Show that nuclear density is almost constant for nuclei with `Zgt10`.

Explanation

Nuclear density : is invariant of the mass of an atom so is constant.
The average nuclear density of any atom = `2.304xx10^(17)kg//m^(2)`
`rho_(N)=("Nuclear mass")/("Nuclear volume")`
mass of an atom = nA
A = mass number, n = mass of a nucleon = `1.675xx10^(-27)kg`
Since most of the mass of an atom is concentrated in the nucleus = nA
The radius of the nucleus `R=R_(0)A^(1/3)`
`R_(0)=1.3` Fermi (or) `1.3xx10^(-15)m`
`therefore` Volume of the nucleus is
`V=4/3piR^(3)=4/3pi(R_(0)A^(1//3))^(3)=4/3piR_(0)^(3)A`
Nuclear density = `(nA)/V=(nA)/(4/3piR^(3))=(3nA)/(4piR_(0)^(3)A)`
`=(3n)/(4piR_(0)^(3))=2.3xx10^(17)kg//m^(3)`