Why are 2, 8, 18, 32 each the maximum capacity for their
electron shell?
The electron shell capacities relate to the surface area
of concentric spheres.
This suggests a geometric basis for electron orbital structure that aligns with the formula 2n2 from Niels Bohr's 1913 atomic model and later with Sommerfeld's 1916 model. These numbers represent the maximum electron capacities of the first four principal shells, which can be conceptually related to the proportional area of increasing concentric spherical surface areas.
Why is The Fine-Structure Constant of dimension 1?
It's because, like π
, a ratio of distance the Fine-Structure Constant
α is a ratio of other physical
quantities. e.g. velocity. The fine-structure constant
is directly related to the electron shell structure of atoms,
and has now led to a deeper insight into the fundamental
nature of reality.
Value:
The fine-structure constant is now known
to have the value 0.0072973525680816596...
Fundamental Constant:
The fine-structure constant is not
derived from other constants; it is a fundamental value
that appears in many physics equations and calculations.
Theoretical Importance:
The fine-structure constant is a central
component of the Standard Model of particle physics,
which describes the fundamental forces and particles
of nature.
Atomic Orbital Speeds:
It dictates that an electron in the
innermost (ground) state of a hydrogen atom orbits at roughly
1/137 the speed of light, tying together quantum mechanics,
electromagnetism, and relativity.
Strength of Electromagnetic Interaction:
It measures how strongly charged
particles like electrons interact with electromagnetic fields,
including light.
Molecular and Chemical Bonds:
Because it sets the scale for electron
binding energies, alpha effectively determines the strength
of chemical bonds. If alpha were significantly larger, atoms
would not form the stable molecules necessary for chemistry
and life.
Atomic Structure:
It determines the gaps between
energy levels in atoms. This controls the specific
colors of light that atoms absorb or emit.
Chemical Bonds:
It sets the size of atoms and the
strength of chemical bonds.
If the number changed slightly, matter could not form.
Without this exact number, the universe could not exist
as we know it.
Expansion parameter:
In QED, the theory describing how light
and matter interact, calculations are done in powers of alpha.
Because alpha is much smaller than 1, it allows physicists
to calculate atomic properties (like the anomalous magnetic
moment of the electron) with extreme precision using
perturbation theory.
Relativistic Fine-Structure:
It determines the precise, subtle
splitting of spectral lines (spin-orbit coupling).
When light is emitted or absorbed, alpha dictates the
tiny shifts in energy levels caused by relativistic
effects on the moving electron.
Size of Atoms:
It is deeply intertwined with the
physical size of atoms (the Bohr radius). It ensures that
electrons maintain a stable, predictable distance from
the nucleus, preventing atoms from collapsing.
Strength of Light-Matter Interactions:
It acts as a coupling constant
representing the probability of a charged particle
(like an electron) emitting or absorbing a photon.
Star Power:
It dictates how stars fuse atoms
together to create energy and heavy elements like carbon.
Mysterious Nature:
Despite its importance, the
fine-structure constant remains somewhat mysterious,
with physicists still seeking a deeper understanding of
why it has the specific value it does.
In the following statements you can connect to corroborating websites by using the arrow links.
The Fine-Structure Constant α is a scalar constant that describes the strength of the electromagnetic interaction between elementary charged particles. →1
In 1928 Charles Janet published his left-step periodic table of chemical elements. He believed that no elements heavier than 120 would be found. →2
What does this equation tell us about the meaning of the Fine-Structure Constant? Arnold Sommerfeld introduced the concept of the fine-structure constant in 1916, during his extension of the Bohr model of the atom to include the relativistic relationship between mass and velocity and elliptical orbits. →3
Concerning the nucleus, Sommerfeld tried to connect the number 8 and the number of corners of a cube. →4
Gluons that mediate the strong interaction between quarks only come in eight varieties. The number 8 figures prominently throughout this equation. →5
There is an electron shell capacity formula about the electron field. There are only four shells. The maximum number of electrons that can occupy shells one through four are, in sequence, 2, 8, 18, 32. →6
For each of the four principal energy levels, the total possible occupying electrons that can fit in any given shell is 2n2. →7
The Stowe Table of Elements shows this 2 8 18 32 sequence in visual form from 1s to 8s. There are eight principal quantum numbers. This seems to relate to the 'octet rule' where elements tend to bond in such a way that each atom has eight electrons in its valence shell, giving it the same electronic configuration as a noble gas. In general, the rule is applicable to the s-block and p-block. Note that this element table suggests the Periodic Table ends at element 120. →8
In the Complete List of Orbitals, there are only sharp, principal, diffuse, and fundamental blocks. This is the meaning of the fine-structure constant, that it is explicitly related to both the nucleus of the atom and the surrounding electron cloud. →9
Predictions:
1. This strongly implies that there will never be more
than 120 elements.
See the Stowe‑Janet‑Scerri periodic table.
If there were more, then the Fine-Structure Constant
would have a different value. This means that only
the s,p,d,f orbitals exist.
2. The sequence 2,8,18,32 suggests a geometric framework
that relates the first four electron shells to the surface area
of the first four concentric spheres of radius 1,2,3,4.
3. The exact value of alpha is not only irrational but
transcendental. Being transcendental means it cannot be the
root of any non-zero polynomial equation with integer
coefficients.