From the relation R

We have the expression for nuclear radius as:

R = R0A1/3

Where,

R0 = Constant.

A = Mass number of the nucleus

Nuclear matter density, $\rho=\frac{\text { Mass of the nucleus }}{\text { Volume of the nucleus }}$

Let m be the average mass of the nucleus.

Hence, mass of the nucleus = mA

$\therefore \rho=\frac{m A}{\frac{4}{3} \pi R^{3}}=\frac{3 m A}{4 \pi\left(R_{0} A^{\frac{1}{3}}\right)^{3}}=\frac{3 m A}{4 \pi R_{0}^{3} A}=\frac{3 m}{4 \pi R_{0}^{3}}$

Hence, the nuclear matter density is independent of A. It is nearly constant.