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!

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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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:

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 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

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 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.

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