(Discovered by Tom Gilmore)

by Tom Gilmore

Copyright 2018

All graphics by Tom Gilmore

**Intro to Isotopes**

**Atomic
Number and Elements**

There are 3 atomic particles (formed from Quarks);
Protons, Electrons, and Neutrons.
Protons and Electrons occur in pairs, although the Electron particle
itself can be absent, in which case the atom is referred to as
"ionized". For the purpose of
this presentation the Proton/Electron pair is simply termed a Proton. The integer number of Protons in an atom is
called its "**atomic number**",
and these integer-based atoms are termed "**Elements**". One Proton is the Element Hydrogen (H), two
Protons is Helium (He), three Protons is Lithium (Li),
and so on.

**Atomic
Weight and Isotopes**

Both Protons and Neutrons have an "**atomic
weight**" of 1. The atomic
weight (Z) of an atom is the sum of Protons (P) and Neutrons (N), or
(Z=P+N). Many Elements occur with
variable numbers of Neutrons, and these are called **"Isotopes"** of the Element.

**Part I – Exact Conformities**

In this presentation the syntax for representing an Isotope is to prefix an
Element with the atomic weight (Z) and suffix with the atomic number (P).

For example (19)Fluorine(9), and has 9 Protons and 10
Neutrons.

**The
derivation of the formula influencing the Isotopes is detailed further on**.

**P is the atomic number** (number of
Protons)

**Z is the atomic weight** (total of
Protons and Neutrons)

(**z **is the atomic weight derived from
the formula).

**Exact
Conformities with the Formula**

**Isotope Balance ****z = (2P + P ^{2}/156)
Rounded**

**100% in one Isotope:**

(**19**)Fluorine(9) -- (2P + P^{2}/156) = (2x9 + 9x9/156) = 18.52 rounds to **19
**(

(27)Aluminum(13) – z = 27.08 rounds to 27

(31)Phosphorus(15) – z = 31.44 rounds to 31

(45)Scandium(21) – z = 44.83 rounds to 45

(59)Cobalt(27) – z = 58.67 rounds to 59

(93)Niobium(41) – z = 92.78 rounds to 93

(103)Rhodium(45) – z = 102.98 rounds to 103

(169)Thulium(69) – z = 168.52 rounds to 169

**99% in one Isotope:**

(12)Carbon(6) – z = 12.23 rounds to 12

(14)Nitrogen(7) – z = 14.31 rounds to 14

(16)Oxygen(8) – z = 16.41 rounds to 16

(238)Uranium(92) – z = 238.26 rounds to 238

Notice that the Elements with 100% have odd atomic weight and those with 99% have even atomic weight.

**Part II – The Derivation of the Balance Formula**

**The
“n-Value”**

With the exception of (1)Hydrogen(1), which has no
Neutrons, every Element has at least as many Neutrons as Protons. Consequently the distinguishing factor of an
Isotope can be expressed as the number of excess Neutrons over the number of
Protons. For purposes of the Isotope
balance equation the **excess** of Neutrons over Protons is called the
”**n-value**”
and by definition it is the atomic weight less twice the number of Protons or
Z-2P.

(**n = Z – 2P**)

**Deriving
the Balance Formula **

The Isotopes of the Elements show a general increase of** excess** Neutrons as atomic
number increases. At Platinum(78)
a proportional relationship of 1/2 between Protons and excess Neutrons
occurs. The Isotope balance equation was
derived by applying the balance ratio of Platinum(78)
to all of the atomic numbers (P).

There are multiple Isotopes of Platinum(78) but the average atomic weight of the Isotopes of Platinum(78) is 195. The equation for excess Neutrons is (n=Z-2P), so

For (195)Platinum(78): n = (Z-2P) = (195 - 2x78) = 39, and 39/78=1/2

The balance is 1/2 of P (or** P/2**) when P is 78 (or **P/78**).

(**P/78 x P/2 = P ^{2}/156**)

This is verified by putting P=78 in the equation (P^{2}/156) as
follows.

For P=78, (P^{2}/156) = (78x78/156) = 39.

**The
n-Gradient and z-Gradient **

**P ^{2}/156 (rounded) **is
termed the

The atomic weight (Z) equals twice
the Proton count plus the excess Neutrons (Z=2P+n). As applied to the n-gradient, the Isotope
balance point is represented by z.

z= (2P + n-gradient) = **(2P + P ^{2}/156)
= "z-gradient"**

**n-gradient**** = P ^{2}/156 **

Example: **z-gradient** calculation
for Mn(25)
is:

z =(2P + P^{2}/156) = (25+25
+(25x25/156)) = (50 + 4.00641) = 54

The z-gradient only represents where the Isotope is in balance, not where it must absolutely reside, but the “pull” of the balance induces Beta decay (discussed further on) toward the balance.

The n-gradient plots as a geometric curve, and the Beta decay gradient is tangent to the curve at P=78, the balance point.

**Part III – The Non-Parity Caused Variances**

**Parity
Demand**

The odd/even (or even/odd) **non-parity** between the atomic number and the atomic weight
is a strong factor in causing a variance in Isotopes from the calculated
balance equation (z-gradient). There is
a **strong
demand** for the odd atomic number
Elements to have an odd-number atomic weight, and a less strong but noticeable
preference for even atomic number Elements to have an even-number atomic
weight.

**Small
Deviations Induced by Non-Parity**

**(Odd atomic number, even z-gradient,
Isotope prefers odd atomic weight).**

Following is a list of 6 non-parity Elements that have 100% (or nearly) in one Isotope, and exhibit a variance of 1 to the z-gradient.

Isotope z-gradient variance

(55)Mn(25) 54 +1 100%

(89)Y(39) 88 +1 100%

(141)Pr(59) 140 +1 100%

(175)Lo(71) 174 +1 97%

(181)Ta(73) 180 +1 99%

(197)Au(79) 198 -1 100%

Notice that Gold(79) is on the other side of the balance at Platinum(78), shifting the variance from +1 to -1.

**Non-Parity
Splitting**

Six Elements of odd atomic number split their Isotopes around their even z-gradient. Their percentage split exhibits a graduated percentage change centered around the Element Silver(47), which nearly equally splits around the z-gradient (see list below). All 6 Elements have averaged atomic weights (average Z) that round to the z-gradient. The reason the percent split increases is that the number of excess Neutrons (n-value) increases with the increase in atomic number.

69% -- (63)Copper(29)

31% -- (65)Cu(29) average Z = 63.62 z-gradient = 64

60% -- (67)Gallium(31)

40% -- (69)Ga(31) average Z =
68.16 z-gradient = 68

51% -- (107)Silver(47)

49% -- (109)Ag(47) average Z =
108.16 z-gradient =108

37% -- (185)Rhenium(75)

63% -- (187)Re(75) average Z =
186.06 z-gradient = 186

37% -- (191)Iridium(77)

63% -- (193)Ir(77) average
Z = 192.01 z-gradient = 192

30% -- (203)Thallium(81)

70% -- (205)Tl(81) average Z =
204.06 z-gradient = 204

Notice that the percentage split is nearly exactly reversed between Copper(29) and Thallium(81).

**Part IV – Even-Atomic-Number Isotope Spreads**

The chart of abundances by n-value shown below is a stripped down version of
the Isotope Abundance Charts displayed in **Part VI**.

A section of Elements from 39 to 46 are shown, illustrating how some of the
even-atomic-number Elements are spread across multiple Isotopes.

**The spread of Isotopes of these even-numbered Elements
average-out near the z-gradient**.

Average atomic weights **(Ave-Z)** are the sum of the isotope percentages
times their atomic weights, divided by 100.

**Ave-Z** z variance

Zr(40) 91 90 +1

Mo(42) 86 85 +1

Ru(44)
101 100 +1

Pd(46) 106 106 zero

*Note: Atomic weight percentages on the
chart are individually rounded to an integer, so the percentages for an Element
will not always sum to 100. Percentages
to 2 decimals are used to calculate ***Ave-Z. ***The “ atomic
mass” is not the average atomic weight of an Element because the mass is
missing the nucleic binding energy.*

**Ave-Z =
Sum [ Isotope% x Z ] / 100**

Example: Ave-Z (of Zr(40))

= ((51.45x90)+(11.32x91)+(17.19x92)+(17.28x94)+(2.76x96))
/100

= (4630.50 + 1030.12 + 1581.48 + 1624.32 + 264.96) /100

= 9131.38/100 = 91.3138 (rounded to 91)

Notice that the spread prefers Isotopes in parity. For example in Zr(40) the percentages in
parity are 51%+17%+17% = 85%.

Zr(40)
is 85% in parity

Mo(42) is 74% in parity.

Ru(44) is 72% in parity.

Pd(46)
is 77%) in parity.

The even numbered Elementa from 72 to 82 have Isotope spread averages that
are also only off 1 or equal to the z-gradient.

*The percentage spreads can be seen on the
Isotope Abundance charts in ***Part VI***.*

Av- Z z variance

Hf(72) 178 177 +1

W(74)
184 183 +1

Os(76) 190 189 +1

Pt(78)
195 195 zero

Hg(80) 201 201 zero

Pb(82) 207 207 zero

**Part V – Radioactive Decay**

**Alpha
Radioactive Decay **

**Alpha** radioactive decay is when an Alpha Particle (of 2 ionized
Protons and 2 Neutrons) splits off of the atom, and becomes an ionized Helium
atom, which due to the positive charge (from being ionized) flies off at great
speed. (In the chart above Alpha decay
is shown by a vertical arrow upward by 2 elements).

**Alpha: ****à**** -2P
-2N = -4Z**

The Element transmutes to the Element with 2 less Protons, retaining the parity or non-parity of the Isotopes. The atomic weight (Z) is reduced by 4.

**Beta
Radioactive Decay**

Beta decay changes the number of Protons, by either converting a Proton into a Neutron (Beta+), or by converting a Neutron into a Proton (Beta-). Since either a Proton changes to a Neutron, or a Neutron changes to a Proton, the atomic weight (Z=P+N) is unaltered. Transmutation changes the Element, and also increases (when Beta+) or decreases (when Beta-) the number of excess Neutrons (n) by 2.

**Beta+ ****à**** -1P ****à**** +2n
Beta- **

Note: Beta decay involves
conversions between mass and gravity.
Refer to article on Gravity for more detail.

**Part VI – The Isotope Abundance Charts**

The isotope abundance charts to follow show Isotope abundance percentages by
the **n-value**. The advantage of this is it compacts the chart, moving each successive Element left by 2
positions from where they would display if the chart was by atomic weight.

To calculate atomic weight (Z) from the chart, use Z=2P+n.

The n-gradient is shown as a **blue line **(with blue boxes marking the integer
jumps). The Isotope Beta-decay target-Element
is pointed to with arrows.

**Shaded boxes are in parity***.* The charts show that with few exceptions **Beta decays are
going from non-parity to parity**.
The variant decays are shown in **red**, and are explained in **Part VII – The Major
Variances.**

Dotted lines plot the converging meeting points of the Beta decay arrows
(the lines either follow the 45 degree angle of the linear **Beta-decay gradient**, or drop straight down).

**The
Complete Isotope Abundance Charts
**

The chart above shows how the beta-decay-gradient is tangent to the n-gradient at Element 78. The beta-decay dotted lines are split around the blue n-gradient line because the n-gradient is out of parity (passes through the un-shaded out-of-parity boxes).

The chart below shows the multiple reductive paths (from 92 to 82) of the radioactive group of Elements

**The
Cosmos of Flux**

Even as the solar bodies create the natural Elements out of clouds of Hydrogen and Helium (see article on fusion), Alpha and Beta decay is ever so gradually, but actively, reducing the Elements back down to Hydrogen and Helium. All Isotopes of atomic number >2 are alpha radioactive, but to varying degrees. Their rate of decomposition is regulated by the half-life law, where the decay rate is not linear, but proportional to the count of atoms of that Isotope in matter. It is the inverse of exponential doubling: 1,2,4,8,16,32,64, meaning that in a given period of time 64 will reduce to 32, and in the same length of time 32 will reduce to 16 (and not to zero as would occur if it were to be a linear decay).

**Part VII – The Major Variances**

The major variances from the z-balance has hidden
the balance formula from conventional academic chemists, and these variances
begin very early in atomic number.

**The Dip in Binding Energy**

Atoms are thought to be held together by nucleonic binding energy (taken
from the mass of the constituent nucleons (Protons and Neutrons). The binding energy is small because it only
needs to hold the nucleons together for the brief interval when the cubic
matrix dematerializes. The binding
energy generally increases with increased atomic number up to Iron(26) and then
gradually decreases, but there is a dip in binding energy between Helium(2) and
Oxygen(8) that results in an aberration in the Isotopes of Beryllium(4) and
Nitrogen(7), where high-abundance non-parity occurs.

In the following, non-parity is highlighted in **red**.

What happens is that (12)Carbon(6) captures a free
neutron and then may Alpha decay to **(9)**Beryllium(4), or capture another free neutron
and Beta- decay to **(14)**Nitrogen(7)

**(12)****C(****6)**
+ n = **(13)**C(6);
aà [(4)He(2)) + **(9)**Be(4)], or

**(12)****C(****6)**
+ n = **(13)**C(6);
+ n = **(14)****C(6); b-****à**** ****(14)****N(7)**

*It is the beta-decay of carbon-14 that
is used in carbon-dating. Such dating assumes that the percentage of
carbon-14 in the air is relatively constant through time, and uses the fact
that the decay of carbon-14 works at a constant rate to calculate how long the
decay has been taking place. By measuring
the residual percentage of carbon-14 in organic matter, a rough date the carbon
was metabolized can be calculated.*

**The Potassium Beta split**

There is only one Isotope (the non-parity Isotope **(40)Potassium(19))**
that splits Beta decay of a single Isotope between both Beta+ and Beta-. This out-of-parity Isotope Beta split results
in the aberrations at **(40)Argon(18)** and **(40)Calcium(20),
**shown in **green** below.

**(40)****K(****19)** **b+ ****à ****(40)Ar(18),
**or** **

**(40)****K(****19)** **b- ****à ****(40)Ca(20).**

**The
****(58)Nickel****(28) Variance **

As shown below, the final phase of fusion in our Sun combines Silicon(14) and Sulphur(16) into Zinc(30), which drops down to Nickel(28) due to the Isotope Balance, which also causes some of the Nickel to drop to Iron(26) where the n-gradient is 4. The remaining (58)Nickel(28) is the source of the -3 variance to the Nickel n-gradient of 5.

(28)Si(14)

(32)S(16)

(60)Zn(30) à
2H + (58)Ni(28) à
2H + (56)Fe(26) or (n=4)

or à
2H + (**58**)Ni(28)
or (n=2).

**The
Inert Bulges**

Since all Elements >2 Alpha decay, to avoid clutter the arrows are not usually shown except where the Alpha decay is significant.

The cluttered chart below shows the pattern of Alpha decay without compensating Beta- decay, that causes the bulge around the inert Element Krypton(36). Notice that Beta+ decays (to the far left) cross the n-gradient at Elements Se(34), Kr(36), Sr(38), and Zr(40.

+

There is a common pattern concerning the bulges around the inert Elements Krypton(36) and Xenon(54).

In both bulges, there is a “ledge” (highlighted yellow) 2 Elements prior to the inert Elements (highlighted red), where the successive alpha decays (green arrows), without adjusting beta decays, terminate. Also, in both bulges Elements with no natural isotopes (labeled “Null”) occur 8 Elements down from the inert Elements,

In the radioactive Element chart below, the bulge can be seen around the inert Element Radon(86).

The inert Elements have no interior Bias energy planes drawing-out energy from the Protons aligned on the planes, and this may be a factor causing the bulges.

Index of all Articles by Tom Gilmore