Question

Nuclear density is essentially the same for all nuclei. Justify.

Given 1 u = 1.66 × 10^-27 kg and R₀ ≈ 1.2 fm, estimate the nuclear density.

Answer 1

Relative atomic mass rounded to the nearest integral value equals the atomic mass number A. Thus, ignoring the masses of the atomic electrons and binding energies, nuclear mass expressed in unified atomic mass unit = A u. Also, it is experimentally found that the volume of a nucleus is directly proportional to the mass number A. As both nuclear mass and volume are proportional to the mass number, nuclear density is essentially the same for all nuclei.

Number volume = \(\cfrac43\)πR₀³A

∴ Nuclear density, \(\rho\) = \(\cfrac{nuclear\,mass}{nuclear\,volume}\)

Substituting the value of R₀ in Eq.(1),

The order of nuclear density is 10¹⁷ kg/m³.

[Note : Some stars, with masses between 1.4 M_⊙ and 3 M_⊙, where M_⊙ denotes the mass of our Sun, undergo supernova at the end of their active life and collapse into neutron stars of densities comparable with nuclear v density.]