Hydrogen Gets Excited

Hydrogen Ground State

Atomic hydrogen is found in a few different varieties. The most abundant isotope is called protium. It is formed by the union of a proton with an electron bound together by a force-carrying collection of field quanta that are noted by An atom of hydrogen is noted by so we write

The proton is represented by the quarks

The electron is modeled from this selection

And the field for hydrogen in its ground-state is given by this collection of field quanta

Ground State Hydrogen
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Protium does not contain any neutrons but there are two naturally occurring isotopes called deuterium and tritium . The rest of this article is devoted to protium, and from here on we just refer to it as hydrogen. Thus an atom of hydrogen in its ground-state is objectified from a space-time event as shown in the accompanying table.

Other excited forms of hydrogen are defined by different fields that involve more quarks. But this ground-state is tiny, it has just 6 quarks per octant.

Atomic hydrogen is also depicted in the movie at the top of the page. But stereochemical quarks are about a million times smaller than thermodynamic quarks, so they are not shown in the movie. Also note that the model only has levo quarks as stereochemical components. So we call this case left handed hydrogen. If all of the levo quarks are replaced by dextro quarks then it is called right-handed hydrogen.

The energy difference between dextrorotatory and levorotatory hydrogen is small enough to usually be ignored. But the distinction is logically important when we specify the handedness of a coordinate system. For the rest of this article we only discuss the levorotatory case, and simply call it hydrogen.

Excited States of Hydrogen

The excited states of atomic hydrogen are built-up from the components shown in the following table. Some rotating quarks are grouped together as rotons. And a magnetic field is specified using a few muonic quarks.

update fields to roton symbols

The set of field-quanta noted by is called a Lamb quantum. This particle is like a little bit of orbital angular momentum because absorbing or emitting it changes the azimuthal quantum number by without altering or . The Lamb quantum is used to explain the Lamb shift because excited states can be accurately constructed such that

So when the spun-up ground-state of hydrogen is excited by the absorption of a photon, there are two possiblities. Either the excited-state of hydrogen is produced. Or, perhaps the yield is a-state, along with some ethereal debris in the form of a Lamb-quantum. Specific excited states are identified using standard atomic spectroscopic notation.

Quark coefficients for the Lyman photons are obtained from the gross structure of the hydrogen spectrum, they bring electrochemical quarks into the description. Quarks are conserved so the following models for excited states are obtained by adding together the quark-coefficients of all their components. This method automatically conserves momentum, charge, etc.

S-states

Here are some quark models for the -states of hydrogen. They are presented in formulae as combinations of protons, electrons, photons and field-quanta. They all have an azimuthal quantum number of

Quark coefficients for the -states are also shown explicitly in the following table. Labels use standard atomic spectroscopic notation.

P-states

Here are some models for the -states of hydrogen. They all have an azimuthal quantum number of The states have a total angular momentum quantum number of one half.

The following states have a total angular momentum quantum number of

D-states

Here are models for the excited -states of hydrogen. They are characterized by an azimuthal quantum number of . Not all these states have been directly measured. But we make models of them anyway because they are used later in calculations about fine structure in the hydrogen spectrum.

The following states have a total angular momentum quantum number of

F-states

And finally, here are models for some -states of excited hydrogen which all have an azimuthal quantum number of .

Energy Levels of Atomic Hydrogen

Let note the mechanical energy of some excited state , on a scale where the null-value of is obtained when the electron is very far away from the proton. For this case¹Hydrogen Atom – Chemistry WebBook NIST Standard Reference Database Number 69. National Institute of Standards and Technology, Gaithersburg MD, USA. the ground-state has a value of (eV). But there are some challenges to making accurate measurements in this context. So we also specify a shifted value for the energy on a scale where, by definition, the ground-state always has a value of exactly zero

Then the excited states of hydrogen are described by the sum

The value of this expression depends strongly on the principal quantum number But there are also a weaker connections to and These atomic quantum numbers are defined from quark coefficients. So the energy of an atomic state is a function of its quark content, and can be formulated as follows.

Gross and Fine Energy

The gross structure of energy levels in hydrogen depend mostly on the principal quantum number. This relationship has already been discussed in detail. Calculations and observations concur to about a part in a million. This agreement is excellent by almost any standard. So EthnoPhysics has used these ‘gross’ results to make quark-models of photons, especially the Lyman photons. Then these Lyman photons have been used to specify the atomic states listed above. Thus the role of the principal quantum number is built-in to our models of hydrogen’s excited states.

The next biggest influence on energy levels is due to the total angular momentum quantum number. This effect has been explored by Arnold Sommerfeld and Paul Dirac. They have established the fine energy terms for describing excited-states as

where

The number is named the Sommerfeld constant. And is another number called the Rydberg constant. For EthnoPhysics, the numerical value of is represented by the distribution of electrochemical quarks. And the Rydberg ‘constant’ is only actually constant for some specific sort of atom. So different atoms and isotopes are modeled using different distributions of electrochemical quarks. This article is all about hydrogen. So the excited states shown above all have the same selection of electrochemical quarks.

Hyperfine Energy

A full discussion of hyperfine energy typically involves lots of talk about quantum mechanics. The level of mathematics is complicated, not good enough for high-school students. And there are also some profound philosophical difficulties. But our biggest issue with these labyrinthine explanations is simple: They depend on dubious presumptions about space and time that we cannot accept without question.

In general, we cope with this problem by trying to make clear definitions of what we are talking about, and thereafter focussing on experimental observations. So instead of deliberating over quantum-mechanics as a whole, we have presented specific quantized models of excited hydrogen that explicitly retain accounts of both up-quarks and down-quarks. Then the chirality of an excited state can be determined and used to express energetic variations that depend on rotation. Thus we write a hyperfine energy term for atomic hydrogen as

where is called the hydrogen hyperfine transition frequency. This frequency describes the size of a split between spun-up and spun-down states. It has an observed²Helmut Hellwig, Robert F. C. Vessot, Martin W. Levine, Paul W. Zitzewitz, David W. Allan, and David J. Glaze. Measurement of the Unperturbed Hydrogen Hyperfine Transition Frequency IEEE Transactions on Instrumentation and Measurement, Volume IM-19, Number 4, November 1970. value of (Hz). This approach is mathematically simple enough to be useful for undergraduates. But the value of is just installed as an experimental fact about hydrogen, like a constant. So although it works for atomic hydrogen, no broader claims are asserted. Yet.

Bethe’s Energy

The next biggest contribution to atomic energy is described by the azimuthal quantum number, and the spin-projection quantum number. Effects are summarized by which is named after Hans Bethe. The functional form of his work is rephrased here as

Bethe has a book-length explanation for relationships like this.³Hans A. Bethe and Edwin E. Salpeter, Quantum Mechanics of One- and Two-Electron Atoms, Springer-Verlag OHG, Berlin 1957. And EthnoPhysics is strongly influenced by his achievement. But his approach maintains a complex dependence on assumptions about length and time. And, it is not very compatible with the premise of EthnoPhysics. Accordingly, for pragmatic purposes and are treated as adjustable parameters, and their values are shown in the accompanying table. So overall we gratefully adopt Bethe’s functional assessment of the quantum numbers, but remain uncommitted to any theoretical interpretation of the constants.

Stereochemical Energy

The foregoing energy terms are sufficient for making an accurate description of inert hydrogen. All direct measurements of excited states can be represented without using an additional stereochemical term. However, there are also many indirect measurements based observing photons emitted during transitions between atomic states. So to make a simple theory that accurately includes transitions, we now associate a few micro electronvolts with the stereochemical quarks in an atom.

The stereochemical energy depends on an particle’s stereochemical quarks, which are ultimately defined from sweet oral sensations. We account for these quarks using the total number of stereochemical quarks. Then

where is the principle quantum number, is the spin-projection quantum number, and is a constant noted in the accompanying table. This is sufficient for the simple case of a solitary atom of hydrogen. More elaborate expressions may be used later to describe particles that have complicated vibrational and rotational spectra.

Experimental Comparison

All the foregoing equations, together with formulae for the atomic quantum numbers, are combined with the quark-models to describe the energy levels of atomic hydrogen. Results are compared with experimental observations⁴Kramida, A., Ralchenko, Yu., Reader, J., and the NIST ASD Team (2018). NIST Atomic Spectra Database (version. 5.6.1). National Institute of Standards and Technology, Gaithersburg, MD, USA. in the table below.

The EthnoPhysics quark-models of hydrogen thus reproduce the quantum-numbers of excited states correctly. And the calculated energy levels for all directly measured states are within experimental uncertainty of observations. So the description of an inert hydrogen atom is good. But the transition energies have yet to be fully considered. So this analysis is continued later for some finer details in the hydrogen spectrum.

Hydrogen Lifetime

The permanence of a particle is described by its mean life which is a function of its thermodynamic temperature. Hydrogen is very stable, so the temperature of a hydrogen atom in its ground state is supposedly very close to zero (K). And, the foregoing model of atomic hydrogen in its ground-state has a calculated temperature of (K). But we doubt that this number has much physical significance for two reasons.

First, by current experimental standards, this number is not especially close to zero. And any expected variation would likely have some arduous dependence on thermometric method. And second, actually generating this number is difficult for the spreadsheets we are currently using.⁵For more detail about any of the foregoing calculations please see the Atoms & Photons spreadsheet. As of January 2019 calculations are being done using; Microsoft Excel for Mac, Version 15.16, running on an iMac Model 16.2 with an Intel Core i5, 3.1 GHz processor and 8 GB of memory. Temperature calculations depend on small differences between large numbers, and rounding errors are inevitable. When the temperature is near zero, these errors can be significant.

Despite these limitations, a mean life of ~10⁵⁶ seconds is calculated for atomic hydrogen in its ground-state. For comparison, measurements of the proton’s mean-life have determined⁶K.A. Olive et al. Particle Data Group Review of Particle Physics, Chin. Phys. C, 38, 090001 (2014). that it is more than ~10³⁶ seconds.

Length

A

Length measurements and Cartesian coordinates are defined. Some atomic shapes and motions are discussed. The Euclidean metric is derived.