Square of Electrical Charge - A New Basic Law of Science

Moseley's Law (of 1913) Explanation

Based on the Square of the Electrical Charge of Atomic Nuclei Explanation of Moseley's Law

There appears to be an amazing law of Nature which has not been recognized before now. Nearly all of the basic laws of science tend to be LINEAR dependencies of effects on one or more variables. There has only been one which is commonly a SECOND-POWER dependency, generally referred to as an INVERSE SQUARE LAW of gravitation and electrical and magnetic effects with distance. There appears to be an unexpected new relationship, where at least two different known effects are due to the SQUARE OF THE ELECTRICAL CHARGE of atomic nuclei.

That does NOT seem to fit in with our generally logical rules of science. I have been aware of this for around five years and it still does not seem palatable!

Quantum Defect

The field of Physics was deeply affected in the 1920s and 1930s when Physicists saw electrons ONLY appearing in the same (energy) orbits. It was interpreted that there are many states that are Excluded, such as with the Pauli Exclusion Principle. And Quantum Physics arose entirely on the basis of these observations! In fact, it was recognized that the spectral lines of radiation emitted were always at specific wavelength or frequency, and by Planck, that means specific energy contents. Quantum Physics said that the energy was defined by exact INTEGER values of the denominator in the fully accepted Rydberg Equation, E = k /(n2). equation-a

and Rydberg:


with the special case for Hydrogen Balmer being:


This integer in the denominator was soon called the Principle Quantum Number.

It turns out that the number was generally close but NEVER EXACT. Therefore, a term was added as a "fudge factor" to make corrections to allow the integer requirement of Quantum Physics to still apply. The equation was then still presented in essentially the same form, but now with an asterisk inserted, E = k /(n*2) or by specifically stating the Quantum Defect as δ and saying E = k /((n + δ)2)

Many different interpretations have been made to try to explain the actual cause of that Fudge Factor, such as extremely elliptical orbits of the electrons where they sometimes get electrically hidden or unhidden by other electrons. But in any case, all have simply assumed that this WAS a Fudge Factor and no serious consideration of it has ever been made. The Fudge Factor has simply been experimentally calculated for each specific element and ion, and then that number has been used in the above equation to allow it to work. It is well known that the Fudge Factor is NOT an integer, and in fact is a decimal.

In a significant sense, the very PRESENCE of such a Fudge Factor entirely denies the basic claim of Quantum Physics! Instead of the INTEGER VALUES that Quantum Physics assumes and demands, these numbers are clearly NOT integers, even though they are pretty close.

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I have discovered that there is a REAL PHYSICAL MEANING of that quantity that has always been referred to as a Fudge Factor, and that it can be accurately calculated from theory! This seems to bring the very basis of Quantum Physics into question, as the near-Integer values are clearly NOT Integers at all!

But the implications of my findings are broader than that, seemingly conclusively proving that at least one of Newton, Coulomb or Planck was dead wrong about a basic assumption of nuclear physics!

The following discussion will show that ALL of the previous speculations have been quite incorrect, and even some basic assumptions have been wrong!

We are going to approach this subject in a unique way, which seems never to have been done before. We will initially consider ONLY atoms that contain a single electron, that is: H I (neutral Hydrogen) (using standard spectroscopic identification system); He II (singly ionized Helium); Li III (doubly ionized Lithium); Be IV (triply ionized Beryllium, and so on. We will exclusively use data from the highly respected NIST database, which contains such single-electron atoms up to Ge XXXII (Germanium 31-times-ionized). We therefore examine 32 specific atoms from atomic number Z = 1 through 32. Each of these 32 atoms in this discussion are therefore electrostatically identical in every way except for the nuclear charge, as each contains a single electron.

Since gravitational effects are extremely tiny in atomic interiors, we can exclusively consider just electrostatic effects between the nucleus and the single electron orbiting it. In other words, these 32 different atoms have only a single variable which is different, the charge of the nucleus. A more complete discussion of that analysis of the NIST data was put on the Internet in July 2007 at Quantum Defect

The Quantum Defect, generally referred to as δ, is here DEFINED as being the reciprocal of the nuclear charge of the atom (which we will call Z here)! It is NOT simply some random Fudge Factor! (For atoms with additional electrons, this becomes slightly modified, but is still valid, as discussed in the complete presentation.)

Therefore we have the Quantum Defect δ as being: For H I, 1.00; for He II, 0.50; for Li III, 0.333; for Be IV, 0.25 and so on, ONLY FOR THIS SPECIFIC SELECTION OF ATOMS WITH ONE ELECTRON. This is an entirely different understanding than is generally assumed! We can now calculate the actual Ionization Potentials for all of these single-electron atoms, based on this simple equation. Since n = 0, the entire denominator (for these specific atoms) is the so-called Quantum Defect number. Therefore we have:

E = k /((n + δ)2) = k /((0 + δ)2) = k /(δ2)

We DEFINED the Quantum Defect as being the reciprocal of the electrical charge of the nucleus Z, or δ = 1/Z or Z = 1/δ. Therefore we have, for only these specific atoms:

E = k * Z2

k is the Ionization Potential of neutral Hydrogen or 13.5984340 eV.

We present here the CALCULATED VALUES of the Ionization Potential for these 32 atoms, as well as the published NIST values.

nuclear charge
Published NIST
ionization Potential
in electron-Volts
Predicted Energy
By the simple formula
given above for
the Quantum Defect
error of the
calculated value
from the NIST data
in percent
1 H I 13.5984340 13.59843 0.0000
2 He II 54.4177630 54.39374 0.0441
3 Li III 122.454353 122.3859 0.0559
4 Be IV 217.718572 217.575 0.0660
5 B V 340.225993 339.9608 0.0779
6 C VI 489.99312 489.5436 0.0917
7 N VII 667.04602 666.3233 0.1083
8 O VIII 871.40969 870.2998 0.1274
9 F IX 1103.1171 1101.473 0.1490
10 Ne X 1362.1986 1359.843 0.1729
11 Na XI 1648.70105 1645.411 0.1996
12 Mg XII 1962.6642 1958.175 0.2288
13 Al XIII 2304.1401 2298.135 0.2606
14 Si XIV 2673.1807 2665.293 0.2951
15 P XV 3069.84143 3059.648 0.3321
16 S XVI 3494.1877 3481.199 0.3717
17 Cl XVII 3946.2907 3929.948 0.4141
18 Ar XVIII 4426.2226 4405.893 0.4593
19 K XIX 4934.0439 4909.035 0.5069
20 Ca XX 5469.8614 5439.374 0.5574
21 Sc XXI 6033.7551 5996.91 0.6107
22 Ti XXII 6625.81 6581.642 0.6666
23 V XXIII 7246.1196 7193.572 0.7252
24 Cr XXIV 7894.8 7832.698 0.7866
25 Mn XXV 8571.94 8499.021 0.8507
26 Fe XXVI 9277.6874 9192.542 0.9177
27 Co XXVII 10012.1 9913.259 0.9872
28 Ni XXVIII 10775.4 10661.17 1.0601
29 Cu XXIX 11567.612 11436.28 1.1353
30 Zn XXX 12388.928 12238.59 1.2135
31 Ga XXXI 13239.4881 13068.1 1.2946
32 Ge XXXII 14119.4287 13924.8 1.3785
33 As XXXIII 15028.6197 14808.7 1.4634
34 Se XXXIV 15967.6759 15719.79 1.5524
36 Kr XXXVI 17936.2076 17623.57 1.7430
37 Rb XXXVII 18964.9937 18616.26 1.8389

This is pretty remarkable! The complete analysis presentation adds a simple small additional factor which eliminates even these small errors in the table above. For a quantity that has always been discarded as a Fudge Factor for 70 years, we have presented a very simple formula to ACCURATELY CALCULATE ITS VALUE (on the order of one part per million accuracy) !

The implications of this are staggering! As the charge of an atomic nucleus is increased, with no other variables in effect, the Binding Energy is increased by the SQUARE OF THAT NUCLEAR CHARGE, and extremely precisely!

That seems to defy all known laws of science!

Moseley's Law

In 1913, Henry Moseley discovered an interesting fact. As described in the Handbook of Chemistry and Physics, Moseley's Law states that the frequencies of the characteristic X-rays of the elements show a strict linear relationship with the SQUARE of the atomic number.

(Mr. Moseley's name is misspelled as Mosely in the Handbook.)

Planck's Law states that the frequency is directly and linearly proportional to the binding energy of the electron.

These two respected facts confirm the same result as I stated above, that there is a factor of the SQUARE OF THE CHARGE OF THE NUCLEUS in the energy content of the electron.

No one seemed to see much importance in Moseley's Law, except that it used the experimentally measured frequencies of X-rays to confirm that different atoms had what Moseley referred to as Atomic Number. In fact, discontinuities in the X-Ray spectral series helped predict elements that had not yet been discovered (around 1913)! But the greater implication of requiring an effect which is based on the SQUARE OF THE NUCLEAR CHARGE, had apparently never been pursued.


These two different approaches, based on the Rydberg formula and on Planck's Law, both make clear that there IS an important new factor in atomic physics.

The denominator of the Rydberg formula had always been ASSUMED to refer to DISTANCE quantities, where it might then seem to make logical sense, but this presention shows that the denominator of the Rydberg formula is NOT distance quantities but instead charge quantities.

By consider it as charge quantities, we have discovered a very simple and precise formula to calculate the Quantum Defect Factor, something which had always been considered as un-calculatable due to that wrong assumption.

This presentation was first placed on the Internet in July 2011.

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Carl W. Johnson, Theoretical Physicist, Physics Degree from Univ of Chicago