Can the radius of an atom be measured directly?
All measurements at atomic distances are by inferences, such as measurable bond lengths with other elements, or wave distortion/diffraction when passing through an element.
Our current understanding of particulate “shape” would also indicate that a regular “radius” is impossible because the accumulation of protons and neutrons will not form a perfect sphere. If we include the electrons surrounding the nucleus it is even more nebulous (pun intended) ;)
As Dr. W. Heisenberg noted, we cannot know BOTH the location and momentum of a particle at the same time. Thus, “orbitals” of specific radii do not exist, and even the distribution of possible locations is a fuzzy probability cloud around the atom.