From the relation R


From the relation R0A1/3, where R0 is a constant and is the mass number of a nucleus, show that the nuclear matter density is nearly constant (i.e. independent of A).


We have the expression for nuclear radius as:



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.

Leave a comment


Click here to get exam-ready with eSaral

For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.

Download Now