_{1}

Application of Maxwell’s equations and the theory of relativity on the processes in atoms with real oscillator leads to the structural constant of atoms s
_{0} = 8.278692517. Measurements show that the ratio of energy of the photon and its frequency is not constant which means that Planck’s
* h* is not constant. The theory which is consistent with these measurements, has been found. This theory covers processes in electron configuration and also at the core of atoms. Based on the structural constant s
_{0} the maximum possible atomic number
*Z* is determined. In order to encompass all atoms and all nuclides a new measurement unit has been proposed. That is the measurement unit for the order of substance. The introduction of structural constant s
_{0} makes 11 fundamental constants redundant, including Planck’s
*h*. The structural constant of atoms s
_{0} stands up as the most stable constant in a very wide range of measurement, so it may replace variable Planck’s
*h* well. Continuity of the bremsstrahlung is explained.

In addition to general interest reaching scientific truth, another motive for publishing this article is finding the answer to Millikan’s question about the linearity of frequency ν and voltage V in the famous Einstein’s formula of the photoelectric effect,

Planck’s h relates to the energy

_{0} = 8.278692517066260, [

where

stand for the action constant [

The continuous spectrum of bremsstrahlung can be explained from Equation (1) as a result of the continuity of the initial velocity of the electron

The total mechanical energy E of an electron in an atom is the sum of its kinetic energy K, and its potential energy U [

The kinetic energy of the electron, with mass m, moving at an arbitrary velocity

In [

where Z is atomic number;

where eV is electrical or (by an amount equal to it) electromagnetic energy E_{em} required for ionization of atom.

Using Equations (4) and (5) we record the kinetic energy:

We assume that the electron in an atom moves in a circular orbit. There is acceleration perpendicular to the direction of motion. With the Coulomb’s law applies [

or

where r is the radius of curvature of the trajectory (in this particular case it is the radius of the circular orbit of the electron in atom), q = −e is electron charge, Q = Ze is the core charge,

Because of the law of conservation of energy, the part of it that is dissipated from the atom is electromagnetic energy E_{em}, which, on the other hand, is the amount equal to the total mechanical energy E of an electron, but with a negative sign [

With Equation (5), Equation (11) gives (see

Previous theoretical considerations and knowledge can be used for several different purposes. Here are three applications that are specifically enabled by the new findings, which enabled the discovery of structural constants of atoms

Stable states and discretization appear in the atom as a result of the harmonization of two different periodical processes; electromagnetic oscillations and the circular motion of electrons [

where

speed of light,

On the smallest orbit (for

From Equations (13) and (14) results:

For example, by choosing discrete state

The mass M of hydrogen atom in the state of n = 1/126 is equal to the sum of the mass of the proton and the electron mass:

This mass correspond to the mass of neutron

where

stands as a mathematical abbreviation for the length L_{0} of the world of atoms. For _{0} is approximately equal to a Bohr radius a_{0}. If we take it as a unit of measurement of length and

Now is from Equation (20) and with Z = 1:

According to the classical concept, Equation (23) is the orbital radius of the electron in the hydrogen, but this hydrogen due to the increased mass of the electron has a mass of neutron. As we see, in addition to well-known stable states ^{0} and hyperons

There are currently 118 known elements with more than 3100 nuclides,

The state of a hydrogen atom (protium) | Velocity of electron | Atomic radius | Atomic mass | Kinetic energy of electron | Potential energy of electron | Electromagnetic energy of atom | All data obtained in a unique way, represent an atom as: |
---|---|---|---|---|---|---|---|

1 | 0.007295356 | 52,945.277127 | 938.7830940^{a} | 0.013598 | −0.027 197 | 0.013598 | |

126 | 0.919214877 | 1.313183 | 939.5698359^{b} | 786.755446 | −1096.545346 | 309.789900 | n^{0} |

137.072929 | 0.999995839 | 0.008129 | 1115.3999999^{c} | 176,616.919499 | −177,126.444257 | 509.524757 | |

137.073373 | 0.999999077 | 0.003829 | 1314.2999989^{c} | 375,516.918528 | −376,027.223058 | 510.304529 |

a. The mass corresponds to the mass of hydrogen (m_{P} + m = 938.272 + 0.511 = 938.783 MeV), 2014 CODATA, http://physics.nist.gov/constants. b. The mass corresponds to the mass of the neutron, 939.5654133 MeV, 2014 CODATA. http://physics.nist.gov/constants, [

https://en.wikipedia.org/wiki/Table_of_nuclides. A nuclide is an atomic species characterized by the specific constitution of its nucleus, i.e., by its number of proton Z, its number of neutrons N, and its nuclear energy state. The number of protons Z within the atom’s nucleus is called atomic number and is equal to the number of electrons in the neutral (non-ionized) atom. Each atomic number Z identifies a specific element, but not the isotope; an atom of a given element may have a wide range in its number N of neutrons. The number of nucleons (both protons Z and neutrons N) in the nucleus is the atom’s mass number A = Z + N, and each isotope of a given element has a different mass number.

With such a large number of nuclides or isotopes, there is a need for their sorting, classification and marking with the use of today’s knowledge. There are also disputes between nuclide concept and isotope concept. Nuclide refers to a nucleus rather than to an atom, because identical nuclei belong to one nuclide, for example each nucleus of the carbon-15 nuclide is composed of 6 protons and 9 neutrons. The nuclide concept (referring to individual nuclear species) emphasizes nuclear properties over chemical properties, whereas the isotope concept (grouping all atoms of each element) emphasizes chemical over nuclear.

No arbitration between the two concepts, it is best to make a clean substrate, with that later these concepts can any self-build further its goals. The existence of isotopes was first suggested in 1913 by the radiochemist Frederick Soddy, who explained, with Ernest Rutherford, that radioactivity is due to the transmutation of elements, now known to involve nuclear reactions.

Since Frederick Soddy deal and chemistry and a nucleus of atoms, just his name connects both of these areas, isotopes and nuclides. So my suggestion is to recognize and accept the existence of a new physical quantity, named the order of substance, that is signified with Soddy’s name, S, so-called Soddy’s number, covering the whole substances with properties of atoms and their nuclei. Any physical quantity has its own unit of measurement. Because this is not only about counting, but it is a combination of different properties of atoms, as new quality, this current quantitative measurement unit (mole) is not suitable for expression of Soddy’s number. Soddy’s number requires a new unit of measurement. The idea is that each nuclide gets its own unique and easily definable number.

In this sense, can be used the knowledge of the maximum possible number of different atoms,

where

this gives:

It is estimated that number of neutrons in a nucleus certainly not exceeds one thousandth (and therefore we put

The Soddy’s number for the carbon, with Z = 6 and N = 7, for example, is:

The Soddy’s number for vacuum (Z = 0, N = 0) is S_{(0,0)} = 0.000 B, for neutron

After the discovery of structural constant of atoms

Name of physical quantity | Sign of physical quantity | Dimension symbol | Unit name | Unit symbol |
---|---|---|---|---|

length | l | L | meter | m |

mass | m | M | kilogram | kg |

time | t | T | second | s |

electric current | I | I | ampere | A |

thermodynamic temperature | T | Q | kelvin | K |

luminous intensity | I_{v} | J | candela | cd |

amount of substance | n | N | mole | mol |

order of substance | S | N | boscovich^{a} | B |

a. “boscovich” is a unit of order of substance amount B = 1/(2s_{0}^{2} + 1) = 1/138.073499584258 = 0.0072425194046.

is associated with the fine-structure constant

_{0} all these differences disappear.

If we share the action constant^{2}, we get another constant, which is in amount equal to the von Klitzing constant h/e^{2}, with the same error 0.027% as in the previous case:

Action constant

A point charge Q created at a distance r from the charge (relative to the potential at infinity, where this potential is calculated as a Zero) the electric potential difference

so that the potential energy U of the charge q, according to Equation (10), is

When moving charge q (masses m) is on the potential

whereas according to Equations (11) and (13) applies:

From Equations (1), (5), (11) and (33) results [

If we divide Equation (35) with potential _{0}, because it converts electrical potential (voltage) to frequency:

The Equation (35) we can now write with the help of Equation (36):

The Equation (37) has the same shape as the equation of the frequencies in the alternating-current Josephson effect, (_{DC},

https://en.wikipedia.org/wiki/Josephson_effect, where _{DC} is the potential difference at the superconducting junction, analogous to the above-mentioned potential difference

From [

where

Using Equations (13) and (20) the magnetic dipole moment [

where I is the electric current and A is the area of the loop, and T is the time required for one orbit (see

Quantity | Symbol | Formula | Value | Unit | Difference^{a} % |
---|---|---|---|---|---|

Six initial fundamental constants: | |||||

structural constant of atoms | ^{b} | 8.278692517066260 | 1 | unknown | |

speed of light in vacuum | 299 792 458 | m×s^{−1} | 0.000 | ||

elementary charge | 1.6021766208 ´ 10^{−19} | A×s | 0.000 | ||

mass of electron | 9.10938356 ´ 10^{−31} | kg | 0.000 | ||

mass of proton | 1.672621898 ´ 10^{−27} | kg | 0.000 | ||

pi; Archimedes’ constant or Ludolph’s number | ^{c} | 3.141592653589793 | 1 | 0.000 | |

Other 12 (without e, redundant 11) constants (derived from 6 initial fundamental constants): | |||||

inverse fine-structure constant | 137.073499584258 | 1 | +0.027^{d} | ||

fine-structure constant | 0.0072953561637514 | 1 | −0.027^{d} | ||

von Klitzing constant | 2.581987123285 ´ 10^{4} | W | +0.027^{d} | ||

action constantA_{0}; Planck’s h | 6.627883290240 ´ 10^{−34} | J×s | +0.027^{d} | ||

conversion constant | 1.208 663875508 ´ 10^{14} | Hz×V^{−1} | unknown | ||

ratio e/h; ratio e/A_{0} | 2.417327751017 ´ 10^{14} | Hz×V^{−1} | −0.027^{d} | ||

Josephson constant | 4.834655502034 ´ 10^{14} | Hz×V^{−1} | −0.027^{d} | ||

elementary charge | 1.6021766208 ´ 10^{−19} | A×s | 0.000 | ||

Rydberg constant | 1.09647274840335 ´ 10^{7} | m^{−1} | −0.082^{d} | ||

Bohr radius | 5.294668730599 ´ 10^{−11} | m | +0.055^{d} | ||

Bohr magneton | 9.276547861521 ´ 10^{−24} | A×m^{2} | +0.027^{d} | ||

nuclear magneton | 5.052165865121 ´ 10^{−27} | A×m^{2} | +0.027^{d} |

a. Difference value in relation to the Committee on Data for Science and Technology, 2014 CODATA. b. Here σ is the structural coefficient of transmission (Lecher) lines representing the electromagnetic oscillator in an atom [

With the current measurement results and with the appropriate theory, Duane- Hunt law which includes Planck’s h has been tested. Using 120 measurements in the range of 13.6 eV to 204.4 keV, i.e., in the range 1:15000, we conclude that Planck’s h is not constant. The results presented here confirm that Planck’s h is approximately constant in the energy range from a few eV, but for energy over a dozen keV h becomes significantly smaller and decreases to zero. That conclusion has been confirmed by statistical analysis of old measurement results from a century ago as well. So far, there was no suitable theory that could explain it, but now this theory exists and it is in accordance with both the old and the new measurements. With this theory it is possible to determine some phenomena in the nucleus of the atom. This theory also shows that the maximum possible atomic number Z is equal to the integer of 2_{0} 11 different previous fundamental constants are redundant, including Planck’s h. Interrelationships among all these constants exist, and therefore it is possible to unite the manner described.

Further work in this area should include the study of possible stable states of atoms in states below the ground state with the expectation, in addition to the neutron and hyperons, some other particles could be found.

In this article, the voltage to 204.4 kV (Z = 110, darmstadtium) has been covered. The future research should broaden that range to 511 kV. In that process not only the voltage, but also corresponding frequency should be measured.

This article explains the continuous spectrum of bremsstrahlung. The formula for calculating the frequency of this radiation has been shown.

The work is based on the use of Maxwell’s equations and Einstein’s theory of relativity and the use of real oscillators, instead of Planck’s virtual oscillators. The quantization is only a consequence of harmonizing two continuous processes in the atom: the propagation of electromagnetic energy and the circular motion of electrons [

The author thanks to Ms. Srebrenka Ursić and Mr. Damir Vuk,

www.systemcom.hr, for useful discussions, to Mr. Branko Balon for the useful discussions, too, to Mr. Velibor Ravlić and Mr. Zlatko A. Voloder for encouragement in the writing this article and for expressing great expectations in benefits of using structural constants s_{0} instead of Planck’s h, then to Prvomajska TZR, Ltd., Zagreb, Croatia, www.prvomajska-tzr.hr, and to Drives-Control, Ltd., Zagreb, Croatia, www.drivesc.com, for logistic support.

Perkovac, M. (2017) Planck’s h and Structural Constant s_{0}. Journal of Modern Physics, 8, 425-438. https://doi.org/10.4236/jmp.2017.83027