Relativistic correction to the Bohr radius and electron distance expectation value via Dirac Equation

TL;DR

This paper derives relativistic corrections to the Bohr radius and electron-proton distance expectation values using the Dirac equation, revealing that for certain atomic numbers, the expectation distance becomes zero, impacting the periodic table.

Contribution

It provides exact relativistic calculations of electron distances in hydrogen-like atoms, extending the understanding beyond non-relativistic models.

Findings

Expectation distance to nucleus becomes zero at Z ≈ 118.

Relativistic corrections significantly alter electron distance expectations.

Supports the limit of the periodic table at element 118.

Abstract

In this article and beginning with the Dirac solution to the Hydrogen atom in its ground state, the exact results corresponding to the expectation value of the distance of the electron to the proton and the maximum probability distance are found. For hydrogen-like atoms and in contrast to the non relativistic Bohr radius and expectation values, for $Z=\frac{\sqrt3}{2}\frac{1}{\alpha}$ (close to 118), the expectation distance to the nucleus is zero thus putting an end to the periodic table for Z = 118 nicely matching the last element discovered (Oganesson).