Nucleus Structure


The atom’s nucleus is composed of nucleons (protons and neutrons). The arrangement of these nucleons, in particular protons, is considered in this section and the section on orbital shapes. The arrangement directly affects the sequence of the Periodic Table of Elements, the orbital shapes and the quantum leaps of the electron to various energy levels.

Nucleus of atom

Credit: CK-12 Foundation

Although the nucleus cannot be observed directly, it is known that the geometric formation of the protons and nucleons in the nucleus leads to different types of elements. This is summarized in the Periodic Table of Elements, below, which has been annotated. Some formations are more stable than others, causing some of the elements to be available in abundance and others are scarce.

Periodic Table of Elements Annotated with Sequence Completion

Periodic Table of Elements – Annotated Marking Sequence Completion 


The arrangement of the atomic nucleus is similar to wave centers that form particles, and it is also similar to elementary particles that create composite particles like nucleons. Law #4 of the theory laws states that wave centers move to nodes in a standing wave to minimize amplitude. Particles that consist of wave centers have certain magic numbers (8, 20, 28, 50, etc) where there is stability. Particles build nucleons, so it is reasonable to expect this behavior to continue as atoms form from nucleons.

Tetrahedral Numbers

Before the nucleus structure is proposed, tetrahedral numbers are revisited since the structure appears to be based upon a tetrahedral structure. Tetrahedrons are geometric 3D stability for waves in all directions. Three properties of a tetrahedron: the level, the number in each level and the total number in a tetrahedron is shown in the figure below. For example, the electron was calculated to have a total wave center count of ten, thus it is proposed to be a 3-level tetrahedron. The pentaquark structure of the proton is proposed to have a total of four electrons at its vertices, a 2-level tetrahedron. For the sequence of the Periodic Table of Elements, the important number for this section is the number in each level. These have been mapped to subshells: s, p, d and f.

Tetrahedral Rows

Tetrahedral Numbers

This tetrahedral structure was annotated in the Periodic Table of Elements (above). The sequence 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p is circled in red in the table. This structure explains the transitions of s, p, d and f blocks as described in the potential nucleon stacking arrangements.

protons in tetrahedral patterns to build the atomic nucleus

Tetrahedral Numbers and the Periodic Sequence

Nucleon Stacking – 1s to 3d

In the following images, a proton is represented in red and a neutron in blue color. To reduce complexity viewing the models, only neutrons that replace a proton are shown. In the atomic nucleus, neutrons separate protons at required distances. These separation neutrons are not shown in the models to simplify the diagrams.  A neutron can also take a proton’s position. For example, argon (Ar) shows an example of completing a stable tetrahedral structure, but using a neutron in the place of a proton. This is validated by the fact that argon (Z=18) has the same nucleon count as calcium (Z=20) as noted by the atomic mass units (amu). These protons will be shown in the models because they are required to complete a tetrahedral row. The periodic table sequence corresponds to a completion of a row in the tetrahedral-based structure.

Nucleon Stacking from 1s to 3d Atomic Elements (He to Zn)

Nucleon Stacking – 4p to 4f 

The nucleon stacking model was continued through the first f orbital (Lu), although the variations and possibilities for symmetry become more complex. Thus, these models are potential arrangements that match the nucleon stacking rules to keep symmetry and stability in the nucleus when it corresponds to the end of a block sequence.

Nucleon Stacking from 4p to 4f Atomic Elements (Kr to Lu)

Nucleon Stacking Rules

A set of rules was established for nucleons (protons and neutrons) stacking in an atomic nucleus to match the sequence of the Periodic Table of Elements and also meeting the proton fill order for orbital shapes.  Each of these rules is ultimately a result of the fundamental rule that subatomic particles that form these composite particles (nucleons) move to minimize wave amplitude.

  1. Nucleons arrange from the center first, then outward.
  2. A neutron may replace a proton (in the proton’s position), but not vice versa, due to proton separation rules.
  3. Each level fills the easiest proton spin first, which is the same spin direction as the atom (it takes less energy). Then, the opposite spin direction is filled.
  4. Protons first form a linear structure (1s), then planar structure (2s), before building in three dimensions in a tetrahedral structure (2p).
  5. After the first complete tetrahedron (2p), the nucleons build symmetrically – a second tetrahedron.


Proof of the energy wave explanation for the atomic nucleus is explanation of:

  • The proposed tetrahedral nucleus structure gives rise to the periodic sequence in the Periodic Table of Elements – see above
  • The same tetrahedral nucleus structure explains orbital shapes and distances.
  • Atomic elements and particles share the same magic numbers, leading to possibility that both share geometric formations that are stable due to the law that wave centers move to standing wave nodes to minimize amplitude.