The Electrical Atom

Factors

The above is true of theoretical [viscous] matter comprising collections of proton-electron pairs. However, real-life atoms comprise collections of deuterium and tritium atoms. The surplus tritium neutrons affect the internal forces, and therefore, the structure of elemental matter; such as density and gas-point temperature.
Therefore, we must consider these when predicting the resistance and resistivity of elemental matter, for example:
Kₜ = Ṯg/Ṯₛ
Kᵨ = ρₛ/ρₘ
But we also need to consider the effect of excess tritium neutrons
ψ' = ψ-1
Electrical resistance; Ω = V/I . Kₜ . Kᵨ . ψ'
Electrical resistivity of elemental matter: ρ = V/I' . Kₜ . Kᵨ . ψ'

Example Calculation

As can be seen in the above Table, and in Fig 3, there are some differences between the calculated resistivity values and those extracted from various sources. It would be helpful to see which are correct.
We can do this by comparing the performance of the calculated and documented resistivity values in a well-known application, such as the tungsten filament in an incandescent light-bulb.
We can make this comparison using two versions of the bulb; say a 60-Watt bulb used in the USA (120V) and the same power rating in the UK (220V).

The majority of sources appear to indicate an operational temperature of 2884K rather than 3136K⁽⁴⁾, and the calculated resistivity gives a closer match for the actual filament diameter.

From the following Table, it would appear, that in its pure-crystalline form (calculated), copper may be a better electrical conductor than silver.

But in its practical (drawn) condition, copper wire may be slighly less conductive than silver in the same condition. Albeit some of the documented values for resistivity declare these materials to be equally conductive (1.63E-08 Ω.m).
An additional consideration must be the orientation of the atomic crystals. The calculated resistivity reflects a theoretical optimum value, whereas the documented values refer to both deformed crystals (drawn) and/or variable orientation.

Discussion

Considering that;
a) it makes perfect sense that voltage (J/C) is the energy required to overcome the potential energy (PEₛ) holding the electron to its proton partner in the atom's outermost proton-electron pairs;
b) it makes perfect sense that current, or electron transit rate, (C/s) is related to the velocity of the electron(s) in the atom's outermost orbiting electrons (ƒₛ);
c) the calculations are very simple and the units are correct;
d) the variable nature of the documented values for resistivity calls some of them into question;
e) respective filament diameters in the above Example Calculation favour the calculated resistivity value;
f) the average discrepancy of 30% between the calculated and documented values for the resistivity of all 92 elements, is less than the discrepancy between sources for many documented values;
g) ten of the calculated values are exactly the same as the documented values;
h) the above example calculation verifies itself; calculated power rating is identical to the design power rating;
i) no fudged formula could generate the pattern correlation shown in Fig 3, together with a) to h) above;
CalQlata concludes that the above is a compelling description of the electrical atom, and how it applies to elemental matter.

It must be pointed out, however, that the calculated values for resistivity apply to perfect crystals of the elemental matter concerned, whereas the documented values apply to imperfect matter.

Mathematical Symbols

A = cross-sectional area of the electrical conductor {m²}
A = filament cross-sectional area {m²}
Aₐ = atom cross-sectional area {m²}
ƒₛ = the orbital frequency of the electron in shell 'Nₛ' {/s}
g = potential acceleration induced on the orbiting electron (Nₛ) by its proton partner {m/s²}
h = Newton's constant of motion for the electron orbiting in shell 'Nₛ' {m²/s}
I = current {C/s}
ℓ = filament length {m}
mₐ = atomic mass {kg}
Nₐ = number of atoms across the filament's cross-sectional area
N₁ = an atom's innermost shell [number]
Nₛ = an atom's outermost shell [number; s = INT((Z-1)/2)+1]
P = power {J/s}
Pₚ = proton-electron power; shell 'Nₛ' {J/s}
Pₐ = filament power {J/s}
PEₛ = the potential energy uniting the proton-electron pair in shell 'Nₛ' {J}
R₁ = orbital radius of an electron in shell 'N₁' {m}
Rₛ = orbital radius of an electron in shell 'Nₛ' {m}
Rₐ = inter-atomic spacing (in elemental matter) {m}
Ṯ & Ṯ₁ = measured temperature of the matter; that of the proton-electron pair whose electron is orbiting shell 'N₁' {K}
Ṯₛ = the temperature of a proton-electron pair whose electron is orbiting in shell 'Nₛ' {K}
Ṯg = the gas-point temperature of elemental matter {K}
vₛ = orbital velocity of an electron in shell 'Nₛ' {m/s}
V = voltage {J/C}
ρ = resistivity {J.s.m / C²}
ρₛ = atomic density (mₐ/Rₛ³) {kg/m³}
ρₘ = mass density of elemental matter {kg/m³}
ψ = RAM/Z (neutronic ratio)
Ω = resistance {J.s / C²}
Ø = filament diameter {m}

Notes

1. a) phosphorus; b) sulphur; c) erbium; d) boron;
2. ρ = Ω.A/ℓ = Ω.A/Rₛ = Ω.Rₛ²/Rₛ = Ω.Rₛ {Ω.m}
3. h/g = vₛ / (2πƒ)² = Rₛ / (2πƒ) {m.s}
4. Wikipedia suggests a filament of diameter 4.6E-05m, length of 0.595m and a temperature of 2000K and 3300K;
   "how stuff works" suggests a filament of diameter 'one-hundredth of an inch', length of about 2m and a temperature of around 2477K;
   the Dutton Institute suggests a filament temperature of around 2823K;
   There are numerous other sources that suggest a diameter of 'one-two-thousandths of inch' and temperatures between 2000K and 3000K

Further Reading

You will find further reading on this subject in reference publications^{(69, 70, 71 & 73)}