Typical nuclear radii are of the order of 10−14 m. Assuming a 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 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.
Nuclear density is the density of the nucleus of an atom, and it is the ratio of mass per unit volume inside the nucleus. Since the atomic nucleus carries most of the atom’s mass and the atomic nucleus is very small compared to the entire atom, the nuclear density is very high.
The nuclear density for a typical nucleus can be approximately calculated from the size of the nucleus and its mass. For example, natural uranium consists primarily of isotope 238U (99.28%). Therefore the atomic mass of the uranium element is close to the atomic mass of the 238U isotope (238.03u). The radius of this nucleus will be:
r = r0 . A1/3 = 7.44 fm.
Assuming it is spherical, its volume will be:
V = 4πr3/3 = 1.73 x 10-42 m3.
The usual definition of nuclear density gives for its density:
ρnucleus = m / V = 238 x 1.66 x 10-27 / (1.73 x 10-42) = 2.3 x 1017kg/m3.
Thus, the density of nuclear material is more than 2.1014 times greater than that of water, and it is an immense density. The descriptive term nuclear density is also applied to situations where similarly high densities occur, such as within neutron stars. Such immense densities are also found in neutron stars.
