The nuclear size is determined from particle scattering experiments using fast electrons or neutrons. The de Broglie wavelength of the bombarding electrons or neutrons should be less than the radius of the nucleus under study.
It is found that the volume of a nucleus is directly proportional to the mass number A, i.e., to the number of nucleons in the nucleus. For many purposes, nuclei may be assumed to be spherical.
Thus, a nucleus of radius R has a volume 4/3 πR3
∴ R3 ∝ A or R ∝ A1/3
∴ R = R0A1/3
where R0 ≈ 1.2 × 10-15 m = 1.2 fm.
∴ R ≈ 1.2 AA1/3 fm
[Note : A nucleus does not have a sharp boundary. Also, electron scattering and neutron scattering yield slightly different values of R0. Hence, the relation above is only representative of effective nuclear size. 1 femtometre or 1 fm = 10-15 m; an earlier nonSI unit of the same value called fermi, in honour of Enrico Fermi (1901-54), Italian-US nuclear physicist, is no longer accepted in SI.]
