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July 2011. 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 SECONDPOWER 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 DefectThe 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 /(n^{2}).and Rydberg:
with the special case for Hydrogen Balmer being:
This integer in the denominator was soon called the Principle Quantum Number.


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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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 singleelectron atoms up to Ge XXXII (Germanium 31timesionized). 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 Îô, 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 Îô 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 singleelectron atoms, based on this simple equation. Since n = 0, the entire denominator (for these specific atoms) is the socalled Quantum Defect number. Therefore we have:
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 Z  Published NIST ionization Potential in electronVolts  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  Kr 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) !
That seems to defy all known laws of science!
(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 Xrays to confirm that different atoms had what Moseley referred to as Atomic Number. In fact, discontinuities in the XRay 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.
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 uncalculatable due to that wrong assumption.
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C Johnson, Theoretical Physicist, Physics Degree from Univ of Chicago