Radius of nuclei is given by formula
[tex]R = R_oA^{1/3}[/tex]
now we can say volume of the nuclei is given as
[tex]V = \frac{4}{3}\pi R_o^3* A[/tex]
now the density is given as
density = mass / volume
mass of nuclei = mass of neutron + mass of protons
[tex]m = z*m_p + (A- z)*m_n[/tex]
[tex]m_p = m_n = 1.008u[/tex]
[tex]m = A*1.008u[/tex]
Now density is given as
[tex]\rho = \frac{A*1.008u}{\frac{4}{3}\pi R_0^3* A}[/tex]
here we know that
[tex]R_0[/tex] = 1.2 fm
[tex]\rho = \frac{1.008u}{\frac{4}{3}\pi*(1.2*10^{-15})^3}[/tex]
[tex]\rho = 2.31 * 10^{17} kg/m^3[/tex]
So from above we can say that density of all nuclei is almost same.
