## Explanation

Named after Amedeo Avogadro, the Avogadro constant is the number of particles in a given mole (e.g. atoms, molecules). The fact that it is a consistent number across atoms, and molecules formed from atoms, leads to a question about the nature of this number. Is it a representation of something that is fundamental to all atoms and molecules? All atoms are formed of protons and electrons, of which the simplest formation of one proton and electron is hydrogen. All molecules are formed from atoms. Thus, the lowest common denominator for all atoms and molecules is hydrogen. In a single hydrogen atom, the electron’s most probable location in an orbit (its distance from the proton) is known as the Bohr radius (a0). In the section on Spacetime, a unit cell of the spacetime lattice was calculated to be based on the Planck length (radius of a granule) and Euler’s number (a mathematical constant appearing in growth functions in nature). The total number of unit cells in hydrogen is exactly Avogadro’s number – 6.022 * 1023. The Avogadro constant is related to the Faraday constant (F) or the gas constant (R), but this requires explaining new constants. In classical constant format, Avogadro’s constant can be reduced to the five fundamental physical constants that most other constants can be derived. Further below, it is derived in terms of the Bohr radius to illustrate its true nature as the number of unit cells in a hydrogen atom. Note that “e” in the wave constant form is the mathematical constant, or Euler’s number (e), not the elementary charge (ee).

### Classical Constant Form ### Wave Constant Form Using classical constants Using energy wave constants

Calculated Value (Classical, Wave): 6.0224E+23, 6.0225E+23
Difference from CODATA: -0.005%
Calculated Units: None (dimensionless)

Note: Avogadro’s constant has units of 1/mol, but it is a numerical count.  Units derived by wave equations support a dimensionless, numerical count.

### Alternative Derivation

An alternative derivation uses the Bohr radius (a0), which itself can be derived by the electron’s classical radius and fine structure constant.  However, the inclusion of the Bohr radius better illustrates the true meaning of Avogadro’s constant.  It is the distance of an electron from a proton in standard hydrogen (a0), divided by the diameter of a granule (2lP) times Euler’s number (e). The Avogadro constant is derived in the Geometry of Spacetime paper. It is used in photon energy calculations, but only as a conversion for comparisons against measured results provided in MJ/mol – found in the Particle Energy and Interaction and Atomic Orbitals papers.

Its value was calculated and shown to match the known value in the Summary of Calculations table. The derivation of this constant is available in the Fundamental Physical Constants paper.