The Theory of Integral and Differential Infinity. 2. Application at the Atomic Scale

The theory of integral and differential infinity (TIDI) was applied at the atomic scale for the Periodic Table of the chemical elements, atomic x-ray emission energies, and nuclear binding energies to identify the unit upon which the physical world is based. The Periodic Table was found to obey the expression A = a ·Zn , where A is the atomic mass; a (1.6672), the TIDI coefficient of the integral infinity component; Z, the atomic number; and n (1.0897), an experimentally found exponent. X-ray emission energies obeyed the expression γ = a ·Zn , where γ is the x-ray emission energy; a , the TIDI coefficient of the integral infinity component; Z, the atomic number; and n , an experimentally found exponent. The values of a ranged from about 6.54 to 0.0114, decreasing for shells in the order K > L > M. Exponents n ranged from about 2.11 to 2.78, increasing in the order K < L < M. Nuclear binding energies per nucleon obeyed the expression BE/N = a ·(A) + C + b ·(A)n , where BE/N is the binding energy per nucleon; a (0.00088), the coefficient of integral infinity; A, the atomic mass; C (0.9364), a constant; b (~60.9), the coefficient of differential infinity; and n 2.737), an experimentally found exponent. The results showed that the atom should be considered the unit upon which the macroscopic physical world of atoms and their accumulations is based, validating that TIDI is consistent with previously existing concepts of the physical world.