Nuclear density is the mass density of nucleus of an atom of an element.
Mass M = m * A,
m = mass of a nucleon , = 1.67 * 10^-27 kg
A = mass number of an atom (nucleus)
= total of numbers of protons and neutrons in the nucleus)
Volume V = 4/3 π R³, where R = radius of nucleus
Nuclear density = ρ = M/V = m A / 4/3πR³
R is written as , R = A^¹/³ * R₀ or, R³ = A * R₀³ ,
Where R₀ = mean atomic radius for single nucleon (proton) nucleus.
Then nuclear density = ρ = 3 m / (4π R₀³)
R₀ = for hydrogen atom, for example, 1.25 * 10^-15 meter = 1.25 fm.
Substituting the values for m and R₀, we get,
approximately, ρ = 2.04 * 10^17 kg/m³