Typical nuclear radii are of the order 10−14 m. Assuming spherical shape, nuclear radii can be calculated according to following formula:
r = r0 . A1/3
where r0 = 1.2 x 10-15 m = 1.2 fm
If we use this approximation, we therefore expect the geometrical cross-sections of nuclei to be of the order of πr2 or 4.5×10−30 m² for hydrogen nuclei or 1.74×10−28 m² for 238U nuclei.
Since there are many nuclear reaction from the incident particle point of view, but, in nuclear reactor physics, neutron-nuclear reactions are of particular interest. In this case the neutron cross-section must be defined.
The volume of an atom is about 15 orders of magnitude larger than the volume of a nucleus. For uranium atom, the Van der Waals radius is about 186 pm = 1.86 ×10−10m. The Van der Waals radius, rw, of an atom is the radius of an imaginary hard sphere representing the distance of closest approach for another atom. Assuming spherical shape, the uranium atom have volume of about 26.9 ×10−30 m3. But this “huge” space is occupied primarily by electrons, because the nucleus occupies only about 1721×10−45 m3 of space. These electrons together weigh only a fraction (let say 0.05%) of entire atom.