A mathematical curiosity in estimating the radius of the first ring electrons of an arbitrary atom

摘要

In this note, we explore an elementary method for approximating the radii and speeds of first ring electrons in atoms. The approach uses only a single algebraic equation with parameters. Any particular atom under study defines all the parameters. A simple hand calculator technique always applies for solving any resulting equation. Results are given through calcium and, to three decimal places, are shown, unexpectedly, to be essentially identical to available quantum mechanics calculations.