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 electron is modeled from this selection
|Ground State Hydrogen
Protium does not contain any neutrons. But there are two naturally occurring isotopes called deuterium and tritium which are discussed later. 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 levorotatory hydrogen. If all of the levo quarks are replaced by dextro quarks then it is called dextrorotatory 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 spin-up or spin-down field quanta. And a magnetic field is specified using a few muonic quarks.
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 spin-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.
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.
The following states have a total angular momentum quantum number of
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
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
The number is named the Sommerfeld constant. And is another number called the Rydberg constant. For EthnoPhysics, the numerical value of is theoretically manifest in the distribution of electrochemical quarks. And the Rydberg ‘constant’ is only actually constant for a given 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.
A full discussion of hyperfine energy levels in hydrogen typically involves lots of talk about electromagnetism and quantum mechanics. These theories are mathematically complicated. And they also present some profound philosophical difficulties. But for EthnoPhysics, the biggest issue with these labyrinthine theories are some more commonplace philosophical difficulties. Specifically, they all make assumptions about mass, time and length that are not compatible with the premise of EthnoPhysics.
In general, EthnoPhysics copes with this issue by trying to make clear definitions of what we are talking about, and thereafter focussing on measurements. So instead of deliberating over quantum mechanics as a whole, we have made specific quantized models of excited hydrogen that explicitly retain accounts of both up-quarks and down-quarks. Then the helicity of an excited state can be resolved and used to express energetic variations that depend on the spin. 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 spin-up and spin-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.
The next biggest contributions to atomic energy levels are described by the azimuthal quantum number, and the spin 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 mass, length and time. And is not very compatible with the premise of EthnoPhysics. Accordingly, for pragmatic purposes, and are treated as adjustable parameters. Their values are shown in the accompanying table. So overall we gratefully adopt Bethe’s functional assessment of quantum numbers, but remain uncommitted to any theoretical interpretation of the constants.
The foregoing energies are sufficient for making an accurate description of inert hydrogen. Direct measurements of all the excited states can be represented without using a chiral energy term. However, there are also many indirect measurements based observing photons emitted during transitions between atomic states. So to make a simple theory that includes transitions, we now associate a few micro electron-volts with the handedness of an atom.
The chiral energy term depends on an atom’s stereochemical quarks. For the simple case of a solitary atom of hydrogen, we can account for them just using the total number of stereochemical quarks
More elaborate expressions may be used later to describe hydrogen molecules that have complicated vibrational and rotational spectra.
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.
The permanence of a particle is described by its mean life which is a function of its thermodynamic temperature . Hydrogen is very stable, and so the temperature of a hydrogen atom in its ground state is supposedly very close to zero (K).
For comparison, the foregoing model of atomic hydrogen in its spin-down 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 anyway, the expected value would likely have an arduous dependence on the details of any thermometric technique.
And second, actually calculating this number is shaky. It shows the limit of our computing techniques. Temperature calculations depend on small differences between large numbers. Some rounding errors are inevitable. When the temperature is near zero, these errors can be significant. We are near the limit of what we can obtain from our present computing arrangements.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.
Nonetheless, given these caveats, the foregoing models indicate a mean life of ~1056 seconds for atomic hydrogen in its ground state.
|Hydrogen Atom – Chemistry WebBook NIST Standard Reference Database Number 69. National Institute of Standards and Technology, Gaithersburg MD, USA.
|Helmut 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.
|Hans A. Bethe and Edwin E. Salpeter, Quantum Mechanics of One- and Two-Electron Atoms, Springer-Verlag OHG, Berlin 1957.
|Kramida, 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.
|For 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.