$ $s$ , $m_{S}$ and $\textsl{\textsf{J}}$ 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 $m_{S}$ are defined from simple sums and differences of quark coefficients, so they are always conserved.

Principal

The principal quantum number $\mathrm{n}$ is defined by

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

This principal number was discussed earlier. It is used to describe how an atom is excited by interactions with other particles.

Azimuthal

The azimuthal quantum number is also known as the orbital quantum number. It is given 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

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

Spin-Projection

The spin-projection quantum number $m_{S}$ was defined and discussed earlier. For the electron in an atom of hydrogen it is

$m_{S} = \dfrac{ \; n^{\mathsf{u}} + n^{\mathsf{\overline{u}}} - 3 n^{\mathsf{d}}+ n^{\mathsf{\overline{d}}} \; }{8} = \widehat{\mathrm{n}} - 2\mathrm{n}$

where $\widehat{\mathrm{n}}$ is the rotary quantum number. Sometimes we are sloppy and refer to $m_{S}$ as $s .$

Total Angular Momentum

The total angular momentum quantum number $\textsl{\textsf{J}} \, ,$ is defined by

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

Sometimes we also use a lower-case $j$ for this quantity when considering two-body problems. For pointy particles, the spin quantum number $s$ is given by $\textsl{\textsf{J}} .$

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 sensation on the right

→

acidic quark

tart sensation on the left

→

acidic anti-quark

soapy sensation on the right

→

basic quark

soapy sensation on the left

→

basic anti-quark

brackish sensation on the right

→

ionic quark

brackish sensation on the left

→

ionic anti-quark

potable sensation on the right

→

aqueous quark

potable sensation on the left

→

aqueous anti-quark

sweet sensation on the right

→

dextro quark

sweet sensation on the left

→

dextro anti-quark

savoury sensation on the right

→

levo quark

savoury sensation 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 and molecules. 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 much smaller than thermodynamic quarks.

Chemical Quark Traits
Quark Type	Quark Index	Internal Energy
$\mathsf{Z}$	$\zeta$	U (eV)
Ⓐ	11	-2.216
Ⓑ	12	-1.801
Ⓘ	13	-2.114
Ⓦ	14	-2.549
Ⓓ	15	-0.049
Ⓛ	16	-0.029

Electrochemical Quarks

Quarks formed from electrochemical seeds are called electrochemical quarks. There are eight of them. The acidic quarks

and

. The basic quarks

and

. The ionic quarks

and

. And finally, the aqueous quarks

and

Stereochemical Quarks

Quarks formed from stereochemical seeds are called stereochemical quarks. There are four of them. The dextro quarks and . And the levo quarks and .

an icon showing tools to indicate work in progress

Construction Zone

We quantify the relevance of stereochemical-quarks using $N^{\textcircled{\raisebox{.5pt}{\sf{\tiny{S}}}}} ,$ the total number of stereochemical-quarks in P.

$N^{\textcircled{\raisebox{.5pt}{\sf{\tiny{S}}}}} \equiv N^{\textcircled{\raisebox{.5pt}{\sf{\tiny{L}}}}} + N^{\textcircled{\raisebox{.5pt}{\sf{\tiny{D}}}}}$

This number $N^{\textcircled{\raisebox{.5pt}{\sf{\tiny{S}}}}}$ is also the stereochemical seed coefficient. So as discussed previously, shifting from quark-coefficients to seed-coefficients assists the description by discounting a distinction between left-handed or right-handed.

Calculations based on $N^{\textcircled{\raisebox{.5pt}{\sf{\tiny{S}}}}}$ give the same result even if there is some confusion or mix-up between left-handed and right-handed rotations. This indifference is useful because it simplifies calculations and makes them less dependent on specific arrangements. Using seed-coefficients instead of quark-coefficients is a way to transcend sensory detail. It is an important way of objectifying a description.

After forgetting about the handedness, stereochemical quarks are subsequently characterized by their average internal energy

$\widetilde{U}^{\textcircled{\raisebox{.5pt}{\sf{\tiny{S}}}}} \equiv \dfrac{ \widetilde{U}^{\textcircled{\raisebox{.5pt}{\sf{\tiny{L}}}}} + \widetilde{U}^{\textcircled{\raisebox{.5pt}{\sf{\tiny{D}}}}} }{2} \simeq -39 \text{ \sf{(meV)}}$

The Intrinsic Parity

Next we reconsider the sweet sensations that were associated with a taste of honey. Recall that these pleasant flavours were given a binary description as either sugary or savoury. Sugary sensations were objectified as dextro quarks, $\mathbf{d}$ or $\overline{\mathbf{d}}$ . And savoury sensations were reified as the levo quarks $\mathbf{l}$ or $\overline{\mathbf{l}}$ . Both dextro and levo quarks were classified together as stereochemical quarks.

Let some particle P be characterized by $N^{\textcircled{\raisebox{.5pt}{\sf{\tiny{L}}}}}$ and $N^{\textcircled{\raisebox{.5pt}{\sf{\tiny{D}}}}} ,$ the coefficients of its stereochemical seeds. That is

$N^{\textcircled{\raisebox{.5pt}{\sf{\tiny{L}}}}} \equiv n^{\overline{\mathbf{\,l}}} + n^{\mathbf{\, l}}$

and

$N^{\textcircled{\raisebox{.5pt}{\sf{\tiny{D}}}}} \equiv n^{\overline{\mathbf{d}}} + n^{\mathbf{d}}$

Then the distribution of stereochemical-quarks in P is characterized by a number called the intrinsic parity which is noted by $\delta_{\! \pi}$ and defined as

$\delta_{\! \pi} \equiv \begin{cases} +1 & \mathsf{\text{if}} \; \; N^{\textcircled{\raisebox{.5pt}{\sf{\tiny{L}}}}} < N^{\textcircled{\raisebox{.5pt}{\sf{\tiny{D}}}}} \\ \; \; 0 & \mathsf{\text{if}} \; \; N^{\textcircled{\raisebox{.5pt}{\sf{\tiny{L}}}}} = N^{\textcircled{\raisebox{.5pt}{\sf{\tiny{D}}}}} \\ -1 & \mathsf{\text{if}} \; \; N^{\textcircled{\raisebox{.5pt}{\sf{\tiny{L}}}}} > N^{\textcircled{\raisebox{.5pt}{\sf{\tiny{D}}}}} \end{cases}$

If $\delta_{\! \pi} \! = \! +1$ then P is said to be even. If $\delta_{\! \pi} \! = \! -1$ then P is odd. And if $\delta_{\! \pi} \! = 0$ then we say that P has no parity, none. The intrinsic parity thus depends only on the quarks contained in P, not on some external reference frame. So a particle that has its parity classified as even, odd or none will remain in the same category for any frame of reference.

The intrinsic parity depends on the total number of dextro or levo seeds. Therefore it does not depend on whether they are contained in ordinary-quarks or anti-quarks. So every particle $\mathsf{P}$ and its conjugate twin $\overline{\mathsf{P}}$ have the same intrinsic-parity. We write

$\delta_{\! \pi} ( \mathsf{P} ) = \delta_{\! \pi} ( \overline{\mathsf{P}} )$

Sensory interpretation: Dextro-quarks and levo-quarks are objectified from sweet oral sensations. So if $\delta_{\! \pi} \! = \! +1$ then sugary sensations outnumber savoury sensations. For $\delta_{\! \pi} \! = \! -1$ savoury sensations are more numerous than sugary sensations. So the intrinsic parity indicates whether a complex oral experience is more sugary or savoury.

Atomic Bonds

Following custom, EthnoPhysics 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 count these atomic bonds, as for example in Lewis dot diagrams or VSEPR theory . So we need to follow some rules of arithmetic and logic. Specifically, by Anaxagorean narrative conventions, Cantor’s definition of a set, and Pauli’s exclusion principle, we cannot have two identical electrons in the same description. So we need to distinguish electrons from each other. And, for 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 various bonds and electrons are distinct because they are in different places. But, by the premise of EthnoPhysics, we cannot innocently resort to any sort of spatial explanation.

So instead we invoke the first hypothesis and assert that bonds are distinguished by association with various oral sensations. That is, we presume that bonds and electrons are logically distinct due to their union with various chemical quarks. Then subsequently, we use atomic bonds to define a Cartesian system for describing spatial relationships.

The letter $\mathbb{B}$ is used to identify specific bonds in the following discussion. Bonds are characterized by $D_{\mathsf{o}}$ a dissociation energy defined by

$D^{\, \mathbb{B}}_{\mathsf{o}} \, \equiv \left| H^{\mathbb{B}} - N_{\!\mathsf{e}}^{\mathbb{B}} \hspace{0.5pt} H^{\mathsf{e}} \rule{0px}{12px} \right|$

where $H$ marks the enthalpy and $N_{\!\mathsf{e}}^{\mathbb{B}}$ gives the number of electrons in the bond. So the quarks that determine the dissociation-energy are not in the electrons. Rather, they are the bond’s chemical quarks. Then recall that the chemical enthalpy of any particle has been defined from the sum

$\displaystyle H_{\! chem} \equiv \sum_{\zeta=11}^{16} \Delta n^{\zeta} U^{\zeta}$

where $U$ marks the internal energy and quark coefficients are written as $\Delta n .$ So the dissociation-energy of a particle’s bond, is directly related to the enthalpy of its chemical quarks by

$D^{\, \mathbb{B}}_{\mathsf{o}} = \left| \, H_{\! chem}^{\mathsf{P}} \, \right|$

Then since $H \! ( \mathsf{P} ) = - H \! ( \mathsf{\overline{P}} )$ we have

$D_{\! \mathsf{o}} ( \mathsf{P} ) = D_{\! \mathsf{o}} ( \mathsf{\overline{P}} )$

Single Bonds

When $N_{\!\mathsf{e}} \! = \! 2 \, ,$ links are called single bonds and depicted by a short line segment. For example H–H indicates the tie between hydrogen atoms in a diatomic molecule of hydrogen gas. Experimental observations report $D_{ \mathsf{o}}$ for the gaseous state.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.^, ³Strengths 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.

Some single bonds are modeled from groups of quarks that are all the same quark-type, they are unusually homogeneous. For a few of these bonds, quark character can be experienced directly as the flavour of an associated molecule. Thus basic quarks are like lye-soap, and ionic quarks are like table-salt, etc. These models are called archetypical bonds. But more often quark-types are varied, and the flavour of a molecule is not specifically related to its chemical quarks.

To start a quantitative analysis of single bonds, we associate one acidic quark with one of the electrons of a bonding pair. This arrangement is called $\mathbb{B} \small{\mathsf{(anti} \, \mathsf{acidic)}} .$ It is the only ligature defined from just one chemical quark

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

This bond correctly models the dissociation energy of Au–Au, a diatomic gold molecule. And here is another bond with two acidic quarks

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

This arrangement accurately represents the bond in H–Cl, a strong acid. So $\mathbb{B} \mathsf{(acidic)}$ is an archetypical bond. The two acidic quarks are distinct from each other because one of them is logically associated with an electron, and the other is not. In the following models, we make extensive use of similar nested sets to satisfy Pauli’s exclusion principle. But no more acidic quarks can be added to this bond. So next we consider a pair of basic quarks

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

This collection of quarks and electrons accurately represents the bond in sodium hydroxide, Na–OH, also known as lye. More archetypical bonds can be defined using ionic and aqueous quarks to model molecules of table-salt and water, as shown in the following table.

Hydrides

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

$\mathbb{B} ( \mathrm{H}_{\mathsf{2}} ) \equiv$ { { $\mathsf{e^{-}}$ , , }, { $\mathsf{e^{-}}$ , , }, }

The following table shows models that all work within experimental uncertainty, even though observations of these molecules are remarkably precise.

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. Models that do not include ionic quarks are also possible. So the following table is not exhaustive, especially for the bonding in salts.

Double Bonds

The single bonds discussed above all involve one pair of electrons. But we may also include more electrons to define double bonds that involve 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 model correctly yields the dissociation energy of sulphur dimers, S=S. And 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. For another example, the link between oxygen atoms in O₂ is accurately given by this double aqueous bond

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

These examples do not specify how pairs of electrons are associated to form a specific single-bond within the molecule’s double-bond. For that, we depend on dextro and levo-quarks. These stereochemical quarks only have about 1% of the internal-energy of other chemical quarks, but nonetheless, they still play an important logical role by distinguishing between similar arrangements. For example consider this double-bond

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

which accurately yields the dissociation energy of 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 The distribution of stereochemical quarks is thus associated with geometric isomerism.

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

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

Triple 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 bonding 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

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

The following table summarizes some of these double and triple bonds

Sensory interpretation: All of the bonds discussed above are defined from three distinct classes of sensation; sour, salty and sweet flavours. 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 stable, three-dimensional particles. So a position $\bar{r}$ , and a time of occurrence $t$ , can be associated with anything that happens to an atom. Assigning a position is discussed later in an article about length. But we can readily assign a time-of-occurrence to atomic events just by thinking of atoms as little 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 generic way to tell time using any atom, $\mathbf{A} .$ Let $\mathbf{A}$ be described by a repetitive chain of events

$\Psi^{\mathbf{A}} = \left( \mathsf{\Omega}_{0}, \, \mathsf{\Omega}_{1}, \, \mathsf{\Omega}_{2} \, \ldots \, \mathsf{\Omega}_{k} \, \ldots \right)$

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 that the period of the atom $\widehat{\tau}^{\, \mathbf{A}}$ has been measured, so that the clock is calibrated. Then we can determine some elapsed time after the initial event just by counting atomic vibrations to determine $k$ . We write

$\Delta t = t_{k} - t_{0} = k \widehat{\tau}$

Without loss of generality, let $t_{0} \! = \! 0$ so that $t_{k} = k \widehat{\tau}$ . And recall that the angular speed is given by $\omega = 4\pi / \widehat{\tau} \, .$ And so event $k$ occurs at a time given by $t_{k} = 4\pi k / \omega \, .$ Also remember that the phase angle $\theta$ is defined by $\theta_{k} \equiv \theta_{0} + 4\pi k \, .$ So we can write

$t_{k} = \dfrac{\, \theta_{k} - \theta_{0} \, }{ \omega}$

This relationship expresses the time-of-occurrence of the $k$ ^th 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

$\theta (t) = \theta_{0} + \omega t$

This form is good for describing the rotating motion of particles when they are framed in a Cartesian view. It can also be used to eliminate $\theta$ from other expressions. For example the displacement previously stated as

$d \! \bar{r} = R \! \left(\rule{0px}{11px} - \! \sin{\theta}, \; \cos{\theta}, \; \lambda / 4\pi \! R \, \right) d \! \theta$

can also be written

$d \! \bar{r} = \omega R \left(\rule{0px}{11px} - \! \sin{\omega t}, \; \cos{\omega t}, \; \lambda / 4\pi \! R \, \right) d \! t$

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.

Atomic Hydrogen

The ground-state of atomic hydrogen is defined. Twenty eight excited states are also specified. Energy levels are compared with experiments.

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References
1	Bond Dissociation Energies in Simple Molecules National Standard Reference Data Series Number 31, B. deB. Darwent, U.S. National Bureau of Standards, 1970.
2	Bond Dissociation Energies of Organic Molecules Stephen J. Blanksby and G. Barney Ellison, Accounts of Chemical Research 36 (4), 2003.
3	Strengths 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.