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Atoms are usually modeled as spheres, and their radii are often calculated using complex computational methods. This applies to the smallest atom as well as to transuranium elements. However, the smallest atom, hydrogen, occupies a special position among atoms, with only one electron and proton. In this combination, the electron's spin can only be parallel or antiparallel to the proton's spin. Due to these orientation options, the interpretation of a spherical atom appears oversimplified. This article offers an easy-to-calculate approach for the volume of atomic hydrogen. Based on Bohr's atomic model and the electron spin, a conical volume shape is derived classically. For this purpose, the electron's spin is interpreted as intrinsic angular momentum with a defined radius, which can be oriented orthogonally to Bohr's orbital plane and parallel or antiparallel to the proton's spin. The volume of the hydrogen atom determined in this way correlates with the spherical volume, which can be calculated from several literature radii.
Detlev Füchtenbusch (Thu,) studied this question.