Typical nuclear radii are of the order 10−14 m. Assuming spherical shape, nuclear radii can be calculated according to the 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 reactions 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 has a 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 the entire atom.